General System Theory By the same author: Modern Theories of Development (in German, English, Spani~h) Nikolaus von Kues Lebenswissenschaft und Bildung J Foundations, Development, Applications Auf den Pfaden des Lebens I Biophysik des Fliessgleichgewichts t by Ludwig von Bertalanffy Theoretische Biologie Das Gefüge des Lebens Vom Molekül zur Organismenwelt Problems of Life (in German, English, French, Spanish, Dutch, Japanese) Robots, Men and Minds University of Alberta Edmonton) Canada GEORGE BRAZILLER New York MANIBUS Nicolai de Cusa Cardinalis, Gottfriedi Guglielmi Leibnitii, ]oannis Wolfgangi de Goethe Aldique Huxleyi, neenon de Bertalanffy Pauli, S.J., antecessoris, cosmographi Copyright © 1968 by Ludwig von Bertalanffy All rights in this hook are reserved. For information address the publisher, George Braziller, lnc. One Park Avenue New York, N.Y. 10016 Foreword The present volume appears to demand some introductory notes clarifying its scope, content, and method of presentation. There is a large number of texts, monographs, symposia, etc., devoted to "systems" and "systems theory". "Systems Science," or one of its many synonyms, is rapidly becoming part of the established university curriculum. This is predominantly a development in engineering science in the broad sense, necessitated by the complexity of "systems" in modern technology, man-machine relations, programming and similar considerations which were not felt in yesteryear's technology but which have become imperative in the complex technological and social structures of the modern world. Systems theory, in this sense, is preeminently a mathematica! field, offering partly novel and highly sophisticated techniques, closely linked with computer science, and essentially determined by the requirement to cope with a new sort of problem that has been appearing. What may he obscured in these developments-important as they are-is the fact that systems theory is a broad view which far transcends technological problems and demands, a reorientation that has become necessary in science in general and in the gamut of disciplines from physics and biology to the behavioral and social sciences and to philosophy. It is operative, with varying degrees of success and exacti~ude, in various realms, and heraids a new world view of considerable impact. The student in "systems science" receives a technica! training which makes systems theory-originally intended to overcome current overspecialization-into another of the hundreds of academie specialties. Moreover, systems science, centered in computer technology, cybernetics, automation and systems engineering, appears to vii make the systems idea another-and indeed the ultimatetechnique to shape man and society ever more into the "megamachine" which Mumford (1967) has so impressively described in its advance through history. The present hook hopes to make a contri bution in both respects implied in the above: offering to the student of systems science a broadened perspective, and to the general reader a panoramic view of a development which is indubitably characteristic of ana important in the present world. While fully realizing his limitations and shortcomings, the author feels entitled to do so because he was among the first to introduce general system theory, which is now becoming an important field of research and application. As Sirnon (1965) correctly remarked, an introduetion into a rapidly developing field largely consists in its conceptual history. It may not he inappropriate, therefore, that the present work consists of studies written over a period of some thirty years. The hook thus presents systems theory not as a rigid doctrine (which at present it is not) but rather in its becoming and in the development of its ideas which, hopefully, can serve as a basis for further study and investigation. In order to serve the purpose, these studies were arranged in logica! rather than chronological order and were carefully edited. Editing was limited, however, to elimination of repetitions, minor stylistic improvements and some suitable rearrangements. Intentionally, no changes in content were made from hindsight gained at a later time. Repetitions could not he completely avoided because similar ideas sometimes appeared in different contexts; but it is hoped they were kept at a tolerabie level. They may even he not undesirable to the student seeking the general idea or its application in a specific field. The original sourees are indicated in the list of Acknowledgments. For evaluation of the material presented and reasous of priority which will become apparent, some major data may he summarized as follows. Chapter 5 (1940) introduced the "theory of the organism as open system." Together with Burton's (1939) work, this was the original statement of the concept which gained increasing importance and application. This publication remained almost unknown among British and American scientists and is therefore reproduced in its entirety, although much can he added, as is partly reviewed in Chapters 7 (1964) and 6 (1967). Similarly, the first announcement of general system theory (1945) is reproduced as Chapter 3, abridged and somewhat rearranged, but otherwise true to the original. The Appendix (review of an address presented in 1947) is reproduced as an early statement long before systems theory and cognate terms and fields appeared academically or in technol@gy. A review in nontechnical Ianguage (1956) serves as Chapter 2; Chapters I and 4 try to bring the story up to date. The author wishes to extend his thanks to many persons and agencies that facilitated the work here presented. Thanks are due to Dr. George Brantl, editor at George Braziller, Inc., for having suggested the publication and for his valuable editorial assistance in presenting the hook to its advantage. The permissions of editors and publishers where the essays were first published, as indicated in the souree list, are gratefully acknowledged. So is the assistance of various agencies, the N ational Research Council and N ational Cancer Institute of Canada, the Canada Council, the University of Alberta General Research Committee and others, which spousored part of the work here reported by research grants and other support. The author's secretary, Mrs. Elizabeth Grundau, took care of the manuscript in its various phases, assisted in bibliographic and library work, and provided translations of the chapters originally published in German, thus far exceeding secretarial routine. Last but not least, my wife, Maria von Bertalanffy, has to he thanked for her untiring help and criticism when these essays were written. Without the encouragement of colleagues, too numerous to mention, the writer, in the face of obstructions and obstacles, would hardly have persevered in the task of introducing and developing general system theory. viii ix L.v.B. University of Alberta Edmonton (Canada) March 1968 Acknowledgments Most of the chapters in this volume have previously appeared, sometimes in modified form. The publication history is given here for each chapter. The author wishes to thank the original publishers of the articles for permission to include them in this volume: Chapter 1: Written for this volume (1967) . Chapter 2: "General System Theory," in Main Currents in Modern Thought, Volume 11, #4, March 1955, pp. 75-83. Reprinted in General Systems, 1 (1956) 1-10; R. W. Taylor (ed.), Life, Language, Law: Essays in Honor of A. F. Bentley, Yellow Springs (Ohio), Antioch Press, 1957, pp. 58-78; J. D. Singer (ed.), Human Behavior and International Polities, Chicago, Rand McNally & Co., 1965, pp. 20-31; N. J. Demerath lil and R. A. Peterson (eds.), System, Change, and Conflict, Glencoe (Ill.), Free Press, 1967. Additions were taken from "Allgemeine Systemtheorie. Wege zu einer neuen Mathesis universalis," Deutsche Universitätszeitung, 5 j6 (1957) 8-12. Also in Italian, "La Teoria generale dei Sistemi," La Voce dell' America, 18-G and 2-H (1956-57), and French, "Histoire et méthodes de la théorie générale des systèmes," Atomes, 21 (1966) 100-104. Chapter 3: Condensed from "Zu einer allgemeinen Systemlehre," Deutsche Zeitschrift für Philosophie, 18, No. 3/4 (1945) ; "An Outline of General System Theory," British ]ournal of the Philosophy of Science, 1 (1950) 139-164; "Zu einer allgemeinen Systemlehre," Biologia Generalis, 19 (1949) 114-129. xi Chapter 4: "Genera! System Theory. A Critica! Review." General Systems, 7 (1962), 1-20. Reprinted in W. Buckley (ed.), Modern Systems Research for the Behaviaral Scientist, Chicago, Aldine Publishing Co., 1968, pp. 11-30. Contents Chapter 5: "Der Organismus als physikalisches System betrachtet," Die Naturwissenschaften, 28 (1940) 521-531. Chapter 6: "Das Modell des offerren Systems," Nova Acta Leopoldina, (1969). Foreword ................................................................................ . vii Chapter 7: "Basic Concepts in Quantitative Biology of Metabolism," Helgoländer Wissenschaftliche Meeresuntersuchunge n, 9 (First International Symposium on Quantitative Biology of Metabolism) (1964) 5-37. Chapter 8: Substance of lectures presented at the University of Western Ontario (London), University of California Medica! School (San Francisco), University of Alberta (Edmonton, Calgary), etc., 1961-64. I 2 Chapter 9: "General System Theory and Psychiatry," from Chapter 43 of The American Handhook of Psychiatry, Vol. 3, edited by Silvano Arieti, © 1966 by Basic Books, Inc., Publishers, New York. Chapter 10: "An Essay on the Relativity of Categories," Philosophy of Science, 22 (1955) 243-263. Reprinted in General Systems, 7 (1962) 71-83. Appendix "Vom Sinn und der Einheit der Naturwissenschaften. Aus einem Vortrag von Prof. Dr. Ludwig von Bertalanffy," Der Student (Wien), 2, No. 7 j8 (1947) 10--11. 3 xii Acknowledgments ................................................................ . xi ............................................................ . Introduetion ...... Systems Everywhere ....................................................... . On the Ristory of Systems Theory ........................... . Trends in Systems Theory ........................................... . 3 3 10 The Meaning of General System Theory ...................... . The Quest for a General System Theory ............... . Aims of General System Theory ............................... . Closed and Open Systems: Limitations of ............. . Conventional Physics ... ............... ........................... . Information and Entropy .............................. . Causality and Teleology What Is Organization? .............................................. . General System Theory and the U nity of Science ... . General System Theory in Education: The Production of Scientific Generalists ........ . Science and Society ............................................. . The Ultimate Precept: Man as the Individual ... 30 30 Some System Concepts in Elementary Mathematica! Consideration .............................................................. . ......................... . The System Concept .... ............... ......................................... . Growth ............... Competition .................................................................. . Wholeness, Sum, Mechanization, Centralization Finality ........................................................................ . Types of Finality Isomorphism in Science The Unity of Science ......................................... . xiii 17 36 39 41 44 46 48 49 51 52 54 54 60 63 66 75 77 80 86 4 The Organism Considered as Physical System .............. The Organism as Open System General Characteristics of Open Chemica! Systems .............................................. . Equifinality ...................... ............................... Biologica! Applications ............................................... 120 6 The Model of Open System ............................................ . The Living Machine and lts Limitations ............... . Some Characteristics of Open Systems Open Systems in Biology ..... Open Systems and Cybernetics .. . .............. . Unsolved Problems ... Condusion .................................... . 139 139 141 145 149 151 153 7 Some Aspects of System Theory in Biology ................... Open Systems and Steady States ... ...... Feedback and Romeostasis ......... ....................... ..................... Allometry and the Surface Rule .... Theory of Animal Growth ... ... . .. ............................ . Summary ... ................... ............. ..................... ... 155 156 160 163 171 184 8 The System Concept in the Sciences of Man .. . The Organismic Revolution .................................... . The Image of Man in Contemporary Thought .... . System-Theoretica! Re-orientation ............. . Systems in the Social Sciences ..................................... . A System-Theoretica! Concept of Ristory ......... . The Future in System-Theoretica! Aspect ............ . 186 186 188 192 194 197 203 9 General System Theory in Psychology and Psychiatry ... . The Quandary of Modern Psychology .................... . System Concepts in Psychopathology ..................... . Condusion ......... . 205 205 208 220 5 10 The Cultural Re1ativity of Categories .... ........... 232 The Perspectivistic View ......... ............................. 239 Notes ............................................................................... 248 Advances in General System Theory .... ... ..... .. 87 Approaches and Aims in Systems Science ...... 87 Methods in General Systems Research ..... .............. 94 Advances of General System Theory ............. 99 12Q I References .............................................................................. 254 Suggestions for Further Reading ........................................ 275 Index ........................................................................................ 279 124 131 134 The Relativity of Categories .......................................... . 222 The Whorfian R ypothesis ........................................... . 222 227 The Biologica! Relativity of Categories xiv Appendix: The Meaning and Unity of Science .............. 251 XV 1 i Introduetion Systems Everywhere If someone were to analyze current notions and fashionable catchwords, he would find "systems" high on the list. The concept has pervaded all fields of science and penetrated into popular thinking, jargon and mass media. Systems thinking plays a dominant role in a wide range of fields from industrial enterprise and armaments to esoterie topics of pure science. Innumerable publications, conferences, symposia and courses are devoted to it. Professions and jobs have appeared in recent years which, unknown a short while ago, go under narnes such as systems design, systems analysis, systems engineering and others. They are the very nucleus of a new technology and technocracy; their practitioners are the "new utopians" of our time (Boguslaw, 1965) who -in contrast to the classic breed whose ideas remained between the covers of hooks-are at work creating a New World, brave or otherwise. The roots of this development are complex. One aspect is the development from power engineering-that is, release of large amounts of energy as in steam or electric machines-to control engineering, which directs processes by low-power devices and has led to computers and automation. Self-controlling machines have appeared, from the humbie dornestic thermostat to the selfsteering missiles of World War II to the immensely improved missiles of today. Technology has been led to think not in terms 4 GENERA L SYSTEM THEORY of single machines but in those of "systems." A steam engine, automob ile, or radio receiver was within the competen ce of the engineer trained in the respectiv e specialty. But when it comes to ballistic missiles or space vehicles, they have to be assembie d from compone nts originati ng in heteroge neons technologies, mechan-, ical, electroni c, chemica!, etc.; relations of man and machine come into play; and innumer able financial, economie , social and politica! problems are thrown into the bargain. Again, air or even automob ile traffic are not just a matter of the number of vehicles in operation , but are systems to be planned or arranged . So innumer able problems are arising in producti on, commerc e, and armamen ts. Thus, a "systems approach " became necessary. A certain objective is given; to find ways and means for its realizatio n requires the systems specialist (or team of specialists) to consider alternative solutions and to choose those promisin g optimiza tion at maximum efficiency and minimal costin a tremendo usly complex network of interactio ns. This requires elaborate techniqu es and compute rs for solving problems far transeen ding the capacity of an individu al mathema tician. Both the "hardwa re" of compute rs, automati on and cybernat ion, and the "software " of systems science represen t a new technolog y. It has been called the Second Industrial Revoluti on and has develope d only in the past few decades. These developm ents have not been limited to the industria lmilitary complex. Politician s frequent ly ask for applicati on of the "systems approach " to pressing problems such as air and water pollution , traffic congestio n, urban blight, juvenile delinquenc y and organize d crime, city planning (Wolfe, 1967), etc., designati ng this a "revoluti onary new concept" (Carter, 1966; Boffey, 1967). A Canadia n Premier (Mannin g, 1967) writes the' systems approach into his politica! platform saying that an interrela tionship exists between all elements and constituents of society. The essential factors in public problems , issues, policies, and program s must always be consider ed and evaluate d as interdep endent compone nts of a total system. These developm ents would be merely another of the many facets of change in our contemp orary technolo gical society were it not for a significa nt factor apt to be overlook ed in the highly sophistic ated and necessarily specializ ed techniqu es of compute r science, systems engineer ing and related fields. This is not 'only Introdue tion 5 a tendency in technolo gy to make things bigger and better (or alternativ ely, more profitabl e, destructi ve, or both). It is a change in basic categorie s of thought of which the complexi ties of modern technolog y are only one-and possibly not the most importa ntmanifest ation. In one way or another, we are forced to deal with complexi ties, with "wholes" or "systems," in all fields of knowledge. This implies a basic re-orient ation in scientific thinking. An attempt to summari ze the impact of "systems" would not be feasible and would pre-empt the considera tions of this hook. A few examples , more or less arbitraril y chosen, must suffice to outline the nature of the problem and conseque nt re-orient ation. The reader should excuse an egocentri c touch in the quotation s, in view of the fact that the purpose of this hook is to present the author's viewpoin t rather than a neutral review of the field. In physics, it is well-kno wn that in the enormou s strides it made in the past few decades, it also generate d new problem sor possibly a new kind of problem -perhaps most evident to the laymen in the indefinit e number of some hundreds of elementary particles for which at present physics can offer little rhyme or reason. In the wordsof a noted represen tative (de-Shalit, 1966), the further developm ent of nuclear physics "requires much experiment al work, as well as the developm ent of addition al powerful methods for the handling of systems with many, but not infinitely many, particles ." The same quest was expressed by A. Szent-Györgyi (1964), the great physiolog ist, in a whimsica l way: [When I joined the Institute for Advance d Study in Princeton] I did this in the hope that by rubbing elbows with those great atomie physicists and mathema ticians I would learn somethin g about living matters. But as soon as I revealed that in any living system there are more than two electrons , the physicists would not speak to me. With all their compute rs they could not say what the third electron might do. The remarkab le thing is that it knows exactly what to do. So that little electron knows somethin g that all the wise men of Princeton don't, and this can only be somethin g very simple. And Bernal (1957), some years ago, formulat ed the still-unso lved problems thus: No one who knows what the difficulties are now believes that the crisis of physics is likely to be resolved by any simple trick 4 GENERAL SYSTEM THEORY of single machines but in those of "systems." A steam engine, automobile, or radio receiver was within the competence of the engineer trained in the respective specialty. But when it comes to ballistic missiles or space vehicles, they have to he assembied from components originating in heterogenea us technologies , mechanica!, electronic, chemica!, etc.; relations of man and machine come into play; and innumerable financial, economie, social and politica! problems are thrown into the bargain. Again, air or even automobile traffic are not just a matter of the number of vehicles in operation, but are systems to he planned or arranged. So innumerable problems are arising in production, commerce, and armaments. Thus, a "systems approach" became necessary. A certain objective is given; to find ways and means for its realization requires the systems specialist (or team of specialists) to consider alternative solutions and to choose those promising optimization at maximum efficiency and minimal cost in a tremendousl y complex network of interactions. This requires elaborate techniques and computers for solving problems far transeending the capacity of an individual mathematici an. Both the "hardware" of computers, automation and cybernation, and the "software" of systems science represent a new technology. It has been called the Second Industrial Revolution and has developed only in the past few decades. These developmen ts have not been limited to the industrialmilitary complex. Politicians frequently ask for application of the "systems approach" to pressing problems such as air and water pollution, traffic congestion, urban blight, juvenile delinquency and organized crime, city planning (Wolfe, 1967), etc., designating this a "revolutiona ry new concept" (Carter, 1966; Boffey, 1967). A Canadian Premier (Manning, 1967) writes the · systems approach into his politica! platform saying that an interrelation ship exists between all elements and constituents of society. The essendal factors in public problems, issues, policies, and programs must always be considered and evaluated as interdepend ent components of a total system. These developmen ts would be merely another of the many facets of change in our contempora ry technologica l society were it not for a significant factor apt to be overlooked in the highly sophisticate d and necessarily specialized techniques of computer science, systems engineering and related fields. This is not only 'I i i' i' Introduetion 5 a tendency in technology to make things bigger and better (or alternatively , more profitable, destructive, or both). It is a change in basic categories of thought of which the complexities of modern technology are only one-and possibly not the most importantmanifestatio n. In one way or another, we are forced to deal with complexities , with "wholes" or "systems," in all fields of knowledge. This implies a basic re-orientatio n in scientific thinking. An attempt to summarize the impact of "systems" would not be feasible and would pre-empt the consideratio ns of this book. A few examples, more or less arbitrarily chosen, must suffice to outline the nature of the problem and consequent re-orientatio n. The reader should excuse an egocenttic touch in the quotations, in view of the fact that the purpose öf this hook is to present the author's viewpoint rather than a neutral review of the field. In physics, it is well-known that in the enormous strides it made in the past few decades, it also generated new problemsor possibly a new kind of problem-pe rhaps most evident to the laymen in the indefinite number of some hundreds of elementary particles for which at present physics can offer little rhyme or reason. In the wordsof a noted representativ e (de-Shalit, 1966), the further developmen t of nuclear physics "requires much experimental work, as well as the developmen t of additional powerful methods for the handling of systenis with many, but not infinitely many, particles." The same quest was expressed by A. Szent-Györgyi (1964), the great physiologist , in a whimsical way: [When I joined the Institute for Advanced Study in Princeton] I did this in the hope that by rubbing elbows with those great atomie physicists and mathematici ans I would learn sarnething about living matters. But as soon as I revealed that in any living system there are more than two electrons, the physicists would not speak to me. With all their computers they could not say what the third electron might do. The remarkable thing is that it knows exactly what to do. So that little electron knows sarnething that all the wise men of Princeton don't, and this can only be sarnething very simple. And Bernal (1957), some years ago, formulated the still-unsolve d problems thus: No one who knows what the difficulties are no~ believes that the crisis of physics is likely to be resolved by any simple trick GENERAL SYSTEM THEORY 6 is m odification of existing theories. Something .radical A eded and it will have to go far wider than phys1cs. new ne ' h . d gu world outlook is being forged, but muc expene~~e an ar ment will be needed before it can take a defimt1ve form. lt must be coherent, it must include and illuminate the n:w. knowledge of fundamental particles and their complex fielûs, it must resolve the paradoxes of wave and particle, it must make the world inside the atom and the wide spaces of the universe equally intelligible. lt must hav~ a diffe~en~ dirneusion from all previous world views, and mclude m 1~self an explanation of development and the origin of ~ew thmgs. ~n this it will fall naturally in line with the convergmg tendennes of the biologica! and social sciences in which a regular pattem blends with their evolutionary history. m :I The triumph in recent years of molecular biology, ~he "bre~k­ ing" of the genetic code, the consequent achievements m geneucs, evolution, medicine, cell physiology and many other fields, has become common knowledge. But in spite of-or just because ofthe deepened insight attained by "molecular" biology, t~e ne~es­ sity of "organismic" biology has become apparent, as th1s wnter had advocated for some 40 years. The concern of biology is not only at the physico-chemical or molecular level but at. the higher levels of living organization as well. As we shall d1scuss lat~r (p. 12), the demand has been posed with renewed strength m consideration of recent facts and knowledge; but hardly an argument not previously discussed (von Bertalanffy, 1928a, 1932, 1949a, 1960) has been added. . Again, the basic conception in psyc~ology used to be . t~e "robot model." Behavior was to be explamed by the meehamstic stimulus-response (S-R) scheme; conditioning, according ~o the pattern of animal experiment, appeared as the founda~1~n of human behavior; "meaning" was to be replaced by cond1t10ned response; specificity of human behavior to be denied,. e~c. Gestalt psychology first made an inroad into the meehamstic scheme some 50 years ago. More recently, many attempts toward a more satisfactory "image of man" have been made an~ the system concept is gaining in importance (Chapter 8); P1aget, for example, "expressly related his conceptions to the general system theory of Bertalanffy" (Hahn, 1967). Introduetion 7 Perhaps even more than psychology, psychiatry has taken up the systems viewpoint (e.g. Menninger, 1963; von Bertalanffy, 1966; Grinker, 1967; Gray et al., in press). To quote from Grinker: Of the so-called global theories the one initially stated and defined by Bertalanffy in 1947 under the title of "general systems theory" has taken hold .... Since then he has refined, modified and applied his concepts, established a society for general systems theory and publislied a General Systems Yearbook. Many social scientists but only a handful of psychiatrists studied, understood or applied systems theory. Suddenly, under the leadership of Dr. William Gray of Boston, a threshold was reached so that at the l22nd annual meeting of the American Psychiatrie Association in 1966 two sessions were held at which this theory was discussed and regular meetings for psychiatrists were ensured for future participation in a development of this "Unified Theory of Human Behavior." If there be a third revolution (i.e. after the psychoanalytic and behavioristic), it is in the development of a general theory (p. ix). A report of a recent meeting (American Psychiatrie Association, 1967) draws a vivid picture: When a room holding 1,500 people is so jammed that hundreds stand through an entire morning session, the subject must be one in which the audience is keenly interested. This was the situation at the symposium on the use of a general systems theory in psychiatry which took place at the Detroit meeting of the American Psychiatrie Association (Damude, 1967). The same in the social sciences. From the broad spectrum, widespread confusion and contradictions of contemporary sociologica! theories (Sorokin, 1928, 1966), one secure condusion emerges: that social phenomena must be considered as "systems" -difficult and at present unsettled as the definition of sociocultmal entities may be. There is a revolutionary General Systems principles, ideas higher degree of scientific perspective (stemming) from the Research movement and (with a) wealth of and insights that have already brought a scientific order and understanding to many 8 GENE RAL SYST EM THEO RY cal sciences.... areas of biology, psychology and some physi of a frame work basis the de Mode rn systems resea rch can provi and dynam ic es lexiti more capab le of doing justic e to the comp 1967). ley, (Buck prope rties of the socio -cultu ral system ar conce ption The cours e of event s in our times suggests a simil all, histo ry 'is in histor y, inclu ding the consi derat ion that, after study . It is the sociology in the maki ng or in "long itudin al" tigate s in their same socio -cultu ral entiti es which sociology inves ing. becom their in prese nt state and histor y themselves by Earli er perio ds of histor y may have conso led d dictat ors, wicke , kings bad on ities blam ing atroc ities and stupid s. Confactor d relate and want rial ignor ance, super stitio n, mate ic," graph "idio kindhat" -did-w seque ntly, histor y was of the "who a was War rs y-Yea Thirt the as it was techn ically know n. Thus an Germ of ies rivalr the and n conse quenc e of religi ous super stitio of his unbri dled princ es; Napo leon overt urned Euro pe becau se blam ed on the be could ambi tion; the Secon d Worl d War the Germ ans. of ivity procl wickedness of Hitie r and the warli ke democracy, of state a In We have lost this intell ectua l comf ort. excuses ous previ these unive rsa! educa tion and gener al affiuence, ary mpor conte ating empl for huma n atroc ity fail miser ably. Cont and ty onali irrati its e histor y in the makin g, it is diffic ult to ascrib them a superbestia lity solely to indiv idual s (unless we grant ity). Rathe r, stupid and hurn an-o r subh uman -capa city for malic e r this may ateve we seem to be victim s of "histo rica! force s"-wh decisions idual indiv mean . Even ts seem to invol ve more than just ral "sys-cultu socio and action s and to be deter mine d more by social s, group tems, " be these preju dices , ideologies, press ure know We not. trend s, grow th and decay of civili zation s, or what of waste tion, precis ely and scientifically what the effects of pollu race, s ment arma natur a! resources, the popu lation explo sion, the count less critics by day every so told are We be. etc., are going to nal leade rs nor citing irrefu table argum ents. But neith er natio ing abou t it. If society as a whole seems to be able to do anyth Deus perdere vult we do not want a theist ic expla natio n-Qu em necessity. deme ntat- we seem to follow some tragic histor ica! as civili zation Whil e realiz ing the vague ness of such conce pts those of Speng ler and the short comin gs of "gran d theor ies" like of socio -cultu ral and Toyn bee, the quest ion of regul aritie s or laws sarily mean hissystems make s sense thoug h this does not neces Intro dueti on 9 1 · h' A 'n torica l inevi. tabili ty accor ding to Sir Isaiah Berl1 . n 1ston ca _ · h h' ) hke· McNe ill's The Rise of the West (1963 , W lC ln pano rama h' . 1 h posit ion even in the t'tl d 1cates 1s anu-S 1 e, never t e ess . pengl erian . penet rates into ption conce a Such s. system 1s a s.tory of hlst.orical "p rocess-sc h oo1 seem mgly outly mg fields so that the view of the · von said to be "borr owed fr om L u d w1g of archa eolog , y" is where systems B~rtalanffy s f:ame work for the devel oping embryo, they have done tngge r behav1or at critic a! junct ures and, once nery, 1967). so, ca1_1not r~turn to their origin al patte rn" (Flan with infor mal Wh.lle ~ocwlogy (and presu mabl y histor y) deals y of forma ! theor the is nt opme devel t organ~zat~ons, anoth er recen uted, such as orgam zatwn s, that is, struct ures planf ully instit prise, etc. This those o~ ~~ army, . burea ucrac y, busin ess enter ts the prem ise accep which theor y lS frame d m a philo sophy · · · study to way l ingfu mean the only " that orgam zatwn 1s to study . . ion as a system 1t as a system, systems analys1s treati ng "orga nizat er n orgam·za"mod fore there · bles" of. mutu ally depen dent varia , of gener al ssion discu a into uon theor y leads almos t inevi tably itione r of pract a of words system. theor y" (Scott, 1963). In the rch, resea l opera twna of th~~. the la~~ two decades we have witnessed the emerg ence of s, System ch. resear ific system as a key conce pt in scient new thing sarne but ries, centu course, have been studi ed for s as an entity has been added . · · · The tende ncy to study system . . f · congl a as than rathe r omer atwn o parts 1s consi stent with . the to isolat e tende ncy m conte mpor ary science no longe r r to open rathe but xts, ~heno~ena m narro wly confi ned conte . 1 e to and n inatio ctwn s for exam mtera xamm e arger and large r . systems research (and of er bann the r Unde e. natur of ~hees conve rgenc e of lts many synonyms) we have also witne ssed a devel opme nts. ific many more speci alized conte mpor ary scient being interare ... The~e resea rch pursu its and many other s an everving w~ven_ mto a coope rative resea rch effort inval g disciplines. Wldenmg sp~c~ru~ of. scientific and engin eerin most compreWe ~re partlClpatm~ m what is proba bly the know ledge yet hensi ve effort to attam a synthesis of scientific made (Ackoff, 1959). to those de In this way, the circle doses and we come back which w~ with y societ velop ments in conte mpor ary techn ologk al sketchy ver howe started. Wha t emerg es from these consi derat ions- GENERAL SYSTEM THEORY 10 and superficial-is that in the gamut of modern .sciences and. life new conceptualizations, new ideas and categones are reqmred, and that these, in one way or another, are centered about the concept of "system." To quote, fora change, from a Soviet author: The elaboration of specific methods for the investigation oL systems is a general trend of present scientific knowl.edge, just as for 19th century science the primary concentratwn of attention to the elaboration of elementary forms and processes in nature was characteristic (Lewada, in Hahn, 1967, p. 185). The dangers of this new development, alas, are obvious and have often been stated. The new cybernetic world, according to the psychotherapist Ruesch (1967) is not concerned with people but with "systems"; man becomes replaceable and expendable. To the new utopians of systems engineering, to use a phrase of Boguslaw (1965), it is the "human element" which is precisely the uureliabie component of their creations. It either has to he eliminated altogether and replaced by the hardware of computers, self-regulating machinery and the like, or it has to be made as reliable as possible, that is, mechanized, conformist, controlled and standardized. In somewhat harsher terms, man in the Big System is to be-and to a large extent has become-a moron, button-pusher or learned idiot, that is, highly trained in some narrow specialization but otherwise a mere part of the machine. This conforms to a well-known systems principle, that of progressive mechanization-the individual becoming ever more a cogwheel dominated by a few privileged leaders, mediocrities and mystifiers who pursue their private interests under a smokescreen of ideologies (Sorokin, 1966, pp. 558ff). Whether we envisage the positive expansion of knowledge and beneticent control of environment and society, or see in the systems movement the arrival of Brave New World and 1984-it deserves intensive study, and we have to come to terros with it. On the Ristory of Systems Theory As we have seen, there is a consensus in all major fieldsfram subatomie physics to history-that a re-orientation of science is due. Developments in modern technology parallel this trend. So far as can be ascertained, the idea of a "genera! system Introduetion 11 theory" was first introduced by the present author prior to cybernetics, systems engineering and the emergence of related fields. The story of how he was led to this notion is briefly told elsewhere in this hook (pp. 89ff.), but some amplification appears to be in order in view of recent discussions. As with every new idea in science and elsewhere, the systems concept has a long history. Although the term "system" itself was not emphasized, the history of this concept includes many illustrious names. As "natura! philosophy," we may trace it back to Leibniz; to Nicholas of Cusa with his coincidence of opposites; to the mystic medicine of Paracelsus; to Vico's and ibn-Kaldun's vision of history as a sequence of cultural entities or "systems"; to the dialeetic of Marx and Regel, to mention but a few narnes from a ric~ panoply of thinkers. The literary gourmet may remember N1cholas of Cusa's De ludo globi (1463; cf. von Bertalanffy, 1928b) and Hermann Hesse's Glasperlenspiel, both of them seeing the working of the world reflected in a cleverly designed, abstract game. There had been a few preliminary works in the field of general system theory. Köhler's "physical gestalten" (1924) pointed in this dire~ti~n b~t did not deal with the problem in full generality, restnctmg Its treatment to gestalten in physics (and biologica! an~ psychological phenomena presumably interpretable on this basis). In a later publication (1927), Köhler raised the postulate of a system theory, intended to elaborate the most general properties of inorganic compared to organic systems; to a degree, this demand was met by the theory of open systems. Lotka's classic (1925) came dosest to the objective, and we are indebted to him for basic formulations. Lotka iudeed dealt with a general concept of systems (not, like Köhler's, restricted to systems of ~hysics). B~ing a statistician, however, with his interest lying m populatwn probieros rather than in biologica! probieros of the individual organism, Lotka, somewhat strangely, conceived communities as systems, while regarding the individual organism as a sum of cells. Nevertheless, the necessity and feasibility of a systems approach became apparent only recently. lts necessity resulted from the fact that the mechanistic scheme of isolable causal trains and meristic treatment had proved insufficient to deal with theoretica! problems, especially in the biosocial sciences, and with the prae- 12 GENERA L SYSTEM THEORY tical probierus posed by modern technolog y. lts feasibilit y resulted from various new developm ents-theo retical, epistemo logical, mathema tica!, etc.-whi ch, although still in their beginnin gs, made it progressi vely realizabl e. The present author, in the early 20's, became puzzled abou~. obvious lacunae in the research and theory of biology. The theri prevalen t mechanis tic approach just mention ed appeared to neglect or actively deny just what is essential in the phenome na of life. He advocate d an organism ic concepti on in biology which emphasiz es consider ation of the organism as a whole or system, and sees the main objective of biologica ! sciences in the discovery of the principle sof organiza tion at its various levels. The author's first statemen ts go back to 1925-26, while Whitehe ad's philosop hy of "organic mechanis m" was publisbe d in 1925. Cannon's work on borneostasis appeared in 1929 and 1932. The organism ic conception had its great precurso r in Claude Bernard, but his work was hardly known outside France; even now it awaits its full evaluatio n (cf. Bernal, 1957, p. 960). The simultan eous appearance of similar ideas independ ently and on different continen ts was symptom atic of a new trend which, however, needed time to become accepted. These remarks are prompte d by the fact that in recent years "organism ic biology" has been re-empha sized by leading American biologist s (Dubos, 1964, 1967; Dobzhan sky, 1966; Common er, 1961) without, however, mention ing the writer's much earlier work, although this is duly recognize d in the literature of Europe and of the socialist countries (e.g., Ungerer, 1966; Blandino , 1960; Tribifio, 1946; Kanaev, 1966; Kamaryt , 1961, 1963; Bendman n, 1963, 1967; Afanasje w, 1962). It can be definite1y stated that recent discussions (e.g., Nagel, 1961; Hempel, 1965; Beckner, 1959; Smith, 1966; Schaffner, 1967), although naturally referring to advances of biology in the past 40 years, have not added any new viewpoin ts in comparis on to the author's work. In philosop hy, the writer's educatio n was in the tradition of neopositi vism of the group of Moritz Schlick which later became known as the Vienna Circle. Obviousl y, however, his interest in German mysticism, the historica ! relativism of Spengler and the history of art, and similar unorthod ox attitudes preclude d his becomin g a good positivist. Stronger were his honds with the Berlin group of the "Society for Empirica ! Philosop hy" of the Introdue tion 13 1920's, in which the philosoph er-physic ist Hans Reichenb ach, the psychoio gist A. Herzberg , the engineer Parseval (inventor of dirigible aircraft) were promine nt. In conneeti on with experime ntal work on metaboli sm and growth on the one hand, and an effort to concretiz e the organismic program on the other, the theory of open systems was advanced, based on the rather trivia! fact that the organism happens to be an open system, but no theory existed at the time. The first presenta tion, which foliowed some tentative trials, is included in this volume (Chapter 5). Biophysics thus appeared to demand an expansio n of conventi onal physical theory in the way of generaliz ation of kinetic principle s and thermody namic theory, the latter becomin g known, later on, as irreversib le thermody namics. But then, a further generaliz ation became apparent . In many phenome na in biology and also in the behavior al and social sciences, mathema tica! expressio ns and roodels are applicabl e. These, obviously , do not pertain to the entities of physics and chemistry, and in this sense transeend physics as the paragon of "exact sdence." (Incident ally, a series Abhandl ungen zur exakten Biologie, in succession of Schaxel's previous Abhandl ungen zur theoretischen Biologt:e, was inaugura ted by the writer but stopped during the war.) The structura l similarity of such roodels and their isomorph ism in different fields became apparent ; and just those probierus of order, organiza tion, wholeness, teleology, etc., appeared central which were program matically exclude<;l in mechanis tic science. This, then, was the idea of "genera! system theory." The time was not favorable for such developm ent. Biology was understo od to he identical with laborator y work, and the writer had already gone out on a limb when publishin g Theoretis che Biologie (1932), another field which has only recently become academic ally respectab le. Nowadays, when there are numerous joumals and publicati ons in this disciplin e and model building has become a fashionab le and generous ly supporte d indoor sport, the resistanc e to such ideas is hard to imagine. Affirmati on of the concept of general system theory, especiall y by the late Professor Otto Pötzl, well-kno wn Vienna psychiatr ist, helped the writer to overcom e his inhibitio ns and to issue a statement (reprodu ced in Chapter 3 of this hook). Again, fate in- GENERAL SYSTEM THEORY 14 tervened. The paper (in Deutsche Zeitschrift f~r Philosophie) had reached the proof stage, but the issue to carry It was destroyed in the catastrophe of the last war. After the war, genera!. system theory was presented in lectures (cf. Appendix), amply discussed with physicists (von Bertalanffy, 1948a) and discussed in lectures, and symposia (e.g., von Bertalanffy et al., 1951). The proposal of system theory was received inc:edulousl! .as fantastic or presumptuous. Either-it was argued-It was trzvtal because the so-called isomorphisms were merely examples of the truism that rnathematics can be applied to all sorts of things, and it therefore carried no more weight than the "discovery" that 2 2 4 holds true for apples, dollars a~d galaxi~s alike: or it was false and misleading because superfiCial analogies-as m the famous simile of society as an "organism" -camouflage actual differences and so lead to wrong and even morally objectionable conclusions. Or, again, it was philosophically and methodologically unsound because the alleged "irreducibility" of higher levels to lower ones tended to impede analytica! research whose success was obvious in various fields such as in the reduction of chemistry to physical principles, or of life phenom~na ~o mol~cular biolo?Y· Gradually it was realized that such obJectwns missed the pomt of what systems theory stands for, namely, attempting scientific interpretation and theory where previously there was none, and higher generality than that in the special sci~nces. ~e.ne:al system theory responded to a secret trend in vanous disciplme~. A letter from K. Boulding, economist, dated 1953, well summanzed the situation: + = I seem to have come to much the same condusion as you have reached, though approaching it from the direction of economics and the social sciences rather than from biologythat there is a body of what I have been calling "genera! empirica! theory," or "genera! system theory" in your e~cellent terminology, which is of wide applicability in many different disciplines. I am sure there are many peopl~ ~ll over the world who have come to essentially the same positiOn that we have, but we are widely scattered and do not know each other, so difficult is it to cross the boundaries of the disciplines. In the first year of the Center for Advanced Study in th~ ~e­ havioral Sciences (Palo Alto), Boulding, the biomathematician Introduetion 15 A. Rapoport, the physio1ogist Ralph Gerard and the present writer found themselves together. The project of a Society for General System Theory was realized at the Annual Meeting of the American Association for the Advancement of Science in 1954. The name was later changed into the less pretentious "Society for General Systems Research," which is now an affiliate of the AAAS and whose meetings have become a well-attended fixture of the AAAS conventions. Local groups of the Society were established at various centers in the United States and subsequently in Europe. The original program of the Society needed no revision: The Society for General Systems Research was organized in 1954 to further the development of theoretica! systems which are applicable to more than one of the traditional departments of knowledge. Major functions are to: (l) investigate the isomorphy of concepts, laws, and models in various fields, and to help in useful transfers from one field to another; (2) encourage the development of adequate theoretica! models in the fields which lack them; (3) minimize the duplication of theoretica! effort in different fields; (4) promote the unity of science through improving communication among specialists. The Society' s Y earbooks, General Systems, under the efficient editorship of A. Rapoport, have since served as its organ. Intentionally General Systems does not follow a rigid policy but rather provides a place for working papers of different intention as seems to be appropriate in a field which needs ideas and exploration. A large number of investigations and publications substantiated the trend in various fields; a journal, Mathematica! Systems Theory, made its appearance. Meanwhile another development had taken place. Norhert Wiener's Cybernetics appeared in 1948, resulting from the then recent developments of computer technology, information theory, and self-regulating machines. It was again one of the coincidences occurring when ideas are in the air that three fundamental contributions appeared at about the same time: Wiener's Cybernetics (1948), Shannon and Weaver's information theory (1949) and von Neumann and Morgenstern's game theory (1947). Wiener carried the cybernetic, feedback and information concepts far beyond the fields of technology and generalized it in the biologica! 16 GENER AL SYSTE M THEOR Y withou t and social rea1ms. It is true that cybern etics was not cornera e becam stasis precur sors. Canno n's concep t of homeo ck feedba d detaile stone in these consid eration s. Less well-known, the by ated elabor heen roodels of physio1ogica1 pheno mena had t~e, Germa n physio logist Richa rd Wagn er (1954) in the 1920's, Erich in and Swiss Nobel prize winne r W. R. Hess (1941, 1942) of cyvon Holst' s Reaffe renzpr inzip. The enorm ous popula rity is, of ity bernetic.s in science, techno1ogy and genera l public IndusSecond course , due to Wiene r and his procla mation of the trial Revo1 ution. shown The close corres ponde nce of the two mover oeuts is well cybera in a progra mmati c statem ent of L. Frank introd ucing netics confer ence: long The concep ts of purpos ive behav ior and te1eology have eking goal-se or g rfectin self-pe been associated with a myster ious, l capaci ty or final cause, usuall y of superh uman or super- natura thinkfic scienti , events of origin . To move forwar d to the study ts ing had to reject these beliefs in purpos e and these concep deand nistic mecha of teleolo gical operat ions for a strictly e termin istic view of nature . This mecha nistic concep tion becam se univer the that n firmly establi shed with the demon stratio g at was based on the operat ion of anony mous particl es movin multitheir by random , in a disord erly fashio n, giving rise, as in p1icity, to order and regula rity of a statist kal nature , of success d classica! physics and gas laws. The uncha llenge and omy, astron these concep ts and metho ds in physics and major later in chemis try, gave biolog y and physio logy their reinwas sms orient ation. This approa ch to probie ros of organi ean Europ foreed by the analyt ica! preocc upatio n of the Weste rn ons traditi cultur e and langua ges. The basic assum ptions of our almost and the persist ent implic ations of the langua ge we use sed of compe l us to approa ch everyt hing we study as compo isolate to separa te, discret e parts or factors which we must try preocand identif y as potent causes. Hence , we derive our We cupati on with the study of the relatio n of two variab les. and are witnes sing today a search for new approa ches, for new e of more compr ehensi ve concep ts and for metho ds capabl alities . dealin g with the large wholes of organi sms and person be The concep t of teleolo gical mecha nisms, howev er it may Introd uetion 17 t to expres sed in differe nt terms, may be viewed as an attemp now that lations formu nistic mecha older escape from these l conappea r inadeq uate, and to provid e new and more fruitfu selfng studyi for es dologi metho ve effecti ceptio ns and more and sms, organi and s system ng ientati self-or regula ting processes, servock, feedba terros the Thus, . alities self-di recting person be mechanisms, circular systems, and circular processes may the much of sions expres lent equiva but viewed as differe nt same basic concep tion. (Frank et al., 1948, conden sed). and A review of the develo pment of cybern etics in techno logy ssary unnece is and hook, this of scope science would exceed the er, the in view of the extens ive literat ure of the field. Howev dermisun certain e becaus riate presen t histori ca! survey is approp y Buckle Thus ed. appear have standi ngs and misint erpret ations seemthough y, Theor s System rn (1967, p. 36) states that "mode be seen ingly spring ing de novo out of the last war effort, can strivin g ctive perspe fic scienti as a cul~ination of a broad shift in second the gh Althou ies." for dornm anee over the last few centur did theory s system not; part .?f t?e senten ce is true, the first is much back goes but " not sprmg out of the last war effort, are furthe r and had roots quite differe nt from milita ry hardw an there is r Neithe s. and related techno logica l develo pment the in s pment develo "emerg ence of system theory from recent a special analysis of engine ering systems" (Shaw, 1965) except in word. sense of the etics Systems theory also is freque ntly identif ied with cybern the as etics, Cybern and contro l theory . This again is incorre ct. and nature and theory of contro l mecha nisms in techno logy is but a founde d on the concep ts of inform ation and feedback, a e~~t.yf a genera l theory of systeJlls; cybern etic systems are n. gulatio special case, howev er impor tant, of systems showin g self-re Trend s in System s Theor y being At a _time when a~y novelty, howev er trivial , is hailed as defic scienti for label this using revolu twnary , one Is weary of revoe teenag called being vel?pm ents. Minisk irts a~d long hair uced lutwn, and any new styhng of autom obiles or drug introd is word the nced, annou so by the pharm aceuti cal indust ry being 18 GENERAL SYSTEM THEORY an advertising slogan hardly fit for serious consideration. It can, however, be used in a strictly technica! sense, i.e., "scientific revolutions" can be identified by certain diagnostic criteria. Following Kuhn (1962), a scientific revolution is defined by the appearance of new conceptual schemes or "paradigms." These bring to the fore aspects which previously were not seel} ór perceived, or even suppressed in "normal" science, i.e., science generally accepted and practiced at the time. Hence there is a shift in the problems noticed and investigated and a change of the rules of scientific practice, comparable to the switch in perceptual gestalten in psychological experiments, when, e.g., the same figure may be seen as two faces vs. cup, or as duck vs. rabbit. Understandably, in such critica! phases emphasis is laid on philosophical analysis which is not felt necessary in periods of growth of "normal" science. The early versions of a new paradigm are mostly crude, solve few problems, and solutions given for individual problems are far from perfect. There is a profusion and competition of theories, each limited with respect to the number of problems covered, and elegant solution of those taken into account. Nevertheless, the new paradigm does cover new problems, especially those previously rejected as "metaphysical". These criteria were derived by Kuhn from a study of the "classica!" revolutions in physics and chemistry, but they are an excellent description of the changes brought about by organismic and systems concepts, and elucidate both their merits and limitations. Especially and not surprisingly, systems theory camprises a number of approaches different in style and aims. The system problem is essentially the problem of the limitations of analytica! procedures in science. This used to be expressed by half-metaphysical statements, such as emergent evolution or "the whole is more than a sum of its parts," but has a clear operational meaning. "Analytica! procedure" means that an entity investigated be resolved into, and hence can be constituted or reconstituted from, the parts put together, these procedures being understood both in their material and conceptual sense. This is the basic principle of "classica!" science, which can be circumscribed in different ways: resolution into isolable causal trains, seeking for "atomie" units in the various fields of science, etc. The progress of science has shown that these principles of Introduetion 19 classica! science-first enunciated by Galileo and Descartes-are highly successful in a wide realm of phenomena. Application of the analytica! procedure depends on two conditions. The first is that interactions between "parts" be nonexistent or weak enough to be neglected for certain research purposes. Only under this condition, can the parts be "worked out," actually, logically, and mathematically, and then be "put together." The second condition is that the relations descrihing the behavior of parts be linear; only then is the condition of summativity given, i.e., an equation descrihing the behavior of the tota1 is of the same form as the equations descrihing the behavior of the parts; partial processes can be superimposed to obtain the total process, etc. These conditions are not fulfilled in the entities called systems, i.e., consisting of parts "in interaction." The prototype of their description is a set of simultaneous differential equations (pp. 55ff.), which are nonlinear in the general case. A system or "organized complexity" (p. 34) may be circumscribed by the existence of "strong interactions" (Rapoport, 1966) or interactions which are "nontrivial" (Simon, 1965), i.e., n~p.Jj~ar. The methodological problem of systems theory, therefore, is to provide for problems which, compared with the analytical-summative ones of classica! science, are of a more general nature. As has been said, there are various approaches to deal with such problems. We intentionaÏly use the somewhat loose expression "approaches" because they are logically inhomogeneous, represent different conceptual models, mathematica! techniques, general points of view, etc.; they are, however, in accord in being "systems theories." Leaving aside approaches in applied systems research, such as systems engineering, operational research, linear and nonlinear programming, etc., the more important approaches are as follows. (For a good survey, cf. Drischel, 1968). "Classic al" system theory applies classica! mathematics, i.e., calculus. lts aim is to state principles which apply to systems in general or defined subclasses (e.g., closed and open systems), to provide techniques for their investigation and description, and to apply these to concrete cases. Owing to the generality of such description, it may be stated that certain formal properties will apply to any entity qua system (or open system, or hierarchical Ii !I GENERAL SYSTEM THEORY 20 system, etc.), even when its particular nature, parts, relations, etc., are unknown or not investigated. Examples include generalized principles of kinetics applicable, e.g., to populations of molecules or biologica! entities, i.e., to chemica! and ecological systems; diffusion, such as diffusion equations in physical c~eVJ.­ istry and in the spread of rumors; application of steady state and statistica! mechanics models to traffic flow (Gazis, 1967); allometric analysis of biologica! and social systems. Computerization and simulation. Sets of simultaneous differential equations as a way to "model" or define a system are, if linear, tiresome to solve even in the case of a few variables; if nonlinear, they are unsolvable except in special cases (Table 1.1) Table 1.1 Classification of Mathematica! Problems* and Their Ease of Solution by Analytica! Methods. After Franks, 1967. Nonlinear Equations Linear Equations Several Equations Many Equations Essentially Very impossiblc dilticuit Vcry difficuit Impossiblc Dillicult Essentially Very impossible dilticuit Impossible lmpossible Essentially impossible Impossible Impossible Impossible Impossiblc Equation One Equation Several Equations Many Equations Algebraic Trivia! Easy Easy Ordinary dift'erential Diflicuit Partial dift'erential One Equation • Courtesy of Electtonic Associates, lnc. For this reason, computers have opened a new approach in systems research; not only by way of facilitation of calculations which otherwise would exceed available time and energy and by replacement of mathematica! ingenuity by routine procedures, but also by opening up fields where no mathematica! theory or ways of solution exist. Thus systems far exceeding conventional mathernaties can be computerized; on the other hand, actual laboratory experiment can be replaced by computer simulation, the model so developed then to be checked by experimental data. In such way, for example, B. Hess has calculated the fourteenstep reaction chain of glycolysis in the cell in a model of more Introduetion 21 than 100 nonlinear differential equations. Similar analyses are routine in economics, market research, etc. Gompartment theory. An aspect of systems which may be listed separately because of the high sophistication reached in the field is compartment theory (Rescigno and Segre, 1966), i.e., the system consists of subunits with certain boundary conditions between which transport processes take place. Such compartment systems may have, e.g., "catenary" or "mammillary" structure (chain of compartments or a central compartment communicating with a number of peripheral ones). Understandably, mathematica! difficulties become prohibitive in the case of three- or multicompartment systems. Laplace transforms and introduetion of net and graph theory make analysis possible. Set theory. The general formal properties of systems, closed and open systems, etc., can he axiomatized in terms of set theory (Mesarovié, 1964; Maccia, 1966). In mathematica! elegance this approach compares favorably with the cruder and more special formulations of "classica!" system theory. The connections of axiomatized systems theory (or its present beginnings) with actual systems problems are somewhat tenuous. Graph theory. Many systems prob1ems concern structural or topologie properties of systems, rather than quantitative re1ations. Some approaches are available in this respect. Graph theory, especially the theory of directed graphs (digraphs), elaborates relational structures by representing them in a topological space. It has been applied to relational aspects of biology (Rashevsky, 1956, 1960; Rosen, 1960). Mathematically, it is connected with matrix algebra; modelwise, with compartment theory of systems containing partly "permeable" subsystems, and from here with the theory of open systems. Net theory, in its turn, is connected with set, graph, compartment, etc., theories and is applied to such systems as nervous networks (e.g., Rapoport, 1949-50). fdl~eJ:'fleLics is a theory of control systems based on communieation (transfer of information) between system and environment and within the system, and control (feedback) of the system's function in regard to environment. As mentioned and to be discussed further, the model is of wide application but should not he identified with "systems theory" in generaL In biology and 22 I' GENERA L SYSTEM THEORY other basic sciences, the cyberne tic model is apt to describe the formal structur e of regulato ry mechan isms, e.g., by block and flow diagram s. Thus the regulato ry structur e can he recognized, even when actual mechan isms remain unknow n and undescr ibed, and the system is a "black box" defined only by input and ovtput. For similar reasons, the same cyberne tic scheme may apply to hydraul ic, electric, physiolo gical, etc., systems. The highly elabora te and sophisti cated theory of servome chanism in technology has been applied to natural systems only in a limited extent (cf. Bayliss, 1966; Ka1mus, 1966; Milsum , 1966). lnforma tion theory, in the sense of Shanno n and Weaver (1949), is based on the concept of informa tion, defined by an express ion isomorp hic to negative entropy of thermod ynamics . Hence the expecta tion that informa tion may he used as measure of organiz ation (cf. p. 42; Quastle r, 1955). While informa tion theory gained importa nce in commu nication enginee ring, its applicatio ns to science have remaine d rather unconvi ncing (E.N. Gilbert, 1966). The relation ship between informa tion and organizati on, informa tion theory and thermod ynamics , remains a major problem (d. pp. 151ff.). Theory of automa ta (see Minsky, 1967) is the theory of abstract automa ta, with input, output, possibly tria1-an d-error and 1earning. A general model is the Turing machin e (1936). Express ed in the simples t way a Turing autorna ton is an abstract machin e capable of imprint ing (or deleting ) "1" and "0" marks on a tape of infinite length. It can he shown that any process of whateve r complex ity can be simulat ed by a machine , if this process can he expresse d in a finite number of logical operatio ns. Whatev er is possible logically (i.e., in an algorith mic symbolism) also can he constru ed-in principl e, though of course by no means a1ways in practice -by an automa ton, i.e., an algorith mic machine . Game theory (von Neuma nn and Morgen stern, 1947) is a differen t approac h but may he ranged among systems sciences because it is concern ed with the behavio r of suppose dly "rationa l" players to obtain maxima l gains and minima l losses by appropr iate strategie s against the other player (or nature). Hence it concerns essentia lly a "system " of antagon istic "forces" with specifications. Decision theory is a mathem atica! theory concern ed with choices among alternat ives. Introdu etion 23 Queuin g theory concern s optimiz ation of arrange ments under conditio ns of crowdin g. Inhomo geneous and incomp lete as it is, confaun ding roodels (e.g., open system, feedbac k circuit) with mathem atica! techniq ues (e.g., set, graph,. game theory), such an enumer ation is apt to show that there IS an array of approac hes to investig ate systems, includin g powerfu l mathem atica! methods . The point to he reiterated is that problem s previou sly not envisaged, not manage able, or consi~ered as being beyond science or purely philoso phical are · progressively explore d. often reality Natural ly, an incongr uence between model and atica! mathem exists. There are highly elabora te and sophisti cated models, but it remains dubious how they can he applied to the concrete case; there are fundam ental problem s for which no mathem atica! techniq ues are availabl e. Disappo intment of overits ~xtended expectat~ons has occurred . Cyberne tics, e.g., proved yielding , sciences basic in but gy technolo m only not Impact roodels for co.ncrete phenom ena and bringin g teleolog ical phenomena -prevwu sly tabooed -into the range of scientifically legitimate pro~!ems; b~t it ,~id .not yield an all-emb racing explana tion or grand world VIew, bemg an extensio n rather than a replacement of the mec~anistic view and machine theory (cf. Bronow ski, 1964). l~forma~10~ t~eory, highly develop ed mathem atically , proved disappomtn~g m psychol ogy and sociology. Game theory was ~opefully apphe~ to war and polities; but one hardly feels that It has led to an Improve rneut of politica ! decisions and the state of the world; a failure not unexpec ted when consiclering how little the powers that he resembi e the "rationa l" players of ga~e theory. Concep ts and roodels of equilibr ium, homeQstasis, ~djustment, etc., are suitable for the mainten ance of systems, but !!!'~,çlequate for phenom ena of change, differen tiation, evolutio n, negentr op!, productio~ of .improb able states, creativit y, building up of tenswns , self-rea hzatwn, emergen ce, etc.; as iudeed Cannon realized when he acknow ledged, beside borneostasis a "heterostasis" includin g phenom ena of the latter nature. The theory of open systems applies to a wide range of phenom ena in biology (and te~hnology), but a warning is necessary against its incautio us e~p~ns~on to fields for which its concept s are not made. Such hm1tat10ns and lacunae are only what is to he expecte d in a field hardly older than twenty or thirty years. In the last resort, 24 GENERAL SYSTEM THEORY disappoin tment results from making what is a useful model in certain respects into some metaphysi cal reality and "nothing-b ut" philosoph y, as bas happened many times in intellectua l history. The advantage s of mathemat ica! models-un ambiguity , possibility of strict deduction , verifiabilit y by observed data-are well known. This does not mean that models formulate d in ordinary language are to be despised or refused. A verbal model is better than no model at all, or a model which, because it can be formulate d mathemati cally, is forcibly imposed upon and falsifies reality. Theories of enormous influence such as psychoana lysis were unmathem atical or, like the theory of selection, their impact far exceeded mathemat ical constructi ons which came only later and cover only partial aspects and a small fraction of empirica! data. Mathernat ies essentially means the existence of an algorithm which is much more precise than that of ordinary language. Ristory of science attests that expression in ordinary language often preceded mathemati ca! formulatio n, i.e., invention of an algorithm. Examples come easily to mind: the evolution from counting in words to Roman numerals (a semiverba l, clumsy, half· algorithm) to Arabic notation with position value; equations, from verbal formulatio n to rudimenta ry symbolism handled with virtuosity (but difficult for us to follow) by Diophantu s and other founders of algebra, to modern notation; theories like those of Darwin or of economics which only later found a (partial) mathemat ical formulatio n. lt may be preferabie first to have some nonmathe matical model with its shortcomin gs but expressing some previously unnoticed aspect, hoping for future development of a suitable algorithm, than to start with premature mathemat ical models following known algorithms and, therefore, possibly restricting the field of vision. Many developme nts in molecular biology, theory of selection, cybernetic s and other fields showed the blinding effects of what Kuhn eaUs "normal" science, i.e., monolithic ally accepted conceptua l schemes. Models in ordinary language therefore have their place in systems theory. The system idea retains its value even where it cannot be formulate d mathemati cally, or remains a "guiding idea" rather than being a mathemat ica! construct. For example, we may not have satisfactor y system concepts in sociology; the mere insight that social entities are systems rather than sums Introdueti on 25 of social atoms, or that history consists of systems (however ill defined) called civilizatio ns obeying principles general to systems, implies a reorientat ion in the fields concerned . As can be seen from the above survey, there are, within the "systems approach, " mechanist ic and organismi c trends and models, trying to master systems either by "analysis," "linear (including circular) causality," "automata ," or else by "wholeness," "interactio n," "dynamics " (or what other words may be used to circumscri be the difference). While these models are not mutually exclusive and the same phenomen a may even be approached by different models (e.g., "cyberneti c" or "kinetic" concepts; cf. Locker, 1964), it can be asked which point of view is the more general and fundamen tal one. In general terms, this is a question to be putto the Turing machine as a general automaton . One considerat ion to the point (not, so far as we have seen, treated in automata theory) is the problem of "immense " numbers. The fundamen tal statement of automata theory is that happening s that can be defined in a finite number of "words" can be realized by an autornaton (e.g., a formal neural network after McCulloch and Pitts, or a Turing machine) (von Neumann, 1951). The question lies in the term "finite." The autornaton can, by definition, realize a finite series of events (however large), but not an infinite one. However, what if the number of steps required is "immense ," i.e., not infinite, but for example transeending the number of particles in the universe (estimated to be of the order 10 80 ) or of events possible in the time span of the universe or some of its subunits (according to Elsasser's, 1966, proposal, a number whose logarithm is a large number)? Such immense numbers appear in many system problems with exponentials , factorials and other explosivel y increasing functions. They are encounter ed in systems even of a moderate number of componen ts with strong (nonneglig ible) interaction s (cf. Ashby, 1964). To "map" them in a Turing machine, a tape of "immense" length would be required, i.e., one exceeding not only practical but physical limitations . Consider, for a simple example, a directed graph of N points (Rapoport , l959b). Between each pair an arrow may exist or may not exist (two possibilitie s). There are therefore 2N<N-l) different ways to conneet N points. If N is only 5, there are over a million ways to conneet the points. With N = 20, the number of ways ex- 26 GENERAL SYSTEM THEORY ceeds the estimated number of atoms in the universe. Similar problems arise, e.g., with possible connections between neurons (estimated of the order of 10 hiliion in the human brain) and with the genetic code (Repge, 1962). In the code, there is a minimum of 20 "words" (nucleotide triplets) spelling the twenty amino acids (actually 64); the code may contain some millibns of units. This gives 20 1 .ooo,ooo possibilities. Supposing the Laplacean spirit is to find out the functional value of every combination; he would have to make such number of probes, but there are only 108° atoms and organisms in the universe. Let us presurne (Repge, 1962) that 103° cells are present on the earth at a certain point of time. Further assuming a new cell generation every minute would give, for an age of the earth of 15 hiliion years (10 16 minutes), 1046 cells in total. To besure to obtain a maximum number, 10 20 life-bearing planets may be assumed. Then, in the whole universe, there certainly would be no more than 10 6 6 living beings-which is a great number but far from being "immense." The estimate can be made with different assumptions (e.g., number of possible proteins or enzymes) but with essentially the same result. Again, according to Hart (1959), human invention can be conceived as new combinations of previously existing elements. If so, the opportunity for new inventions will increase roughly as a function of the number of possible permutations and combinations of available elements, which means that its increase will be a factorial of the number of elements. Then the rate of acceleration of social change is itself accelerating so that in many cases not a logarithmic but a log-log acceleration will be found in cultural change. Hart presents interesting curves showing that increases in human speed, in killing areas of weapons, in life expectation, etc., actually foliowed such expression, i.e., the rate of cultural growth is not exponential or compound interest, but is super-acceleration in the way of a log-log curve. In a general way, limits of automata will appear if regulation in a system is directed not against one or a limited number of disturbances, but against "arbitrary" disturbances, i.e., an indefinite number of situations that could not possibly have been "foreseen"; this is widely the case in embryonic (e.g., experiments of Driesch) and neural (e.g., experimentsof Lashley) regulations. Regulation here results from interaction of many components (cf. discussion in Introduetion 27 Jeffries, 1951, pp. 32ff.). This, as von Neumann himself conceded, seems connected with the "self-restoring" tendencies of organismic as contrasted to technological systems; expressed in more modern terms, with their open-system nature which is not provided even in the abstract model of autornaton such as a Turing machine. It appears therefore that, as vitalists like Driesch have emphasized long ago, the mechanistiè conception, even taken in the modern and generalized form of a Turing automaton, founders with reguiadons after "arbitrary" disturbances, and similarly in happenings where the number of steps required is "immense" in the sense indicated. Problems of realizability appear even apart from the paradoxes connected with infinite sets. The above considerations pertain particularly to a concept or complex of concepts which indubitably is fundamental in the general theory of systems: that of hierarchic order. We presently "see" the universe as a tremenclous hierarchy, from elementary particles to atomie nuclei, to atoms, molecules, high-molecular compounds, to the wealth of structures (electron and lightmicroscopie) between molecules and cells (Weiss, 1962b), to cells, organisms and beyond to supra-individual organizations. One attractive scheme of hierarcbic order (there are others) is that of Boulding (Table 1.2). A similar hierarchy is found both in "structures" and in "functions." In the last resort, structure (i.e., order of parts) and function (order of processes) may be the very same thing: in the physical world matter dissolves into a play of energies, and in the biologica! world structures are the expression of a flow of processes. At present, the system of physical laws relates mainly to the realm between atoms and molecules (and their summation in macrophysics), which obviously is a slice of a much broader spectrum. Laws of organi1;ation and organizational forces are insufficiently known in the subatomie and the supermolecular realms. There are inroads into bath the subatomie world (high energy physics) and the supermolecular (physics of high molecular compounds); but these are apparently at the beginnings. This is shown, on the one hand, by the present confusion of elementary particles, on the other, by the present lack of physical understanding of structures seen under the electronmicroscope and the lack of a "grammar" of the genetic code (cf. p. 153). A general theory of hierarcbic order obviously will be a main- 28 GENERAL SYSTEM THEORY stay of general systems theory. Principles of hierarchic order can he stated in verbal language (Koestler, 1967; in press); there are semimathematical ideas (Simon, 1965) connected with matrix theory, and formulations in terms ofmathematicallog ic (Woodger, 1930-31). In graph theory hierarchic order is expressed by the "tree," and relational aspects of hierarchies can he represented:iii this way. But the problem is much broader and deeper: The question of hierarchic order is intimately connected with those of differentiation, evolution, and the measure of organization which does not seem to he expressed adequately in terms either of energetics (negative entropy) or of information theory (bits) (cf. pp. l50ff.). In the last resort, as mentioned, hierarchic order and dynamics may he the very same, as Koestier has nicely expressed in his simile of "The Tree and the Candle." Thus there is an array of system models, more or less progressed and elaborate. Certain concepts, models and principles of general systems theory, such as hierarchic order, progressive differentiation, feedback, systems characteristics defined by set and graph theory, etc., are applicable broadly to material, psychological and sociocultural systems; others, such as open system defined by the exchange of matter, are limited to certain subclasses. As practice in applied systems analysis shows, diverse system models will have to he applied according to the nature of the case and operational criteria. Table 1.2 DESCRIPTION AND LEVEL Static structures Clock works Control mechanisms DESCRIPTION AND EXAMPLES THEORY AND Atoms, molecules, crystals, biologica! structures from the electron-microscopie to the macroscopie level Clocks, conventional machines in genera!, solar systems E.g. structural formulas of chemistry; crystallography; anatomical descriptions Conventional physics such as laws of mechanics (Newtonian and Einsteinian) and others Thermostat, servomechanisms, homeostatic mechanism in organisms Cybernetics; feedback and information theory EXAMPLES THEORY AND MODELS Open systems Flame, cells and organisms in general (a) Expansion of physical theory to systems maintaining themselves in flow of matter (metabolism) . (b) Information storage in genetic code (DNA). Conneetion of (a) and (b) presently unclear Lower organisms "Plant-like" organisms: Increasing differentiation of system (so-called "division of labor" in the organism) ; distinction of reproduetion and functional individual ("germ track and soma") Increasing importance of traffic in information (evolution of receptors, nervous systems) ; learning; beginnings of consciousness Symbolism; past and future, self and world, self-awareness, etc., as consequences; communieation by language, etc. Theory and roodels airoost lacking Socio-cul tural systems Populations of organisms (humans included) ; symbol-determined communities (cultures) in man only Statistica! and possibly dynamic laws in population dynamics, sociology, economics, possibly history. Beginnings of a theory of cultural systems. Symbolic systems Language, logic, mathematics, sciences, arts, morals, etc. Algorithms of symbols (e.g. mathematics, grammar) ; "rules of the game" such as in visual arts, music, etc. Animals Man An Informal Survey of Main Levels in the Hierarchy of Systems. Partly in pursuance in Boulding, l956b LEVEL 29 Introduetion MODELS Beginnings in automata theory (S-R relations) , feedback (regulatory phenomena) , autonomous behavior (relaxation oscillations) , etc. Incipient theory of symbolism NB.-This survey is impressionistic and intuitive with no claim for logica! rigor. Higher levels as a rule presuppose lower ones (e.g. life phenomena those at the physico-chemical level, socio-cultural phenomena the level of human activity, etc.) ; but the relation of levels requires ciarifkation in each case (cf. probieros such as open system and genetic code as apparent prerequisites of "life"; relation of "conceptual" to "real" systems, etc.) . In this sense, the survey suggests both the limits of reductionism and the gaps in actual knowledge. The Meaning of General System Theory 2 The Meaning of Genera l System Theory The Quest fora General System Theory Modern science is characterize d by its ever-increas ing specialization, necessitated by the enormous amount of data, the complexity of techniques and of theoretica! structures within every field. Thus science is split into innumerable disciplines continually generating new subdisciplin es. In consequence , the physicist, the biologist, the psychoiogist and the social scientist are, so to speak, encapsulate d in their private universes, and it is difficult to get word from one cocoon to the other. This, however, is opposed by another remarkable aspect. Surveying the evolution of modern science, we encounter a surprising phenomeno n. Independen tly of each other, similar problems and conceptions have evolved in widely different fields. It was the aim of classica! physics eventually to resolve natmal phenomena into a play of elementary units governed by "blind" laws of nature. This was expressed in the ideal of the Laplacean spirit which, from the position and momentu~ of_ par_ticles, ca~ predict the state of the universe at any pomt m ttme. Thts mechanistic view was not altered but rather reinforeed when deterministi c laws in physics were replaced by statistica! laws. According to Boltzmann's derivation of the second principle of thermodynam ics, physical events are directed toward states of maximum probability, and physicallaw s, therefore, are essentially 31 "laws of disorder," the outcome of unordered, statistica! events. In contrast to this mechanistic view, however, problems of ~hole­ ness, dynamic interaction and organization have appeared m ~he various branches of modern physics. In the Heisenberg relatwn and quanturn physics, it became impossible to resolve phenomena into local events; problems of order and organization appear whether the question is the structure of atoms, the architecture of proteins, or interaction phenomena in thermodynam ics. Similarly biology, in the mechanistic conception, saw its goal in t~e resolution of life phenomena into atomie entities and parttal processes. The living organism w_as resolved ~nto cel~s, its activities into physiologica l and ulttmately phystcochem tcal processes, behavior into uncondition ed and conditioned reflexes, the substratum of heredity into particulate genes, and so forth. In contradistin ction, the or:g'!rrismic conception is basic for modern biology. It is necessary to study not only parts and processes in isolation, but also to solve the decisive probieros found in the organization and order unifying them, resulting from dynamic interaction of parts, and making the behavior of parts different when studied in isolation or within the whole. Again, similar trends appeared in psychology. While classica! association psychology attempted to resolve mental phenomena into elementary units-psycho logical atoms as it were-such as elementary sensations and the like, gestalt psychology showed the existence and primacy of psychological wholes which are not a summation of elementary units and are governed by dynamic laws. Finally, in the social sciences the concept of society as a sum of individuals as social atoms, e.g., the model of Economie Man, was replaced by the tendency to consider society, economy, nation as a whole superordina ted to its parts. This implies the great probieros of planned economy, of the deification of nation and state, but also reflects new ways of thinking. This parallelism of general cognitive principles in different fields is even more impressive when one considers the fact that those developmen ts took place in mutual independene e and mostly without any knowledge of work and research in other fields. There is another important aspect of modern science. Up to recent times, exact science, the corpus of laws of nature, was almost identical with theoretica! physics. Few attempts to state 32 GENERAL SYSTEM THEORY exact laws in nonphysical fields have gained recognition. However, the impact of and progress in the biological, behaviaral and social sciences seem to make necessary an expansion of our conceptual schemes in order to allow for systems of laws in fields where application of physics is not sufficient or possible. Such a trend towards generalized theories is taking place .:in many fields and in a variety of ways. For example, an elaborate theory of the dynamics of biologica! populations, the struggle for existence and biologica! equilibria, has developed, starting with the pioneering work by Lotka and Volterra. The theory operates with biologica! notions, such as individuals, species, coefficients of competition, and the like. A similar procedure is applied in quantitative economics and econometrics. The models and families of equations applied in the latter happen to be similar to those of Lotka or, for that matter, of chemica! kinetics, but the model of interacting entities and farces is again at a different level. To take another example: living organisms are essentially open systems, i.e., systems exchanging matter with their environment. Conventional physics and physical chemistry deal with closed systems, and only in recent years has theory been expanded to include irreversible processes, open systems, and states of disequilibrium. If, however, we want to apply the model of open systems to, say, the phenomena of animal growth, we automatically come to a generalization of theory referring not to physical but to biologica! units. In other words, we are dealing with generalized systems. The same is true of the fields of cybernetics and information theory which have gained so much interest in the past few years. Thus, there exist models, principles, and laws that apply to generalized systems or their subclasses, irrespective of their particular kind, the nature of their component elements, and th,e relations or "farces" between them. It seems legitimate to ask for a theory, not of systems of a more or less special kind, but of universa! principles applying to systems in generaL In this way we postulate a new discipline called General System Theory. lts subject matter is the f()D:J!l1}<!-ÛQ1l~ and det:ivation of those P!:incipl~Lwhich are va1i<:lJor "systems". in generaL The meaning of this discipline can be circumscribed as follows. Physics is concerned with systems of different levels of generality. The Meaning of General System Theory 33 Jt extends from rather special systems, such as those applied by the engineer in the construction of a bridge or of a machine; to special laws of physical disciplines, such as mechanics or opties; to laws of great generality, such as the principles of thermodynamics that apply to systems of intrinsically different nature, mechanic, calorie, chemica! or whatever. Nothing prescribes that we have to end with the systems traditionally treated in physics. Rather, we can ask for principles app}yill.K to ~ystefi1sill ge:n~J:al, irrespective of whether they are of physical, biologica! or S()c:;iological nature. If we pose this question and conveniently define the concept of system, we find that models, principles, and laws exist which apply to generalized systems irrespective of their particular kind, elements, and the "farces" involved. A consequ~nce of the existence of general system properties is the appearance of structural similarities or isQinorpl.lisms in different fields. There are correspondences in the principles that góvern ihe behavior of entities that are, intrinsically, widely different. To take a simple example, an exponentiallaw of growth applies to certain bacterial cells, to populations of bacteria, of animals or humans, and to the progress of scientific research measured by the number of publications in genetics or science in generaL The entities in question, such as bacteria, animals, men, hooks, etc., are completely different, and so are the causal mechanisms involved. Nevertheless, the mathematica! law is the same. Or there are systems of equations descrihing the competition of animal and plant species in nature. But it appears that the same systems of equations apply in certain fields in physical chemistry and in economics as well. This correspondence is due to the fact that the entities concerned can be considered, in certain respects, as "systems," i.e., complexesof elements standing in ipt~raction, The fact that the fields mentioned, and others as well, are concerned with "systems," leads to a correspondence in general principles and even in special laws when the conditions correspond in the phenomena under consideration. In f<~_ct, similar concepts, models and laws have often appeared in widely different fields, independently and based upon totally different facts. There are many instances where identical principles were discovered several times because the workers in one field were unaware that the theoretica! structure required was 34 GENERAL SYSTEM THEORY already well developed in some other field. General system theory will go a long way towards avoiding such unnecessary duplication of labor. • System isomorphisms also appear in problems which are recalcitrant to quantitative analysis but are nevertheless of great intrinsic interest. There are, for example, isomorphies between biologica! systems and "epiorganisms" (Gerard) like animal communities and human societies. Which principles are common to the several levels of organization and so may legitimately be transferred from one level to another, and which are specific so that transfer leads to dangerous fallacies? Can societies and civilizations be considered as systems? It seems, therefore, that a general theory of systems would be a usef~L!~~!_pr;;~idil'lg, on the one hand, models that can be used in, and transferred to, different fields, and safeguarding, on the other hand> from vague analogies which often have marred the progress in the~e fields. There is, however, another and even more important aspect of general system theory. It can be paraphrased by a felicitous formulation due to the well-known mathematician and founder of information theory, Warren Weaver. Classica! physics, Weaver said, was highly successful in developing the theory of unorganized complexity. Thus, for example, the behavior of a gas is the result of the unorganized and individually untraceable movemeuts of innumerable molecules; as a whole it is governed by the laws of thermodynamics. The theory of unorganized complexity is ultimately rooted in the laws of chance and probability and in the second law of thermodynamics. In contrast, the fundamental problem .tQllily is that of organized complexi~y. Concepts like those of organization, wholeness, directiveness, teleology, and differentiation are alien to conventional physics. However, they pop up everywhere in the biologica!, behavioral and social sciences, and are, in fact, indispensable for dealing with living organisms or social groups. Thus a basic problem posed to modern science is a general the()ry of organization. General system theory is, in principle, capable of giving exact definitions for such concepts and, in suitable cases, of putting them to quantitative analysis. If we have briefly indicated what general system theory means, The Meaning of General System Theory 35 it will avoid misunderstanding also to state what it is not. It has been objected that system theory amounts to no more than the trivia! fact that rnathematics of some sort can be applied to different sorts of problems. For example, the law of exponential growth is applicable to very different phenomena, from radioactive decay to the extinction of human populations with insuflident reproduction. This, however, is so because the formula is one of the simplest differential equations, and can therefore be applied to quite different things. Therefore, if so-called isomorphic laws of growth occur in entirely different processes, it bas no more significanee than the fact that elementary arithmethic is applicable to all count~ble objects, that 2 plus 2 make 4, irrespective of whether the counted objects are apples, atoms or galaxies. The answer to this is as follows. Notjustin the example quoted by way of simple illustration, but in the development of system theory, the question is not the application of well-known mathematica! expressions. Rather, problems are posed that are novel and partly far from solution. As mentioned, the method of dassical science was most appropriate for phenomena that either can be resolved into isolated causa! chains, or are the statistica! outcome of an "infinite" number of chance processes, as is true of statistica! mechanics, the second principle of thermodynamics and all laws deriving from it. The classica! modes of thinking, however, fail in the case of interaction of a large but limited number of elements or processes. Here those problems arise which are circumscribed by such notions as wholeness, organization and the like, and which demand new ways of mathematica! thinking. · Another objection emphasizes the danger that general system theory may end up in meaningless analogies. This danger indeed exists. For example, it is a widespread idea to look at the state or the nation as an organism on a superordinate level. Such a theory, however, would constitute the foundation for a totalitarian state, within which the human individual appears like an insignificant cell in an organism or an unimportant worker in a beehive. But general system theory is not a search for vague and supertidal analogies. Analogies as such are of little value since besides similarities between phenomena, dissimilarities can always be 36 GENERAL SYSTEM THEORY found as well. The isomorphism under discussion is more than mere analogy. It is a consequence of the fact that, ÜL,,<;:~!J;:tin r~~p~cts, corresponding abstractions and conceptual models can be appliedto differentphenomena. Only in view of these aspects wilfsysieffi~i<t;8 appiy. This~is- not different from the genen~1 procedure in science. It is the same situation as when the hw of gravitation applies to Newton's apple, the planetary system, and tidal phenomena. This means that in view of certain limited aspects a theoretica! system, that of mechanics, holds true; it does not mean that there is a particular resemblance between apples, planets, and oceans in a great number of other aspects. A third objection claims that system theory lacks explanatory value. For example, certain aspects of organic purposiveness, such as the so-called equifinality of developmental processes (p. 40), are open to system-theoretical interpretation. Nobody, however, is today capable of defining in detail the processes leading from an animal ovum to an organism with its myriad of cells, organs, and highly complicated functions. Here we should consider that there are degrees in scientific explanation, and that in complex and theoretically little-developed fields we have to be satisfied with what the economist Hayek has justly termed "explanation in principle." An example may show what is meant. Theoretica! economics.is a highly developed system, presenting elaborate models for the processes in question. However, professors of economics, as a rule, are not millionaires. In other words, they can explain economie phenomena well "in principle" but they are not able to predict ftuctuations in the stock market with respect to certain shares or dates. Explanation in principle, however, is better than none at all. If and when we are able to insert the necessary parameters, system-theoretical explanation "in principle" becomes a theory, similar in structure to those of physics. Aims of General System Theory We may summarize these considerations as follows. Similar general conceptions and viewpoints have evolved in various disciplines of modern science. While in the past, science tried to explain observable phenomena by reducing them to an i i' The Meaning of General System Theory 37 interplay of elementary units investigatable independently of each other, conceptions appear in contemporary science that are concerned with what is somewhat vaguely termed "wholeness," i.e., problems of organization, phenomena not resolvable into local events, dynamic interactions manifest in the difference of behavior of parts when isolated or in a higher configuration, etc.; in short, "systems" of various orders not understandable by investigation of their respective parts in isolation. Conceptions and problems of this nature have appeared in all branches of science, irrespective of whether inanimate things, living organisms, or social phenomena are the object of study. This correspondence is the more striking because the developments in the individual sciences were mutually independent, largely unaware of each other, and based upon different facts and contradicting philosophies. They indicate a general change in scientific attitude and conceptions. Not only are general aspects and viewpoints alike in different sciences; frequently we find formally identical or isomorphic laws in different fields. In many cases, isomorphic laws hold for certain classes or subclasses of "systems," irrespective of the nature of the entities involved. There appear to exist general system laws which apply to any system of a certain type, irrespective of the particular properties of the system and of the elements involved. These considerations lead to the postulate of a new scientific discipline which we call general system theory. lts subject matter is formulation of principles that are valid for "systems" in genera!, whatever the nature of their component elements and the relations or "forces" between them. General system theory, therefore, is a general science of "wholeness" which up till now was considered a vague, hazy, and semimetaphysi~al concept. In elaborate form it would be a logicomathematical discipline, in itself purely formal but applicable to the various empirica! sciences. For sciences concerned with "or?anized wholes," it would be of similar significanee to that wh1ch probability theory has for sciences concerned with "chance events"; the latter, too, is a formal mathematica! discipline which c~n b~ applied to most diverse fields, such as thermodynamics, bwlog1cal and medical experimentation, genetics, life insurance statistics, etc. 38 i GENERAL SYSTEM THEORY This indicates major aims of general system theory: (1) There is a general tendency towards integration in the various sciences, natural and social. (2) Such integration seems to be centered in a general theory of systems. . . ~ (3) Such theory may be an important means for aimmg at exact theory in the nonphysical fields of science. (4) Developing unifying principles running ":ertically" t~rough the universe of the individual sciences, this theory bnngs us nearer to the goal of the unity of science. . . . . (5) This can lead to a much-needed integratwn m sCientific education. A rema~k as to the delimitation of the theory here discussed seems to be appropriate. The term and program of a general system theory was introduced by the present author a number of years ago. It has turned out, however, that qui~e _a large nu~ber of workers in various fields had been led to simtlar concluswns and ways of approach. It is suggested, therefore, to ~aintain this name which is now coming into general use, be It only as a convenient label. It looks, at first, as if the definition of systems as "sets of elements standing in interaction" is so general and vague that not much can be learned from it. This, however, is not true. For example, systems can be defined by certain famili~s of diffe:ential equations and if, ~n the usual way of mathem~ucal reasomng, more specified conditions are introduced, many Important pr~p­ erties can be found of systems in general and more speCial cases (cf. Chapter 3). The mathematica! approach followed in general system theory is not the only possible or most general one. There are a number of related modern approaches, such as information theory, cybernetics, game, decision, and net theories, stochastic models, operadons research, to mention only the most import~nt ones. However, the fact that differential equations cover extensive fields in the physical, biologica!, economical, and probably also the behavioral sciences, makes them a suitable access to the study of generalized systems. I am now going to illustrate general system theory by way of some examples. The Meaning of General System Theory 39 Closed and Open Systems: Limitations of Conventional Physics My first example is that of closed and open systems. Conventional physics deals only with closed systems, i.e., systems which are considered to be isolated from their environment. Thus, physical chemistry tells us about the reactions, their rates, and the chemical equilibria eventually established in a dosed vessel where a number of reactants is brought together. Thermodynamics expressly dedares that its laws apply only to clos~d systems. In particular, the second principle of thermodynamics states that, in a dosed system, a certain quantity, called entropy, must increase to a maximum, and eventually the process comes to a stop at a state of equilibrium. The second principle can be formulated in different ways, one being that entropy is a measure of probability, and so a dosed system tends to a state of most probable distribution. The most probable distribution, however, of a mixture, say, of red and blue glass beads, or of molecules having different velocities, is a state of complete disorder; having separated all red beads on one hand, and all blue ones on the other, or having, in a dosed space, all fast molecules, that is, a high temperature on the right side, and all slow ones, a low temperature, at the left, is a highly improbable state of affairs. So the tendency towards maximum entropy or the most probable distribution is the tendency to maximum disorder. However, we find systems which by their very nature and definition are not dosed systems. Every living organism is essentially 1:1n open system. It maintains itself in a continuous inflow and outflow, a building up and breaking down of components, never being, so long as it is alive, in a state of chemical and thermodynamic equilibrium but maintained in a so-called st<:~~I~~~t~~ which is distinct from the latter. This is the very essence of that fundamental phenomenon of life which is called metabolism, the chemical processes within living cells. What now? Obviously, the conventional formulations of physics are, in principle, inapplicable totheliving organism qua open system and steady state, and we may well suspect that many characteristics of living systems which are paradoxkal in view of the laws of physics are a consequence of this fact. It is only in recent years that an expansion of physics, in order 40 GENERAL SYSTEM THEORY to include open systems, has taken place. This theory has shed light on many obscure phenomena in physics and biology, and has also led to important general conclusions of which I will mention only two. The first is the principle of equifinality. In any closed system, the final state is unequivocally determined by the initial conditions: e.g., the motion in a planetary system where the positions of the planets at a time t are unequivocally determined by their positions at a time t 0 • Or in a chemica! equilibrium, the final concentrations of the reactants naturally depend on the initial concentrations. If either the initial conditions or the process is altered, the final state will also be changed. This is not so in open systems. Here, the same final state may be reached from different initial conditions and in different ways. This is what is called equifinality, and it has a significant meaning for the phenomena of biologica! regulation. Those who are familiar with the history of biology will remember that it was just equifinality that led the German biologist Driesch to embrace vitalism, i.e., the doctrine that vital phenomena are inexplicable in terms of natural science. Driesch's argument wasbasedon experiments on embryos in early development. The same final result, a normal individual of the sea urchin, can develop from a complete ovum, from each half of a divided ovum, or from the fusion product of two whole ova. The same applies to embryos of many other species, including man, where identical twins are the product of the splitting of one ovum. Equifinality, according to Driesch, contradiets the laws of physics, and can be accomplished only by a soul-like vitalistic factor which governs the processes in foresight of the goal, the normal organism to be established. It can be shown, however, that open systems, insofar as they attain a steady state, must show equifinality, so the supposed violation of physical laws disappears (cf. pp. 132f.). Another apparent contrast between inanimate and animate nature is what sometimes was called the violent contradiction between Lord Kelvin's degradation and Darwin's evolution, between the law of dissipation in physics and the law of evolution in biology. According to the second principle of thermodynamic s, the general trend of events in physical nature is toward states of maximum disorder and levelling down of differences, with the so-called heat death of the universe as the final outlook, when The Meaning of General System Theory 41 all energy is degraded into evenly distributed heat of low temperature, and the world process comes to a stop. In contrast, the living world shows, in embryonic development and in evolution, a transition towards higher order, heterogeneity, and organization. B~t ~n the basis of the theory of open systems, the apparent contradictwn between entropy and evolution disappears. In all irreversible processes, entropy must increase. Therefore, the change of entropy in closed systems is always positive; order is continually destroyed. In open systems, however, we have not only production of entropy due to irreversible processes, but also import of entropy which may well be negative. This is the case in the living organism which imports complex molecules high in free energy. Thus, living systems, maintaining themselves in a steady state, can avoid . the increase of entropy, and may even develop towards states of increased order and organization. From these examples, you may guess the hearing of the theory of open. syst~ms. Among. other things, it shows that many supposed vwlatwns of physical laws in living nature do. not exist, or rather that they disappear with the generalization of physical theory. !n a generalize~ version the concept of open systems can be apphed to ~onphysical levels. Examples are its use in ecology and the evolutwn towards a climax formation (Whittacker), in psycho~ogy where "neurological systems" were considered as "open dynamiC systems" (Krech), in philosophy where the trend toward "trans-actional" as opposed to "self-actional" and "inter-actional" viewpoints closely corresponds to the open system model (Bentley). lnformation and Entropy Anot~er development which is closely connected with system theory Is that of the modern theory of communication , It has often b~en said that energy is the currency of physics, just as economie values can be expressed in dollars or pounds. There are, however, certain fields of physics and technology where this currency is not readily acceptable. This is the case in the field of co~munication which, due to the development of telephones, radw, radar, calculating machines, servomechanism s and other devices, has led to the rise of a new branch of physics. The general notion in communication theory is that of in- 42 GENERAL SYSTEM THEORY formation. In many cases, the flow of information corresponds to a flow of energy, e.g., if light waves emitted by some objects reach the eye or a photoelectric cell, elicit some reaction of the organism or some machinery, and thus convey information. However, examples can easily be given where the flow of information is opposite to the flow of energy, or where information is transmitted without a flow of energy or matter. The first is the case in a telegraph cable, where a direct current is flowing in one direction, but information, a message, can be sent in either direction by interrupting the current at one point and recording the interruption at another. For the second case, think of the photoelectric door openers as they are installed in many supermarkets: the shadow, the cutting off of light energy, informs the photocell that somebody is entering, and the door opens. So information, in genera!, cannot be expressed in terms of energy. There is, however, another way to measure information, namely, in terms of decisions. Take the game of Twenty Questions, where we are supposed to find out an object by receiving simple "yes" or "no" answers to our questions. The amount of information conveyed in one answer is a decision between two alternatives, such as animal or nonanimaL With two questions, it is possible to decide for one out of four possibilities, e.g., mammal-nonmammal, or flowering plant-nonflowering plant. With three answers, it is a decision out of eight, etc. Thus, the logarithm at the base 2 of the possible decisions can be used as a measure of information, the unit being the so-called binary unit or bit. 2 bits, The information contained in two answers is log2 4 3 bits, etc. This measure of informaof three answers, log2 8 tion happens to be similar to that of entropy or rather negative entropy, since entropy also is defined as a logarithm of probability. But entropy, as we have already heard, is a measure of disorder; hence negative entropy or information is a measure of order or of organization since the latter, compared to distribution at random, is an improbable state. A second central concept of the theory of communication and control is that of feedback. A simple scheme for feedback is the following (Fig. 2.1). The system comprises, first, a receptor or "sense organ," be it a photoelectric cell, a radar screen, a thermometer, or a sense organ in the biologica! meaning. The message may be, in technological devices, a weak current, or, in a = = 43 The Meaning of General System Theory MESSAGE STIMULUS MESSAGt RESPONSE ,~ 1-IL-..A-~-P-AA_:_~~-s---J_.,~r ~ FEEOSACK ~ Fig. 2.1. Simple feedback scheme. living organism, represented by nerve conduction, etc. Then there is a center recombining the incoming messages and transmitting them to an effector, consisting of a machine like an electromotor, a heating coil or solenoid, or of a muscle which responds to the incoming message in such a way that there is power output of high energy. Finally, the functioning of the effector is monitored back to the receptor, and this makes the system self-regulating, i.e., guarantees stabilization or direction of action. Feedback arrangements are widely used in modern technology for the stabilization of a certain action, as in thermostats or in radio receivers; or for the direction of actions towards a goal where the aberration from that goal is fed back, as information, till the goal or target is reached. This is the case in self-propelled missiles which seek their target, anti-aircraft fire control systems, ship-steering systems, and other so-called servomechanisms. There is indeed a large number of biologica! phenomena which correspond to the feedback model. First, there is the phenomenon of so-called homeostasis, or maintenance of balance in the living organism, the prototype of which is thermoregulation in warmblooded animals. Cooling of the blood stimulates certain centers in the brain which "turn on" heat-producing mechanisms of the body, and the body temperature is monitored back to the center so that temperature is maintained at a constant level. Similar homeostatic mechanisms exist in the body for maintaining the constancy of a great number of physicochemical variables. Furthermore, feedback systems comparable to the servomechanisms of technology exist in the animal and human body for the regulation of actions. If we want to piek up a pencil, a report is made 44 GENERAL SYSTEM THEORY to the central nervous system of the distance by which we have failed to grasp the pencil in the first instance; this information is then fed back to the central nervous system so that the motion is controlled till the aim is reached. So a great variety of systems in technology and in living nature follow the feedback scheme, and it is well-known that il ne~ discipline, called Cybernetics, was introduced by Norhert Wiener to deal with these phenomena. The theory tries to show that mechanisms of a feedback nature are the base of teleological or purposeful behavior in man-made machines as well as in living organisms, and in social systems. It should be borne in mind, however, that the feedback scheme is of a rather special nature. It presupposes structural arrangements of the type mentioned. There are, however, many regulations in the living organism which are of essentially different nature, namely, those where the order is effectuated by a dynamic interplay of processes. Recall, e.g., embryonic regulations where the whole is reestablished from the parts in equifinal processes. It can be shown that the prim{lry regulations i11 organic systems, i.e., those which are most fundamental and prin{itive in embryonic development as well as in evolution are. of the nature ofciYil<lllliç~inter!l&t!Qil· They are based u po~ th~~ f~~t~·that the living organism is an open system, maintaining itself in, or approaching a steady state. Superposed are those regulations which we may call secondary, and which are controlled by fixed arrangements, especially of the feedback type. This state of affairs is a consequence of ageJ!(!r<!l prinçiple of 0 rg<:~.nization which may be calle<fp~ogr_es~~~V{! rneçl!<mization. At.fir~t, systems-biological, neurological, E~ychological or social-are governeci ~y dynamic ill~t~r;;t.c;!L211~ aLtheir components; later on, fixed arrangements and conditions of constraint are established which render the system and its parts more efficient, but also gradually diminish and eventually abolish its equipotentiality. Thus, dynamics is the braader aspect, since we can always arrive from general system laws to machinelike function by introducing suitable conditions of constraint, but the opposite is not possible. Causality and Teleology Another point I would like to mention 1s the change the The Meaning of General System Theory 45 scientific world picture has undergone in the past few decades. In the world view called mechanistic, which was born of classica! physics of the pineteenth century, the aimless play of the atoms, governed by the inexorable laws of causality, produced all phenomena in the world, inanimate, living, and mentaL No room was left for any directiveness, order, or telos. The world of the organisms appeared a product of chance, accumulated by the senseless play of random mutations and selection; the mental world as a curious and rather inconsequential epiphenomenon of material events. The only goal of science appeared to be analytica!, i.e., the splitting up of reality into ever smaller units and the isolation of individual causal trains. Thus, physical reality was split up into mass points or atoms, the living organism into cells, behavior into reflexes, perception into punctual sensations, etc. Correspondingly, causality was essentially one-way: one sun attracts one planet in Newtonian mechanics, one gene in the fertilized ovum produces such and such inherited character, one sort of bacterium produces this or that disease, mental elements are lined up, like the beads in a string of pearls, by the law of association. Remember Kant's famous table of the categories which attempts to systematize the fundamental notions of classical science: it is symptomatic that the notions of interaction and of organization were only spacefillers or did not appear at all. We may state as characteristic of modern science that this scheme of isolable units acting in one-way causality has proved to be insufficient. Hence the appearance, in all fields of science, of notions like wholeness, holistic, organismic, gestalt, etc., which all signify that, in the last resort, we must think in terms of systems of elements in mutual interaction. Similarly, notions of teleology and directiveness appeared to be outside the scope of science and to be the playground of mysterious, supernatural or anthropomorphic agencies; or else, a pseudoproblem, intrinsically alien to science, and merely a misplaced projection of the abserver's mind into a nature governed by purposeless laws. Nevertheless, these aspects exist, and you cannot conceive of a living organism, not to speak of behavior and human society, without taking into account what variously and rather loosely is called adaptiveness, purposiveness, goal-seeking and the like. 46 GENERAL SYSTEM THEORY It is characteristic of the present view that these aspects are taken seriously as a legitimate problem for science; moreover, we can well indicate models simulating such behavior. Two such models we have already mentioned. One is equifinality, the tendency towards a characteristic final state from different initia! states and in different ways, based upon dynamic interaction in an open system attaining a steady state; the second, feedback, the homeostatic maintenance of a characteristic state or the seeking of a goal, based upon circular causa! chains and mechanisms monitoring back information on deviations from the state to be maintained or the goal to be reached. A third model for adaptive behavior, a "design for a brain," was developed by Ashby, who incidentally started with the same mathematica! definitions and equations for a general system as were used by the present author. Both writers have developed their systems independently and, following different lines of interest, have arrived at different theorems and conclusions. Ashby's model for adaptiveness is, roughly, that of step functions defining a system, i.e., functions which, after a certain critica! value is passed, jump into a new family of differential equations. This means that, having passed a critica! state, the system starts off in a new way of behavior. Thus, by means of step functions, the system shows adaptive behavior by what the biologist would call trial and error: it tries different ways and means, and eventually setties down in a field where it no longer comes into conflict with critica! values of the environment. Such a system adapting itself by trial and error was actually constructed by Ashby as an electromagnetic machine, called the homeostat. I am not going to discuss the merits and shortcomings of these models of teleological or directed behavior. What should be stressed, however, is the fact that teleological behavior directed towards a characteristic final state or goal is not something off limits for natura! science and an anthropomorphic misconception of processes which, in themselves, are undirected and accidental. Rather it is a form of behavior which can well be defined in scientific terms and for which the necessary conditions and possibie mechanisms can be indicated. What Is Organization? Similar considerations apply to the concept of organization. The Meaning of General System Theory 47 Organization also was alien to the mechanistic world. The probIem did not appear in classica! physics, mechanics, electrodynamics, etc. Even more, the second principle of thermodynamics indicated destruction of order as the general direction of events. It is true that this is different in modern physics. An atom, a crystal, or a molecule are organizations, as Whitehead never failed to emphasize. In biology, organisms are, by definition, organized things. But although we have an enormous amount of data on biologica! organization, from biochemistry to cytology to histology and anatomy, we do not have a theory of biologica! organization, i.e., a conceptual model which permits explanation of the empirica! facts. Characteristic of organization, whether of a living organism or a society, are notions like those of wholeness, growth, differentiation, hierarchical order, dominance, control, competition, etc. Such notions do not appear in conventional physics. System theory is well capable of dealing with these matters. It is possible to define such notions within the mathematica! model of a system; moreover, in some respects, detailed theories can be developed which deduce, from general assumptions, the special cases. A good example is the theory of biologica! equilibria, cyclic fluctuations, etc., as initiated by Lotka, Volterra, Gause and others. It will certainly be found that Volterra's biologica! theory and the theory of quantitative economics are isomorphic in many respects. There are, however, many aspects of organizations which do not easily lend themselves to quantitative interpretation. This difficulty is not unknown in natura! science. Thus, the theory of biologica! equilibria or that of natura! selection are highly developed fields of mathematica! biology, and nobody doubts that they are legitimate, essentially correct, and an important part of the theory of evolution and of ecology. It is hard, however, to apply them in the field because the parameters chosen, such as selective value, rate of destruction and generation and the like, cannot easily be measured. So we have to content ourselves with an "explanation in principle," a qualitative argument which, however, may lead to interesting consequences. As an example of the application of general system theory to human society, we may quote a recent book by Boulding, entitled The Organizational Revolution. Boulding starts with a general model of organization and states what he calls Iron Laws which 48 GENERAL SYSTEM THEORY hold good for any organization. Such Iron Laws are, for example, the Malthusian law that the increase of a population is, in general, greater than that of its resources. Then there is a law of optimum size of organizations: the larger an organization grows, the langer is the way of communication and this, depending on the nature of the organization, acts as a limiting factor and does not allow an organization to grow beyoud a certain critical size. According to the law of instability, many organizations are not in a stabie equilibrium but show cyclic fiuctuations which result from the interaction of subsystems. This, incidentally, could probably be treated in terms of the Volterra theory, Volterra's socalled first law being that of periadie cycles in populations of two species, one of which feeds at the expense of the other. The important law of oligopoly states that, if there are competing organizations, the instability of their relations and hence the danger of friction and confiicts increases with the decrease of the number of those organizations. Thus, so long as they are relatively small and numerous, they muddie through in some way of coexistence. But if only a few or a competing pair are left, as is the case with the colossal polideal blocks of the present day, confiicts become devastating to the point of mutual destruction. The number of such general theorems for organization can easily be enlarged. They are well capable of being developed in a mathematica! way, as was actually done for certain aspects. General System Theory and the Unity of Science Let me close these remarks with a few words about the general implications of interdisciplinary theory. The integrative function of general system theory can perhaps be summarized as follows. So far, the unification of science has been seen in the reduction of all sciences to physics, the final resolution of all phenomena into physical events. From our point of view, unity of science gains a more realistic aspect. ."A un!tary (;C)~~C::C:E~i.Qn of the world may be based, not upon the possibly futile and certainly farfetched hope finally to reduce all levels of reality to the level of physics, but rather on the iso1llo:rphy of la"\\'s_ in different fi~Lcl§, Speaking in what has been called the "fg.rmal': mode, i.e., looking at the conceptual constructs of science, this means structural uniformities of the schemes we are The Meaning of General System Theory 49 applying. Speaking in "material" language, it means that the world, i.e., the total of observable events, shows structural uniformities, manifesting themselves by isomorphic traces of order in the different levels or realms. We come, then, to a conception which in contrast to reductionism, we may call E~E.~~iYi.ll!l· We cannot reduce the biologica!, behavioral, and social levels to the lowest level, that of the constructs and laws of physics. We can, however, find constructs and possibly laws within the individual levels. The world is, as Aldous Huxley once put it, like a Neapolitan ice cream cake where the levels-the physical, the biologica!, the social and the moral universe-represent the chocolate, strawberry, and vanilla layers. We cannot reduce strawberry to chocolate-the most we can say is that possibly in the last resort, all is vanilla, all mind or spirit. Th~ unifying principle is that we find organi,zationat aJileyels. The mechanistic world view, taking the play of physical particles as ultimate reality, found its expression in a civilization which glorifies physical technology that has led eventually to the catastrophes of our time. Possibly the model of the world as a great organization can help to reinforce the sense of reverence for the living which we have almast lost in the last sanguinary decades of human history. General System Theory in Education: The Production of Scientific Generalists After this sketchy outline of the meaning and aims of general system theory, let me try to answer the question of what it may contribute to integrative education. In order not to appear partisan, I give a few quotations from authors who were not themselves engaged in the development of general system theory. A few years ago, a paper, entitled "The Education of Scientific Generalists," was publisbed by a group of scientists including the engineer Bode, the sociologist Mosteller, the mathematician Tukey, and the biologist Winsor. The authors emphasized the "need for a simpler, more unilied approach to scientific problems." They wrote: We often hear that "one man can no langer cover a broad enough field" and that "there is too much narrow specializa- 50 GENERAL SYSTEM THEORY tion." ... We need a simpler, more unified approach to scientific problems, we need men who practice science-not a particular science, in a word, we need scientific generalists (Bode et al., 1949). The authors then make clear how and why generali~ts, are needed in fields such as physical chemistry, biophysics, the application of chemistry, physics, and rnathematics to medicine, and they continue: Any research group needs a generalist, whether it is an institutional group in a university or a foundation, or an industrial group .... In an engineering group, the generalist would naturally be concerned with system problems. These problems arise whenever parts are made into a balanced whole (Bode et al., 1949). In a symposium of the Foundation for Integrated Education, Professor Mather (1951) discussed "Integrative Studies for General Education." He stated: One of the criticisms of general education is based upon the fact that it may easily degenerate into the mere presentation of information picked up in as many fields of enquiry as there is time to survey during a semester or a year.... If you were to overhear several senior students talking, you might hear one of them say "our professors have stuffed us full, but what does it all mean?" ... More important is the search for basic concepts and underlying principles that may be valid throughout the entire body of knowledge. In answer to what these basic concepts may be, Mather states: Very similar general concepts have been independently developed by investigators who have been working in widely different fields. These correspondences are all the more significant because they are based upon totally different facts. The men who developed them were largely unaware of each other's work. They started with conflicting philosophies and yet have reached remarkably similar conclusions .... Thus conceived, [Mather concludes], integrative studies would prove to be an essential part of the quest for an understanding of reality. The Meaning of General System Theory 51 No comments seem to be necessary. Conventional education in physics, biology, psychology or the social sciences treats them as separate domains, the general trend being that increasingly smaller subdomains become separate sciences, and this process is repeated to the point where each specialty becomes a triflingly small field, unconnected with the rest. In contrast, the educational demands of training "Scientific Generalists" and of developing interdisciplinary "basic principles" are precisely those general system theory tries to fill. They are not a mere program or a pious wish since, as we have tried to show, such theoretica! structure is already in the process of development. In this sense, general system theory seems to be an important headway towards interdisciplinary synthesis and integrated education. Science and Society However, if we speak of education, we do not mean solely scientific values, i.e., communication and integration of facts. We also mean ethical values, contributing to the development of personality. Is there sarnething to be gained from the viewpoints we have discussed? This leads to the fundamental problem of the value of science in general and the behaviaral and social sciences in particular. An often-used argument about the value of science and its impact upon society and the welfare of mankind runs sarnething like this. Our knowledge of the laws of physics is excellent, and consequently our technological control of inanimate nature almost unlimited. Our knowledge of biologica! laws is not so far advanced, but suflicient to allow for a good amount of biologica! technology in modern medicine and applied biology. It has extended the life expectancy far beyond the limits allotted to human beings in earlier centuries or even decades. The application of the modern methods of scientific agriculture, husbandry, etc., would well suflice to sustain a human population far surpassing the present one of our planet. What is lacking, however, is knowledge of the laws of human society, and consequently a sociological technology. So the achievements of physics are put to use for ever more eflicient destruction; we have famines in vast parts of the world while harvests rot or are destroyed in other parts; war and indiscriminate annihilation of human life, 52 i GENERAL SYSTEM THEORY culture, and means of sustenance are the only way out of uncontrolled fertility and consequent overpopulation. They are the outcome of the fact that we know and control physical forces only too well, biologica! forces tolerably well, and social farces not at all. If, therefore, we would have a well-developed scie11ce of human society and a conesponding technology, it woufd he the way out of the chaos and impending destruction of our present world. This seems to he plausible enough and is, in fact, but a modern version of Plato's precept that only if the rulers are philosophers, humanity will he saved. There is, however, a catch in the argument. We have a fair idea what a scientifically controlled world would look like. In the best case, it would he like Aldous Huxley's Brave New World, in the worst, like Orwell's 1984. It is an empirica! fact that scientific achievements are put just as much, or even more, to destructive as constructive use. The sciences of human behavior and society are no exception. In fact, it is perhaps the greatest danger of the systems of modern totalitarianism that they are so alarmingly up-to-date not only in physical and biologica!, but also in psychological technology. The methods of mass suggestion, of the release of the instincts of the human beast, of conditioning and thought control are developed to highest efficacy; just because modern totalitarianism is so terrifically scientific, it makes the àbsolutism of former periods appear a dilettantish and comparatively harmless makeshift. Scientific control of society is no highway to Utopia. The Ultimate Precept: Man as the Individual We may, however, conceive of a scientific understanding of human society and its laws in a somewhat different and more modest way. Such knowledge can teach us not only what human behavior and society have in common with other organizations, but also what is their uniqueness. Here the main tenet will be: Man is not only a politica! anima!; he is, befare and above all, an individual. The real values of humanity are not those which it shares with biologica! entities, the function of an organism or a community of animals, but those which stem from the individual mind. Human society is not a community of ants or termites, governed by inherited instinct and controlled by the The Meaning of General System Theory 53 Iaws of the superordinate whole; it is based upon the achievements of the individual and is doomed if the individual is made a cog in the social machine. This, I believe, is the ultimate precept a theory of organization can give: not a manual for dictators of any denomination more efficiently to subjugate human beings by the scientific application of Iron Laws, but a warning that the Leviathan of organization must not swallow the individual without sealing its own inevitable doom. Some System Concepts 3 Same System Concepts in Elemen tary Mathematica! Consid eration The System Concept In dealing with complexes of "elements," three different kinds of distinction may be made-i.e., I. according to their number; 2. according to their species; 3. according to the relations of elements. The following simple graphical illustration may clarify this point (FIG. 3.1) with a and b symbolizing various c::>mplexes. a 0 0 0 0 ó 0 0 0 0 2) a 0 0 0 0 ó 0 0 0 • :Va o---o----o--.o i) b D Fig. 3.1. See text. In cases I and 2, the complex may be understood as the (cf. pp. 66ff.) sum of elements considered in isolation. Iu case 3, not only the elements should be known, but also the relations between them. Characterist ics of the first kind may be called summative, of the second kind constitutive. We can also say that summative characteristi cs of an element are those which are 0 55 the same within and outside the complex; they may therefore be obtained by means of summation of characteristi cs and behavior of elements as known in isolation. Constitutive characteristics are those which are dependent on the specific relations within the complex; for understandi ng such characteristi cs we therefore must know not only the parts, but also the relations. Physical characteristi cs of the first type are, for example, weight or molecular weight (sum of weights or atomie weights respectively), heat (considered as sum of movements of the molecules), etc. An example of the second kind are chemica! characteristi cs (e.g., isomerism, different characteristi cs of compounds with the same gross composition but different arrangement of radicals in the molecule). The meaning of the somewhat mystica! expression, "the whole is more than the sum of parts" is simply that constitutive characteristics are not explainable from the characteristi cs of isolated parts. The characteristi cs of the complex, therefore, compared to those of the elements, appear as "new" or "emergent." If, however, we know the total of parts contained in a system and the relations between them, the behavior of the system may be derived from the behavior of the parts. We can also say: While we can conceive of a sum as being composed gradually, a system as total of parts with its interrelation s has to he conceived of as being composed instantly. Physically, these statements are trivia!; they could become probiernatie and lead to confused conceptions in biology, psychology and sociology only because of a misinterpret ation of the mechanistic conception, the tendency being towards resolution of phenomena into independen t elements and causal chains, while interrelation s were bypassed. In rigarous developmen t, general system theory would be of an axiomatic nature; that is, from the notion of "system" and a suitable set of axioms propositions expressing system properties and principles would be deduced. The following consideratio ns are much more modest. They merely illustrate some system principles by formulation s which are simple and intuitively accessible, without attempt at mathematica ! rigor and generality. A system can be defined as a complex of interacting elements. Interaction means that elements, p, stand in relations, R, so that the behavior of an element p in R is different from its behavior 56 GENERAL SYSTEM THEORY in another relation, R'. If the behaviors in R and R' are not different, there is no interaction, and the elements behave independently with respect to the relations R and R'. A system can be defined mathematically in various ways. For illustration, we choose a system of simultaneous differential equ~­ tions. Denoting some measure of elements, p, (i = 1, 2, .. :n), by Q" these, for a finite number of elements and in the simplest case, will be of the form: (3.1) 57 Some System Concepts of the system ("hysteresis" in a broad sense); consideration of this would make the system into integro-differential equations as discussed by Volterra (1931; cf. also d'Ancona, 1939) and Donnan (1937). Introduetion of such equations would have a definite meaning: The system under consideration would be not only a spatial but also a temporal whole. Notwithstanding these restrictions, equation (3.1) can be used for discussing several general system properties. Although nothing is said about the nature of the measures Q, or the functions /,-i.e., about the relations or interactions within the systemcertain general principles can be deduced. There is a condition of stationary state, characterized by disappearance of the changes dQj dt ]! = fz = · · ·fn = 0 Change of any measure Q, therefore is a function of all Q's, from Q1 to Qn; conversely, change of any Q, entails change of all other measures and of the system as a whole. Systems of equations of this kind are found in many fields and represent a general principle of kinetics. For example, in Simultankinetik as developed by Skrabal (1944, 1949), this is the general expression of the law of mass action. The same system was used by Lotka (1925) in a broad sense, especially with respect to demograpbic problems. The equations for biocoenotic systems, as developed by Volterra, Lotka, D'Ancona, Gause and others, are special cases of equation (3.1). So are the equations used by Spiegelman (1945) for kinetics of cellular processes and the theory of competition within an organism. G. Werner (1947) has stated a similar though somewhat more general system (considering the system as continuous, and using therefore partial differential equations with respect to x) y) z, and t) as the basic law of pharmacodynamics from which the various laws of drug action can be derived by introducing the relevant special conditions. Such a definition of "system" is, of course, by no means generaL It abstracts from spatial and temporal conditions, which would be expressed by partial differential equations. It also abstracts from a possible dependenee of happenings on the previous history (3.2) By equating to zero we obtain n equations for n variables, and by solving them obtain the values: Q1 = Q1* Qz = Qz* 0 • 0 ••••• Qa = Qn* } (3.3) These values are constants, since in the system, as presupposed, the changes disappear. In genera!, there will be a number of stationary states, some stable, some instable. We may introduce new variables: Q; = Q;*- Q/ (3.4) and reformulate system (3.1): dQ/ dt = j 1 dQ>2 dt =j 1 I (Q1,I Qz,I ... Q n I) I (Q1,I Q z,I ... Qn I) 2 dQ>nl = j n dt I (3.5) (Q1,I Q z,I ... Qn I) Let us assume that the system can be developed in Taylor series: 58 GENERAL SYSTEM THEORY 59 Same System Concepts For illustration, consider the simplest case, n consisting of two kinds of elements: 2, a system (3.9} (3.6) dQn' = ani Qt' + an2 Q2 1 + ... dt 1 1 ann Qn' + anll Q/ 2 + an12 Q1 Q2 + an22 Q2 12 Again provided that the functions can he developed into Taylor series, the solution is: + · ·· QI = QI * - Gne:>.It - GI2eXzt - A general solution of this system of equations is: Qt' Q2' = = Gn e:>.It G21 e' 11 •••••••••• Qn' = 0 + G12 e' 21 + ... G1a eXnt + Gn1 e2hit + . . . } + G22 e' 21 + ... Gzn eXnt + G211 e2hlt + ... ••••••••••••••• Gnl e' 11 + Gn2 e' 21 0 Qz with (3.7) ••••••••••••••••••• + ... Gnn eXnt + Gnn e where the G are constants and the teristic equation: À 2 ' 11 + ... f1 = Qz * Gine2X1! - ... } (3 .10} - G21e' 11 - Gzze' 21 - Gzne 2' 11 - ... Q1 *, Q2 * as stationary va1ues of Qv Q2 , obtained by setting = f 2 = 0; the G's integration constants; and the of the characteristic equation: the roots of the charac- À 's roots 0, or developed: 0 (an (3.8) 'A=~ ±~-n+(~y, ann- À The roots À may he real or imaginary. By inspeetion of equations (3.7) we find that if all À are real and negative (or, if complex, negative in their real parts), Q,', with increasing time, approach 0 because e-ro = 0; since, however, according to (3.5) Q, Q,* - Q,', the Q, thereby obtain the stationary values Q,*. In this case the equilibrium is stable, since in a suflident period of time the system comes as close to the stationary state as possible. However, if one of the À is positive or 0, the equilibrium is unstable. If finally some À are positive and complex, the system contains periodic terms since the exponential function for complex exponents takes the form: = eCa-ib)t = eat (cos bt - i sin bt). In this case there will he periadie fluctuations, which generally are damped. À) (a22 - À) - a12a21 = 0, 'A 2 - 'AC+ D = 0, with In the case: C < 0, D > 0, E = C2 - 4D > 0, both solutions of the characteristic equation are negative. Therefore a node is given; the system will approach a stabie stationary state (Q1 *, Q2 *) as e-ro = 0, and therefore the second and following terms continually decrease (FIG. 3.2). In the case: C < 0, D > 0, E = C2 - 4D < 0, both solutions of the characteri§'tic equation are complex with negative real part. In this case we have a loop, and point (Qv Q2) tends towards (Q1 *, Q 2 *) descrihing a spiral curve. 60 GENERAL SYSTEM THEORY 61 Some System Concepts which may he developed into a Taylor series: ~node (3.12) gL..._ __:.;~--,... This series does not contain an absolute term in the case in which there is no "spontaneous generation" of elements. Then dQ/ dt must disappear for Q = 0, which is possible only if the absolute term is equal to zero. The simplest possibility is realized when we retain only the first term of the series: dQ dt This signifies that the growth of the system is directly proportional to the number of elements present. Depending on whether the constant a 1 is positive or negative, the growth of the system is positive or negative, and the system increases or decreases. The solution is: Fig. 3.2. See text. In the case: C (3.13) = atQ, = 0, D > 0, E < 0, both solutions are imaginary, therefore the solution contains periodic terms; there will he oscillations or cycles around the stationary values. Point (Qv Q2 ) describes a closed curve around (3.14) Q0 signifying the number of elements at t = 0. This is the exponential law (FIG. 3.3) found in many fields. (Qt*, Q2*). In the case: C > 0, D < 0, E > 0, both solutions are positive, and there is no stationary- state. Growth Equations of this type are found in a variety of fields, and we can use system (3.1) to illustrate the formal identity of system laws in various realms, in other words, to demonstrate the existence of a general system theory. This may he shown for the simplest case-i.e., the system consisting of elements of only one kind. Then the system of equations is reduced to the single equation: ~7 =J(Q), t b a Fig. 3.3. Exponential curves. (3.11) 62 GENERAL SYSTEM THEORY In mathematics, the exponential law is called the "law of natura! growth," and with (a 1 > 0) is valid for the growth of capita! by compound interest. Biologically, it applies to the individual growth of certain bacteria and animals. Sociologically, it is valid for the unrestricted growth of plant or animal populations, in the simplest case for the increase of bacteria when each individual divides into two, these into four, etc. In social science, it is called the law of Malthus and signifies the unlimited growth of a population, whose birth rate is higher than its death rate. It also describes the growth of human knowledge as measured by the number of textbook pages devoted to scientific discoveries, or the number of publications on drasophila (Hersh, 1942). With negative constant (a 1 < 0), the exponential law applies to radioactive decay, to the decomposition of a chemica! compound in monomolecular reaction, to the killing of bacteria by rays or poison, the loss of body substance by hunger in a multicellular organism, the rate of extinction of a population in which the death rate is higher than the birth rate, etc. Going back to equation (3.12) and retaining two terms, we have: (3.15) A salution of this equation is: 63 Some System Concepts Q Fig. 3.4. Logistic curve. the basis of experience, but also in a purely formal way. The equations discussed signify no more than th~t the rather gene~al system of equation (3.1), its developme~t mto a :raylor senes and suitable conditions have been apphed. In th1s sense such laws are "a priori," independent from their physical, chemica!, biologica!, sociological, etc., interpretation. In other words, th1s shows the existence of a general system theory which deals with formal characteristics of systems, concrete facts appearing as their special applications by defining variables and parameters. In still other terms, such examples show a formal uniformity of nature. Competition (3.16) Keeping the secoud term has an important consequence. The simple exponential (3.14) shows an infinite increase; taking into account the secoud term, we obtain a curve which is sigmoid and attains a limiting value. This curve is the so-called logistic curve (FIG. 3.4), and is also of wide application. In chemistry, this is the curve of an autocatalytical reaction, i.e., a reaction, in which the reaction product obtained accelerates its own production. In sociology, it is the law of Verhulst (1838) descrihing the growth of human populations with limited resources. Mathematically trivia! as these examples are, they illustrate a point of interest for the present consideration, namely the fact that certain laws of nature can be arrived at not only on Our system of equations may also indicate competition between parts. . The simplest possible case is, again, that all coeffiCients (a 1,."i) = 0, - i.e., that the increase in each element depends only on this element itself. Then we have, for two elements: dQl dt = dQ2 dt = a1Q1 a2Q2 } (3.17) or Q1 = c1ealt Q2 = C2ea2t } (3.18) 64 GENERAL SYSTEM THEORY Eliminating time, we obtain: t = In Q1 - In c1 = In Qz - In cz ' {3.19) of such simplicity) is explained by equation (3.22). According to this equation, it can he interpreted as a result of a process of distribution. Take Q2 for the whole organism; then equation (3.22) states that the organ Q 1 takes, from the increase resulting from the metabolism of the total organism ( dJtz) , a share which and {3.20) with 65 Same System Cancepts a = ar/ az, b = er/ Cza. This is the equation known in biology as the allametrie equatian. In this discussion, the simplest form of growth of the parts -viz., the exponential-has been assumed (3.17 and 3.18). The allametrie relation holds, however, also for somewhat more complicated cases, such as growth according to the parabola, the logistic, the Gompertz function, either strictly or as an approximation (Lumer, 1937). The allametrie equation applies to a wide range of morphological, biochemical, physiological and phylogenetic data. It means that a certain characteristic, Qv can he expressed as a power function of another characteristic, Q2 • Take, for instance, morphogenesis. Then the length or weight of a certain organ, Qv is, in genera!, an allametrie function of the size of another organ, or of the total length or weight of the organism in question, Q2 • The meaning of this becomes clear if we write equations (3.17) in a slightly different form: dQ1 1 . dQz 1 _ -·-.-·--a, dt Q1 dt Qz {3.21) dQ1 Q1 dQz -=a·-·dt Qz dt {3.22) or Equation (3.21) states that the relative growth rates (i.e., increase calculated as a percentage of actual size) of the parts under consideration, Q 1 and Q2 , stand in a constant proportion throughout life, or during a life cycle for which the allametrie equation holds. This rather astonishing relation (because of the immense complexity of growth processes it would seem, at first, unlikely that the growth of parts is governed by an algebraic equation is proportional to its actual proportion to the latter (~~). rJ. is a partition coefficient indicating the capacity of the organ to seize its share. If a 1 > a 2-i.e., if the growth intensity of Q1 is greater than that of Q2 -then a = -aza1 > 1; t h e organ captures more than other parts; it grows therefore more rapidly than these or with positive allometry. Conversely, if a 1 < a 2 -i.e., rJ. > 1-the organ grows more slowly, or shows negative allometry. Similarly, the allometric equation applies to biochemica! changes in the organism, and to physiological functions. For instance, basal metabolism increases, in wide groups of animals, with rJ. = 2f3, with respect to body weight if growing animals of the same species, or animals of related species, are compared; this means that basal metabolism is, in genera!, a surface function of body weight. In certain cases, such as insect larvae and snails, rJ. = 1, i.e. basal metabolism is proportional to weight itself. In sociology, the expression in question is Pareto's law (1897) of the distribution of income within a nation, whereby Q1 = bQ2a, with Q1 = number of individuals gaining a certain income, Q2 = amount of the income, and b and rJ. constants. The explanation is similar to that given above, substituting for "increase of the total organism" the national income, and for "distribution constant" the economie abilities of the individuals concerned. The situation becomes more complex if interactions between the parts of the system are assumed-i.e., if ai"''~ 0. Then we come to systems of equations such as those studied by Volterra (1931) for competition among species, and, correspondingly, by Spiegelman (1945) for competition within an organism. Since these cases are fully discussed in the literature we shall not enter into a detailed discussion. Only one or two points of general interest may be mentioned. 66 GENERAL SYSTEM THEORY It is an interesting consequence that, in Volterra's equations, competition of two species for the same resources is, in a way, more fatal than a predator-prey relation-i.e., partial annihilation of one species by the other. Competition eventually leads to the extermination of the species with the smaller growth capacity; a predator-prey relation only leads to periadie asciilation of the numbers of the species concerned around a mean value. These relations have been stated for biocoenotic systems, but it may well be that they have also sociological implications. Another point of philosophic~l interest should be mentioned. If we are speaking of "systems," we mean "wholes" or "unities." Then it seems paradoxkal that, with respect to a whole, the concept of competition between its parts is introduced. In fact, however, these apparently COntradietory statements both belang to the essentials of systems. Every whole is based upon the competition of its elements, and presupposes the "struggle between parts" (Roux). The latter is a general principle of organization in simple physico-chemical systems as well as in organisms and social units, and it is, in the last resort, an expression of the coincidentia oppositorum that reality presents. Wholeness) Sum) Mechanization) Centralization The concepts just indicated have often been considered to describe characteristics only of living beings, or even to be a proof of vitalism. In actual fact they are formal properties of systems. (I) Let us assume again that the equations (3.1) can be developed into Taylor series: We see that any change in some quantity, Qv is a function of the quantities of all elements, Q1 to Q". On the other hand, a change in a certain Q, causes a change in all other elements and in the total system. The system therefore behaves as a whole, the changes in every element depending on all the others. (2) Let the coeffi.cients of the variables Q3 (j ~ i) now become zero. The system of equations degenerates into: 67 Some System Concepts dQi - dt = ai1Qi + ail1Qi + ... 2 (3.24) This means that a change in each element depends only on that element itself. Each element can therefore be considered independent of the others. The variation of the total complex is the (physical) sum of the variations of its elements. We may call such behavior physical summativity ar independence. We may define summativity by saying that a complex can be built up, step by step, by putting tagether the first separate elements; conversely, the characteristics of the complex can be analyzed completely into those of the separate elements. This is true for those complexes which we may call "heaps," such as a heap of bricks or odds and ends, or for mechanica! farces, acting according to the parallelogram of farces. It does not apply to those systems which were called Gestalten in German. Take the most simple example: three dectrical conductors have a certain charge which can be measured in each conductor separately. But if they are connected by wires, the charge in each conductor depends on the total constellation, and is different from its charge when insulated. Though this is trivial from the viewpoint of physics, it is still necessary to emphasize the non-summative character of physical and biologica! systems because the methodological attitude· has been, and is yet to a large extent, determined by the mechanistic program (von Bertalanffy, 1949a, 1960). In Lord Russell's book (1948), we find a rather astonishing rejection of the "concept of organism." This concept states, according to Russell, that the laws governing the behavior of the parts can be stated only by consiclering the place of the parts in the whole. Russell rejects this view. He uses the example of an eye, the function of which as a light receptor can be understood perfectly well if the eye is isolated and if only the internal physico-chemical reactions, and the incoming stimuli and outgoing nerve impulses, are taken into account. "Scientific progress has been made by analysis and artificial isolation.... It is therefore in any case prudent to adopt the mechanistic view as a working hypothesis, to be abandoned only where there is clear evidence against it. As regards biologica! phenomena, such evidence, so far, is entirely absent." It is true that the principles of summativity are applicable to the living 68 GENERAL SYSTEM THEORY organism to a certain extent. The beat of a heart, the twitch of a nerve-muscle preparation, the action potentials in a nerve are much the same if studied in isolation or within the organism as a whole. This applies to those phenomena we shall define later as occurring in highly "mechanized" partial systems. But Russell's statement is profoundly untrue with respect exactly to the basic and primary biologica! phenomena. If you take any realm of biologica! phenomena, whether embryonic development, metaboIism, growth, activity of the nervous system, biocoenoses, etc., you will always find that the behavior of an element is different within the system from what it is in isolation. You cannot sum up the behavior of the whole from the isolated parts, and you have to take into account the relations between the various subordinated systems and the systems which are super-ordinated to them in order to understand the behavior of the parts. Analysis and artificial isolation are useful, but in no way sufficient, methods of biologica! experimentation and theory. (3) Summativity in the mathematica[ sense means that the change in the total system obeys an equation of the same form as the equations for the parts. This is possible only when the functions on the right side of the equation contain linear terros only; a trivia! case. (4) There is a further case which appears to be unusual in physical systems but is common and basic in biologica!, psychological and sociological systems. This case is that in which the interactions between the elements decrease with time. In terros of our basic model equation (3.1), this means that the coefficients of the Q, are not constant, but decrease with time. The simplest case will be: lim t a;j = 0 --t ro (3.25) In this case the system passes from a state of wholeness to a state of independenee of the elements. The primary state is that of a unitary system which splits up gradually into independent causa! chains. We may call this progressive segregation. As a rule, the organization of physical wholes, such as atoms, molecules, or crystals, results from the union of pre-existing elements. In contrast, the organization of biologica! wholes is built up by differentiation of an original whole which segregates Same System Concepts 69 into parts. An example is determination in embryonic development, when the germ passes from a state of equipotentiality to a state where it behaves like a mosaic or sum of regions which develop independently into definite organs. The same is true in the development and evolution of the nervous system and of behavior starting with actions of the whole body or of large regions and passing to the establishment of definite centers and Iocalized reflex arcs, and for many other biologica! phenomena. The reason for the predominanee of segregation in. living nature seems to be that segregation into subordinate partial systems implies an increase of complexity in the system. Such transition towards higher order presupposes a supply of energy, and energy is delivered continuously into the system only if the latter is an open system, taking energy from its environment. We shall come back to this question later on. In the state of wholeness, a disturbance of the system leads to the introduetion of a new state of equilibrium. If, however, the system is split up into individual causa! chains, these go on independently. Increasing mechanization means increasing determination of elements to functions only dependent on themselves, and consequent loss of regulability which rests in the system as a whole, owing to the interrelations present. The smaller the interaction coefficients become, the more the respective terros Q, can be neglected, and the more "machine-Iike" is the system-i.e., like a sum of independent parts. This fact, which may be termed "progressive mechanization," plays an important role in biology. Primary, it appears, is behavior resulting from interaction within the system; secondarily, determination of the elements on actions dependent only on these elements, transition from behavior as a whole to summative behavior takes place. Examples are found in embryonic development, where originally the performance of each region depends on its position within the whole so that regulation following arbitrary disturbance is possible; later on, the embryonic regions are determined for one single performance-e.g., development of a certain organ. In the nervous system, similarly, certain parts become irreplaceable centers for certain-e.g., reflex-performances. Mechanization, however, is never complete in the biologica! realm; even though the organism is partly mechanized, it still remains a unitary system; this is the basis of regulation and of 70 GENERAL SYSTEM THEORY the interaction with changing demands of the environment. Similar considerations apply to social structures. In a primitive community every memher can perform almost anything expected in its conneetion with the whole; in a highly differentiated community, each memher is determined for a certain performance, or complex of performances. The extreme case is reached in certain insect communities, where the individuals are, so to speak, transformed into machines determined for certain performances. The determination of individuals into workers or soldiers in some ant communities by way of nutritional differences at certain stages amazingly resembles ontogenetic determination of germinal regions to a certain developmental fate. In this contrast between wholeness and sum lies the tragical tension in any biological, psychological and sociological evolution. Progress is possible only by passing from a state of undifferentiated wholeness to differentiation of parts. This implies, however, that the parts become fixed with respect to a certain action. Therefore progressive segregation also means progressive mechanization. Progressive mechanization, however, implies Ioss of regulability. As long as a system is a unitary whole, a disturbanee will he foliowed by the attainment of a new stationary state, due to the interactions within the system. The system is self.regulating. If, however, the system is split up into independent causa! chains, regulability disappears. The partial processes will go on irrespective of each other. This is the behavior we find, for example, in embryonic development, determination going hand in hand with decrease of regulability. Progress is possible only by subdivision of an initially unitary action into actions of specialized parts. This, however, means at the same time impoverishment, loss of performances still possible in the undetermined state. The more parts are specialized in a certain way, the more they are irreplaceable, and Ioss of parts may lead to the breakdown of the total system. To speak Aristotelian language, every evolution, by unfolding some potentiality, nipsin the bud many other possibilities. We may find this in embryonic development as well as in phylogenetic specializ.ation, or in specialization in science or daily life (von Bertalanffy, 1949a, 1960, pp. 42 ff.). Behavior as a whole and summative behavior, unitary and elementalistic conceptions, are usually regarded as being an- Same System Concepts 71 titheses. But it is frequently found that there is no opposition between them, but gradual transition from behavior as a whole to summative behavior. (5) Connected with this is yet another principle. Suppose that the coefficients of one element, p., are large in all equations while the coefficients of the other elements are considerably smaller or even equal to zero. In this case the system may look like this: (3.26) if for simplicity we write the linear memhers only. Then relationships are given which can he expressed in several ways. We may call the element P. a teading part, or say that the system is centered around p •. If the coefficients a,. of P. in some or all equations are large while the coefficients in the equation of P. itself are small, a small change in P. will cause a considerable change in the total system. P. may he then called a trigger. A small change in P. will he "amplified" in the total system. From the energetic viewpoint, in this case we do not find "conservation causality" (Erhaltungskausalität) where the principle "causa aequat effectum" holds, but "instigation causality" (Anstosskausalität) (Mittasch, 1948), an energetically insignificant change in p. causing a considerable change in the total system. The principle of centralization is especially important in the biologica! realm. Progressive segregation is often connected with progressive centralization, the expression of which is the timedependent evolution of a leading part-i.e., a combination of the schemes (3.25) and (3.26). At the same time, the principle of progressive centralization is that of progressive individualization. An "individual" can he defined as a centralized system. Strictly speaking this is, in the biologica! realm, a limiting case, only approached ontogenetically and phylogenetically, the organism growing through progressive centralization more and more unified and "more indivisible." 72 GENERAL SYSTEM THEORY All these facts may be observed in a variety of systems. Nicolai Hartmann even demands centralization for every "dynamic structure." He therefore recognizes only a few kinds of structures, in the physical realm, those of smallest dimensions (the atom as a planetary system of electrous around a nucleus) and of large dimensions (planetary systems centralized by a sun). From the biologica! viewpoint, we would emphasize progressive mechanization and centralization. The primitive state is that where the behavior of the system results from the interactions of equipotential parts; progressively, subordination under dominant parts takes place. In embryology, for example, these are called organizers (Spemann); in the central nervous system, parts first are largely equipotential as in the diffuse nervous systems of lower animals; later on subordination to leading centers of the nervous system takes place. Thus, similar to progressive mechanization a principle of progressive centralization is found in biology, symbolized by timedependent formation of leading parts-i.e., a combination of schemes (3.25) and (3.26). This viewpoint casts light on an important, but not easily definable concept, that of the individual. "Individual" stands for "indivisible." Is it, however, possible to call a planarian or hydra an "individual" if these animals may be cut up into any uurober of pieces and still regenerate a complete animal? Double-headed hydras cin easily be made by experiment; then the two heads may fight for a daphnia, although it is immaterial on which side the prey is caught; in any case it is swallowed to reach the common stomach where it is digested to the benefit of all parts. Even in higher organisms individuality is doubtful, at least in early development. Not only each half of a divided sea urchin embryo, but also the halves of a salamander embryo develop into complete animals; identical twins in man are, so to speak, the result of a Driesch experiment carried out by nature. Similar considerations apply to the behavior of animals: in lower animals tropotaxis may take place in the way of antagonistic action of the two halves of the body if they are appropriately exposed to stimuli; ascending the evolutionary scale, increasing centralization appears; behavior is not a resultant of partial mechanisms of equal rank but dominated and unified by the highest centers of the nervous system (cf. von Bertalanffy, 1937; pp. 13lff., l39ff.). Same System Concepts 73 Thus strictly speaking, biologica! individuality does not exist, but only progressive individualization in evolution and development resulting from progressive centralization, certain parts gaining a dominant role and so determining behavior of the whole. Hence the principle of progressive centralization also constitutes progressive individualization. An individual is to be defined as a centered system, this actually being a limiting case approached in development and evolution so that the organism becomes more unified and "indivisible" (cf. von Bertalanffy, 1932; pp. 269ff.). In the psychological field, a similar phenomenon is the "centeredness" of gestalten, e.g., in perception; such centeredness appears necessary so that a psychic gestalt distinguishes itself from others. In contrast to the "principle of ranklessness" of association psychology, Metzger states (1941, p. 184) that "every psychic formation, object, process, experience down to the simplest gestalten of perception, exhibits a certain weight distribution and centralization; there is rank order, sometimes a derivative relationship, among its parts, loci, properties." The same applies again in the sociological realm: an amorphous mob has no "individuality"; in order that a social structure be distinguished from others, grouping around certain individuals is necessary. For this very reason, a biocoenosis Iike a lake or a forest is not an "organism," because an individual organism always is centered to a more or less large extent. Neglect of the principle of progressive mechanization and centralization has frequently led to pseudoproblems, beçause only the limiting cases of independent and summative elements, or else complete interaction of equivalent elements were recognized, not the biologically important intermediates. This plays a role with respect to the probieros of "gene" and "nervous center." Older genetics (not modern genetics any more) was inclined to consider the hereditary substance as a sum of corpuscular units determining individual characteristics or organs; the objection is obvious that a sum of macromolecules cannot produce the organized wholeness of the organism. The correct answer is that the genome as a whole produces the organism as a whole, certain genes, however, preeminently determining the direction of deve1opment of certain characters-i.e., acting as "leading parts." This is expressed in the insight that every hereditary trait is co-determined by many, perhaps all genes, and that every gene 74 GENERAL SYSTEM THEORY influences not one single trait but many, and possibly the total organism (polygeny of characteristics and polypheny of genes). In a similar way, in the function of the nervous system there was apparently the alternative of consiclering it either as a sum of mechanisms for the individual functions, or else as a homogeneous nervous net. Here, too, the correct conception is that any function ultimately results from interaction of all parts, but that certain parts of the central nervous system influence it decisively and therefore can be denoted as "centers" for that function. (6) A more general (but less visualizable) fotmulation of what was said follows. If the change of Q, be any function F, of the Q, and their derivates in the space coordinates we have: (2) If oF; oQ; -- 0' x· .J.J. ,..... ·. "'llld epend ence" ; 75 Some System Concepts (8) An important distinction is that of closed and open systems. This will be discussed in Chàpters 6-8. Finality As we have seen, systems of equations of the type considered may have three different kinds of solution. The system in question may asymptotically attain a stabie stationary state with increasing time; it may never attain such state; or there may be periodic oscillations. In case the system approaches a stationary state, its variation can be expressed not only in terms of the actual conditions but also in terms of the distance from the stationary state. If Q;* are the solutions for the stationary state, new variables: Q; = Q;*- Q/ can be introduced so that (4) If oF; = j(t), lim oF; = 0: "progressive mechanization"; t~ co oQ; oQ; oF; oQ, part." (5) If oF; oF; . = 0 : Q, is the "dominant ;é s, or even: oQ; oQ; » -, J (7) The system concept as outlined asks for an important addition. Systems are frequently structured in a way so that their individual memhers again are systems of the next lower level. Hence each of the elements denoted by Qv Q 2 ••• Q,. is a system of elements 0 ,v 0,2 ••• 0 ,,., in which each system 0 is again definable by equations similar to those of (3.1): Such superposition of systems is called hierarchical order. For its individual levels, again the aspects of wholeness and summativity, progressive mechanization, centralization, finality, etc., apply. Such hierarchical structure and combination into systems of ever higher order, is characteristic of reality as a whole and of fundamental importance especially in biology, psychology and sociology. (3.27) We may express this as follows. In case a system approaches a stationary state, changes occurring may be expressed not only in terms of actual conditions, but also in terms of the distance from the equilibrium state; the system seems to "aim" at an equilibrium to be reached only in the future. Or else, the happenings may be expressed as depending on a future final state. It has been maintained for a long time that certain formulations in physics have an apparently finalistic character. This applies in two respects. Such teleology was especially seen in the minimum principles of mechanics. Already Maupertuis considered his minimum principle as proof that the world, where among many virtual movements the one leading to maximum effect with minimum effort is realized, is the "best of all worlds" and work of a purposeful creator. Euler made a similar remark: "Since the construction of the whole world is the most eminent and since it originated from the wisest creator, nothing is found in the world which would not show a maximum or minimum characteristic." A similar teleological aspect can be seen in Le Chatelier's principle in physical chemistry and in Lenz's rule of electricity. All these principles express that in case of disturbance, 76 GENERAL SYSTEM THEORY the system develops farces which counteract the disturbance and restare a state of equilibrium; they are derivations from the principle of minimum effect. Principles homologous to the principle of minimum action in mechanics can be construed for any type of system; thus Volterra (cf. d'Ancona, 1939; pp. 98ff.) has shown that a population dynamics homologous to mechanica! dynamics can be developed where a similar principle of minimum action appears. The conceptual error of an anthropomorphic interpretation is easily seen. The principle of minimum action and related prin" ciples simply result from the fact that, if a system reaches a state of equilibrium, the derivatives become zero; this implies that certain variables reach an extremum, minimum or maximum; only when these variables are denoted by anthropomorphic terms like effect, constraint, work, etc., an apparent teleology in physical processes emerges in physical action (cf. Bavink, 1944). Finality can be spoken of also in the sense of dependenee on the future. As can be seen from equation (3.27), happenings can, in fact, be considered and described as being determined not by actual conditions, but also by the final state to be reached. Secondly, this formulation is of a general nature; it does not only apply to mechanics, but to any kind of system. Thirdly, the question was frequently misinterpreted in biology and philosophy, so that clarification is fairly important. Let us take, for a change, a growth equation formulated by the author (von Bertalanffy, 1934 and elsewhere). The equation is: l = l*- (l*- l0e-kt) (cf. pp. l7lff.), where l represents the length of the animal at time t, l* the final length, 10 the initial length, and k a constant. This looks as if the length l of the animal at time t were determined by the final value l* which will be reached only after infinitely long time. However, the final state (l*) simply is an extremum condition obtained by equating the differential quotient to zero so that t disappears. In order to do so, we must first know the differential equation by which the process is actually determined. This differential equation is: ~ = E - kt and states that growth 1s determined by a counteraction of processes of anabolism and catabolism, with parameters E and k respectively. In this equation, the process at time t is determined only by the actual conditions and no Same System Concepts 77 future state appears. By equating to zero, l* is defined by Ejk. The "teleological" final-value formula therefore is only a transformation of the differential equation indicating actual conditions. In other words, the directedness of the process towards a final state is not a process differing from causality, but another expression of it. The final state to be reached in future is not a "vis a fronte" mysteriously attracting the system, but only another expression for causal "vires a tergo." For this reason, physics makes ample use of such final-value formulas because the fact is mathematically clear and nobody attributes an anthropomorphic "foresight" of the goal to a physical system. Biologists, on the other hand, often regarded such formulas as somewhat uncanny, either fearing a. hidden vitalism, or else considering such teleology or goal-directedness as "proof" for vitalism. For with respect to animate rather than to inanimate nature, we tend to campare finalistic processes with human foresight of the goal; while, in fact, we are dealing with obvious, even mathematically trivial relations. This matter was frequently misinterpreted even by philosophers. From E. von Hartmann to modern authors like Kafka (1922) and myself, finality was defined as the reverse of causality, as dependenee of the process on future instead of past conditions. This was frequently objected to because, according to this conception, a state A would depend on a state B in the future, an existent on a non-existent (e.g., Gross 1930; similarly Schlick). As the above shows, this formulation does not mean an inconceivable "action" of a not existent future, but merely a sametimes useful formulation of a fact which can be expressed in terms of causality. Types of Finality No detailed discussion of the problem of finality is intended here, but enumeration of several types may be useful. Thus we can distinguish: (I) Static teleology or fitness, meaning that an arrangement seems to be useful for a certain "purpose." Thus a fur coat is fit to keep the body warm, and so are hairs, feathers, or layers of fat in animals. Thorns may proteet plants against grazing cattle, or imitative colorations and mimicries 78 GENERAL SYSTEM THEORY may be advantageous to proteet animals against enemies. (2) Dynamic teleology, meaning a directiveness of processes. Here different phenomena can be distinguished which are often confused: (i) Direction of events towards a final state which can be expressed as if the present behavior were dependent on that final state. Every system which attains a timeindependent condition behaves in this way. (ii) Directiveness based upon structure, meaning that an arrangement of structures leads the process in such way that a certain result is achieved. This is true, of course, of the function of man-made machines yielding products or performances as desired. In living nature we find a structural order of processes that in its complication widely surpasses all man-made machines. Such order is found from the function of macroscopie organs, such as the eye as a sort of camera or the heart as a pump, to microscopie cell structures responsible for metabolism, secretion, excitability, heredity and so forth. Whilst man-made machines work in such a way as to yield certain products and performances, for example, fabrication of airplanes or moving a railway train, the order of process in living systems is such as to maintain the system itself. An important part of these processes is represented by borneostasis (Canon)-i.e., those processes through which the material and energetica! situation of the organism is maintained constant. Examples are the mechanisms of thermoregulation, of maintenance of osmotic pressure, of pH, of salt concentration, the regulation of posture and so forth. These regulations are governed, in a wide extent, by feedback mechanisms. Feedback means that from the output of a machine a certain amount is monitored back, as "information," to the input so as to regulate the latter and thus to stabilize or direct the action of the machine. Mechanisms of this kind are well known in technology, as, for instance, the governor of the steam-engine, self-steering missiles and other "servomechanisms." Feedback mechanisms appear to be responsible for a large part of organic regulations and phenomena of homeostasis, as recently emphasized by Cybernetics (Frank et al., 1948; Wiener, 1948). Same System Concepts 79 (iii) There is, however, yet another basis for organic regulations. This is equifinality-i.e., the fact that the same final state can be reached from different initia! conditions and in different ways. This is found to be the case in open systems, insofar as they attain a steady state. It appears that equifinality is responsible for the primary regulability of organic systems-i.e., for all those regulations which cannot be based upon predetermined structures or mechanisms, but on the contrary, exclude such mechanisms and were regarded therefore as arguments for vitalism. (iv) Finally, there is true finality or purposiveness, meaning that the actual behavior is determined by the foresight of the goal. This is the original Aristotelian concept. It presupposes that the future goal is already present in thought, and directs the present action. True purposiveness is characteristic of human behavior, and it is connected with the evolution of the symbolism of language and concepts (von Bertalanffy, 1948a, 1965). The confusion of these different types of finality is one of the factors responsible for the confusion occurring in epistemology and theoretica! biology. In the field of man-made things, fitness (a) and teleological working of machines (b, ii) are, of course, due to a planning intelligence (b, iv ). Fitness in organic structures (a) can presumably be explained by the causal play of random mutations and natmal selection. This explanation is, however, much less plausible for the origin of the very complicated organic mechanisms and feedback systems (b, ii). Vitalism is essentially the attempt to explain organic directiveness (b, ii and iii) by means of intelligence in foresight of the goal (b, iv). This leads, methodologically, beyond the limits of natmal science, and is empirically unjustified, since we have, even in the most astonishing phenomena of regulation or instinct, no justification for, but most definite reasous against, the assumption that for example an embryo or an insect is endowed with superhuman intelligence. An important part of those phenomena which have been advanced as "proofs of vitalism," such as equifinality and anamorphosis, are consequences of the char- 80 GENERAL SYSTEM THEORY acteristic state of the organism as an open system, and thus accessible to scientific interpretation and theory. Isomorphism in Science The present study merely intended to briefly point out the general aim and several concepts of general system theory. Further tasks on the one hand would he to express this theory in a logico-mathematically strict form; on the other hand the principles holding for any type of systems would have to he further developed. This is a concrete problem. For example, demograpbic dynamics may he developed homologous to mechanica! dynamics (Volterra, cf. d'Ancona, 1939). A principle of minimum action may he found in various fields, in mechanics, in physical chemistry as Le Chatelier's principle which, as may he proved, is also valid for open systems, in electricity as Lenz's rule, in population theory according to Volterra, etc. A principle of relaxation oscillations occurs in physical systems as well as in many biologica! phenomena and certain roodels of population dynamics. A general theory of periodicities appears as a desideratum of various fields of science. Efforts will therefore have to he made towards a development of principles such as those of minimum action, conditions of stationary and periadie solutions (equilibria and rhythmic fluctuations), the existence of steady states and similar problems in a form generalized with respect to physics and valid for systems in generaL General system theory therefore is not a catalogue of wellknown differential equations and their solutions, but raises new and well-defined problems which partly do not appear in physics, but are of basic importance in non-physical fields. Just because the phenomena concerned are not dealt with in ordinary physics, these problems have often appeared as metaphysical or vitalistic General system theory should further he an important regulative device in science. The existence of laws of similar structure in different fields makes possible the use of roodels which are simpler._or better known, for more complicated and less manageable phenomena. Therefore general system theory should he, methodologically, ..a.n important means of controlling and instigating the transfer of piinciples from one field to another, and it will no longer he necessary to duplicate or triplicate the discovery of the same principles in different fields isolated from Same System Concepts 81 each other. At the same time, by formulating exact criteria, general system theory will guard against superficial analogies which are useless in science and harmful in their practical consequences. This requires a definition of the extent to which "analogies" in science are permissible and useful. We have previously seen the appearance of similar system laws in various sciences. The same is true of phenomena where the general principles can he described in ordinary language though they cannot he formulated in mathematica! terms. For instance, there are hardly processes more unlike phenomenologically and in their intrinsic mechanisms than the formation of a whole animal out of a divided sea-urchin or newt germ, the reestablishment of normal function in the central nervous system after removal or injury to some of its parts, and gestalt perception in psychology. Nevertheless, the principles governing these different phenomena show striking similarities. Again, when we investigate the development of the Germanic languages, it may he observed that, beginning with a primitive language, certain sound mutations occurred in parallel development in various tribes, though these were geographically located far apart from each other; in Iceland, on the British Isles, on the Iberian peninsula. Mutual influence is out of question; the languages rather developed independently after separation of the tribes, and yet show definite parallelism. * The biologist may find a conesponding principle in certain evolutionary developments. There is, for instance, the group of extinct hoofed animals, the titanotheres. During the Tertiary, they developed from smaller into gigantic forms, while with increasing body size formation of ever larger horns took place. A more detailed investigation showed that the titanotheres, starting from those small, early forms, split up into several groups which developed independently of each other but still showed parallel characteristics. Thus we find an interesting similarity in the phenomenon of parallel evolution starting from common origins but developing independently-here: the independent evolution of tribal languages;· there: independent evolution of groups within a certain class of mammals. • In simple cases, the reason for isomorphism is readily seen. "I am obliged to Prof. Otto Höfler for having indicated this phenomenon to me. 82 GENERAL SYSTEM THEORY For example, the exponenti al law states that, given a complex of a number of entities, a constant percentage of these elements decay or multiply per unit time. Therefore this law will apply to the pounds in a banking account as well as to radium atoms, molecules, bacteria, or individual s in a population . The logistic law says t~at. the incr~~se, originally exponenti al, is limited by some restnctlilg conditwns . Thus in autocataly tic reaction, a compound catalyzes its own formation ; but since the number of molecules is finite in a closed reaction vessel, the reaction must stop when all molecules are transforme d, and must therefore a~proach. a limi~ing value. A populatio n increases exponenti ally with ~h~ lilcreaslilg number of individual s, but if space and food are hmited, the amount of food available per individual decreases; therefore the increase in number cannot be unlimited, bu~ must app~oach ~ steady state defined as the maximum populatiOn compatibl e with resources available. Railway lines which already exist in a country lead to the intensifica tion of traffic and industry which, in turn, make necessary a denser railway network, tlll. a state of saturation is eventually reached; thus, railways be~ave hke autocataly zers acceleratin g their own increase, and ~heu growth .follows the autocataly tic curve. The parabolic law Is an express10n for competitio n within a system, each element taki~g its share according to its capacity as expressed by a spenfic constant. Therefore the law is of the same form whether it applie~ to the competitio n of individual s in an economie system, accor~lilg to Pareto's law, or to organs competing within an orgamsm for nutritive material and showing allometric growth. . There are obviously three prerequisi tes for the existence of ~somorph~sms in different fields and sciences. Apparentl y, the ~somorphisms of laws rest in our cognition on the one hand, and lil reality on the other. Trivially, it is easy to write down any compli~ated differentia l equation, yet even innocent-l ooking expresswn s may be hard to solve, or give, at the least, cumberson:-e sol~tions. The number of simple mathemati ca! expression s ~h~ch. wlll be preferably applied to describe natmal phenomen a ~s l~mi~ed: For th.is reason, laws identical in structure will appear lil I~trlilsically different fields. The same applies to statements in ordlilary language; here, too, the number of intellectua l schemes is restricted, and they will be applied in quite different realms. However, these laws and schemes would be of little help if the Same System Concepts 83 world (i.e., the totality of observable events) was not such that they could be applied to it. We can imagine a chaotic world or a world which is too complicat ed to allow the applicatio n of the relatively simple schemes which we are able to construct with our limited intellect. That this is not so is the prerequisi te that science is possible. The structure of reality is such as to permit the applicatio n of our conceptua l constructs. We realize, however, that all scientific laws merely represent abstraction s and idealizatio ns expressing certain aspects of reality. Every science means a schematize d picture of reality, in the sense that a certain conceptua l construct is unequivoc ally related to certain features of order in reality; just as the blueprint of a building isn't the building itself and by no means represents it in every detail such as the arrangeme nt of bricks and the forces keeping them together, but neverthele ss an unequivoc al correspond ence exists between the design on paper and the real constructi on of stone, iron and wood. The question of ultimate "truth" is not raised, that is, in how far the plan of reality as mapped by science is correct or in need or capable of improvem ent; likewise, whether the structure of reality is expressed in one single blueprint -i.e., the system of human science. Presumabl y different representations are possible or even necessary -in a similar way as it is meaningle ss to ask whether central or parallel projection , a horizontal or a vertical plan are more "correct." That the latter may be the case is indicated by instauces where the same physical "given" can be expressed indifferen t "language s"-e.g., by thermodynamics and statistica! mechanics ; or even compleme ntary considerations become necessary, as in the corpuscle and wave roodels of microphys ics. Independe nt of these questions, the existence of science proves that it is possible to express certain traits of order in reality by conceptua l constructs. A presuppos ition for this is that order exists in reality itself; similarly- to quote the illustratio n mentione d-as we are able to draw the plan of a house or a crystal, but not of stones whirling around after an explosion or of the irregularly moving molecules in a liquid. Yet there is a third reasou for the isomorphi sm of laws in different realms which is important for the present purpose. In our considerat iohs we started with a general definition of "system" defined as "a number of elements in interaction " and expressed by the system of equations (3.1). No special hypotheses 84 GENERAL SYSTEM THEORY or statements were made about the nature of the system, of its elements or the relations between them. Nevertheless from this purely formal definition of "system," many properties follow which in part are expressed in laws well-known in various fields of science, and in part concern concepts previously regarcled ~s anthropomorphic, vitalistic or metaphysical. The parallelisni of general conceptions or even special laws in different fields therefore is a consequence of the fact that these are concerned with "systems," and that certain general principles apply to systems irrespective of their nature. Hence principles such as those of wholeness and sum, mechanization, hierarcbic order, approach to steady states, equifinality, etc., may appear in quite different disciplines. The isomorphism found in different realms is based on the existence of general system principles, of a more or less well-developed "genera! system theory." The limitations of this conception, on the other hand, can he indicated by distinguishing three kinds or levels in the description of phenomena. At first, there are analogies-i.e., superficial similarities of phenomena which correspond neither in their causal factors nor in their relevant laws. Of this kind are the simuiaera vitae, popular in previous times, such as when the growth of an organism was compared to the growth of a crystal or of an osmotic cell. There are superficial similarities in the one or other respect, while we are safe to say that the growth of a plant or an animal does not follow the pattern of crystal growth or of an osmotic structure, and the relevant laws are different in both cases. The same applies to the consideration of a biocoenosis (e.g., a forest) as an "organism," with the obvious difference between the unification of an individual organism and the looseness of a plant association; or the comparison of the development of a population with birth, growth, aging and death of an organism where the comparison of life cycles remains highly dubious. A second level are homologies. Such are present when the efficient factors are different, but the respective laws are formally identical. Such homologies are of considerable importance as conceptual models in science. They are frequently applied in physics. Examples are the consideration of heat flow as a flow of a heat substance, the comparison of electrical flow with the flow Same System Concepts 85 of a fluid, in general the transfer of the originally hydrodynamic notion of gradient to electrical, chemica!, etc., potentials. We know exactly, of course, that there is no "heat substance" but heat is to he interpreted in the sense of kinetic theory; yet the model enables the stipulation of laws which are formally correct. It is logica! homologies with which the present investigation is concerned. We may express this as follows: If an object is a system, it must have certain general system characteristics, irrespective of what the system is otherwise. Logica! homology makes possible not only isomorphy in science, but as a conceptual model has the capacity of giving instructions for correct consideration and eventual explanation of phenomena. The third level finally is explanation-i.e., the statement of specific conditions and laws that are valid for an individual object or for a class of objects. In logico-mathematical language, this means that the general functions f of our equation (3.1) are replaced by specified functions applicable to the individual case. Any scientific explanation necessitates the knowledge of these specific laws as, for example, the laws of chemica! equilibrium, of growth of an organism, the development of a population, etc. It is possible that also specific laws present formal correspondence or homologies in the sense discussed; but the structure of individual laws may, of course, be different in the individual cases. Analogies are scientifically worthless. Homologies, in contrast, often present valuable models, and therefore are widely applied in physics. Similarly, general system theory can serve as a regulatory device to distinguish analogies and homologies, meaningless similarities and meaningful transfer of models. This function particularly applies to sciences which, like demography, sociology, and large fields in biology, cannot he fitted in the framework of physics and chemistry; nevertheless, there are exact laws which can be stated by application of suitable models. The homology of system characteristics does not imply reduction of one realm to another and lower one. But neither is it mere metaphor or analogy; rather, it is a forma! correspondence founded in reality inasmuch as it can be considered as constituted of "systems" of whatever kind. Speaking philosophically, general system theory, in its developed form, would replace what is known as "theory of 84 GENERAL SYSTEM THEORY or statements were made about the nature of the system, of its elements or the relations between them. Nevertheless from this purely formal definition of "system," many properties follow which in part are expressed in laws well-known in various fields of science, and in part concern concepts previously regarded as anthropomorphic, vitalistic or metaphysical. The parallelism of general conceptions or even special laws in different fields therefore is a consequence of the fact that these are concerned with "systems," and that certain general principles apply to systems irrespective of their nature. Hence principles such as those of wholeness and sum, mechanization, hierarchic order, approach to steady states, equifinality, etc., may appear in quite different disciplines. The isomorphism found in different realms is based on the existence of general system principles, of a more or less well-developed "general system theory." The limitations of this conception, on the other hand, can be indicated by distinguishing three kinds or levels in the description of phenomena. At first, there are analogies-i.e., superficial similarities of phenomena which correspond neither in their causal factors nor in their relevant laws. Of this kind are the simuiaera vitae, popular in previous times, such as when the growth of an organism was compared to the growth of a crystal or of an osmotic cell. There are superficial similarities in the one or other respect, while we are safe to say that the growth of a plant or an animal does not follow the pattern of crystal growth or of an osmotic structure, and the relevant laws are different in both cases. The same applies to the consideration of a biocoenosis (e.g., a forest) as an "organism," with the obvious difference between the unification of an individual organism and the looseness of a plant association; or the comparison of the development of a population with birth, growth, aging and death of an organism where the comparison of life cycles remains highly dubious. A second level are homologies. Such are present when the efficient factors are different, but the respective laws are formally identical. Such homologies are of considerable importance as conceptual models in science. They are frequently applied in physics. Examples are the consideration of heat flow as a flow of a heat substance, the comparison of electrical flow with the flow Same System Concepts 85 of a fluid, in general the transfer of the originally hydrodynamic notion of gradient to electrical, chemical, etc., potentials. We know exactly, of course, that there is no "heat substance" but heat is to be interpreted in the sense of kinetic theory; yet the model enables the stipulation of laws which are formally correct. It is logical homologies with which the present investigation is concerned. We may express this as follows: If an object is a system, it must have certain general system characteristics, irrespective of what the system is otherwise. Logical homology makes possible not only isomorphy in science, but as a conceptual model has the capacity of giving instrucdons for correct consideration and eventual explanation of phenomena. The third level finally is explanation-i.e., the statement of specific conditions and laws that are valid for an individual object or for a class of objects. In logico-mathematical language, this means that the general functions f of our equation (3.1) are replaced by specified functions applicable to the individual case. Any scientific explanation necessitates the knowledge of these specific laws as, for example, the laws of chemical equilibrium, of growth of an organism, the development of a population, etc. It is possible that also specific laws present formal correspondence or homologies in the sense discussed; but the structure of individual laws may, of course, be different in the individual cases. Analogies are scientifically worthless. Homologies, in contrast, often present valuable models, and therefore are widely applied in physics. Similarly, general system theory can serve as a regulatory device to distinguish analogies and homologies, meaningless similarities and meaningful transfer of models. This function particularly applies to sciences which, like demography, sociology, and large fields in biology, cannot be fitted in the framework of physics and chemistry; nevertheless, there are exact laws which can be stated by application of suitable models. The homology of system characteristics does not imply reduction of one realm to another and lower one. But neither is it mere metaphor or analogy; rather, it is a formal correspondence founded in reality inasmuch as it can be considered as constituted of "systems" of whatever kind. Speaking philosophically, general system theory, in its developed form, would replace what is known as "theory of 86 GENERAL SYSTEM THEORY categories" (N. Hartmann, 1942) ·by an exact system of logicomathematic al laws. General notions as yet expressed in the vernacular would acquire'the unambiguou s and exact expression possible only in mathematica ! language. The Unity of Science We may summarize the main results of this presentation as follows: (a) The analysis of general system principles shows that many concepts which have often been considered as anthropomo rphic, metaphysica l, or vitalistic are accessible to exact formulation . They are consequence s of the definition of systems or of certain system conditions. (b) Such investigatio n is a useful prerequisite with respect to concrete problems in science. In particular, it leads to the elucidation of problems which, in the usual schematisms and pigeonholes of the specialized fields, are not envisaged. Thus system theory should prove an important means in the process of developing new branches of knowledge into exact science-i.e., into systems of mathematica ! laws. (c) This investigation is equally important to philosophy of science, major problems of which gain new and often surprising aspects. (d) The fact that certain principles apply to systems in genera!, irrespective of the nature of the systems and of the entities concerned, explains that conespondin g conceptions and laws appear independen tly in different fields of science, causing the remarkable parallelism in their modern developmen t. Thus, concepts such as wholeness and sum, mechanizati on, centralizatio n, hierarchical order, stationary and steady states, equifinality, etc., are found in different fields of natmal science, as well as in psychology and sociology. These consideratio ns have a definite hearing on the question of the Unity of Science. The current apinion has been well represented by Carnap (1934). As he states, Unity of Science is granted by the fact that all statements in science can ultimately be expressed in physical language-i.e ., in the form of statements that attach quantitative values to definite positions in a spacetime system of co-ordinates . In this sense, all seemingly non- Same System Concepts 87 physical concepts, for instanee specifically biologica! notions such as "species," "organism," "fertilization ," and so forth, are defined by means of certain perceptible criteria-i.e., qualitative determinations capable of being physicalized .. The physical language is therefore the universallan guage of science. The question whether biologica! laws can be reduced to physical ones-i.e., whether the natura! laws sufficient to explain all inorganic phenomena are also sufficient to explain biologica! phenomena -is left open by Carnap, though with preferenee given to an answer in the affirmative. From our point of view, Unity of Science wins a much more concrete and, at the same time, profaunder aspect. We too leave open the question of the "ultimate reduction" of the laws of biology (and the other non-physica l realms) to physics-i.e., the question whether a hypothetico- deductive system embracing all sciences from physics to biology and sociology may ever be established. But we are certainly able to establish scientific laws for the different levels or strata of reality. And here we find, speaking in the "forma! mode" (Carnap), a corresponde nce or isomorphy of laws and conceptual schemes in different fields, granting the Unity of Science. Speaking in "material" language, this means that the world (i.e., the total of observable phenomena) shows a structural uniformity, manifesting itself by isomorphic traces of order in its different levels or realms. Reality, in the modern conception, appears as a tremenclous hierarchical order of organized entities, leading, in a superpositio n of many levels, from physical and chemica! to biologica! and sociological systems. U nity of Science is granted, nat by a utopian reduction of all sciences to physics and chemistry, but by the structural uniformities of the different levels of reality. Especially the gap between natura! and social sciences, or, to use the more expressive German terms, of Natur- und Geisteswissenschaften, is greatly diminished, not in the sense of a reduction of the latter to biologica! conceptions but in the sense of structural similarities. This is the cause of the appearance of cortesponding general viewpoints and notions in both fields, and may eventually lead to the establishme nt of a system of laws in the Jatter. The mechanistic world-view found its ideal in the Laplacean spirit-i.e., in the conception that all phenomena are ultimately 88 GENERAL SYSTEM THEORY aggregates of fortuitous actions of elementary physical units. Theoretically, this conception did not lead to exact sciences outside the field of physics-i.e., to laws of the higher levels of reality, the biologica!, psychological and sociological. Practically, its consequences have been fatal for our civilization. The attitude that considers physical phenomena as the sole standard of reality has lead to the mechanization of mankind and to the devaluation of higher values. The unregulated domination of physical technology finally ushered the world into the catastrophical crises of our time. After having overthrown the mechanistic view, we are careful not to slide into "biologism," that is, into consiclering mental, sociologkal and cultural phenomena from a merely biologica! standpoint. As physicalism considered the living organism as a strange combination of physico-chemical events or machines, biologism considers man as a curious zoological species, human society as a beehive or stud-farm. Biologism has, theoretically, not proved its theoretica! merits, and has proved fatal in its practical consequences. The organismic conception does not mean a unilateral dominanee of biologica! conceptions. When emphasizing general structural isomorphies of different levels, it asserts, at the same time, their autonomy and possession of specific laws. We believe that the future elaboration of general system theory will prove to he a major step towards unification of science. It may he destined in the science of the future, to play a role similar to that of Aristotelian logic in the science of antiquity. The Greek conception of the world was statie, things being considered to he a mirroring of eternal archetypes or ideas. Therefore classification was the central problem in science, the fundamental organon of which is the definition of subordination and superordination of concepts. In modern science, dynamic interactiçm appears to he the central problem in all fields of reality. ItSteneral principles are to he defined by system theory. 4 Advances in General System Theory Since creative thought is the most important thing that makes people different from monkeys, it should be treated as a commodity more precious than gold and preserved with great care. A. D. Hall, A Methodology for Systems Engineering Approaches and Aims in Systems Science When, some 40 years ago, I started my life as a scientist, biology was involved in the mechanism-vitalism controversy. The meehanistic procedure essentially was to resolve the living organism into parts and partial processes: the organism was an aggregate of cells, the cell one of colloids and organic molecules, behavior a sum of unconditional and conditioned reflexes, and so forth. The problems of organization of these parts in the service of maintenance of the organism, of regulation after disturbances and the like were either by-passed or, according to the theory known as vitalism, explainable only by the action of soul-like factors-little hobgoblins as it were-hovering in the cell or the organism-which obviously was nothing less than a declaration of the bankruptcy of science. In this situation, I and others were led to the so-called organismic viewpoint. In one brief sentence, it means that organîsms are organized things and, as biologists, we have to find out about it. I tried to implement this organismic program in various studies on metabolism, growth, and the bio- 90 GENERAL SYSTEM THEORY physics of the organism. One step in this direction was the socalled theory of open systems and steady states which essentially is an expansion of conventional physical chemistry, kinetics and thermodynamics. It appeared, however, that I could not stop on the way once taken and so I was led to a still further generalization which I called "General System Theory." The idea goesback some considerable time: I presented it first in 1937 in Charles Morris' philosophy seminar at the University of Chicago. However, at that time theory was in bad repute in biology, and I was afraid of what Gauss, the mathematician, called the "clamor of the Boeotians." So I left my drafts in the drawer, and it was only after the war that my first publications on the subject appeared. Then, however, sarnething interesting and surprising happened. It turned out that a change in intellectual elimate had taken place, making model building and abstract generalizations fashionable. Even more: quite a number of scientists had foliowed similar lines of thought. So general system theory, after all, was not isolated, not a personal idiosyncrasy as I had believed, but corresponded to a trend in modern thinking. There are quite a number of novel developments intended to meet the needs of a general theory of systems. We may enumerate them in a brief survey: (1) Cybernetics, based upon the principle of feedback or circular causal trains providing mechanisms for goal-seeking and self-controlling behavior. (2) Information theory, introducing the concept of information as a quantity measurable by an expression isomorphic to negative entropy in physics, and developing the principles of its transmission. (3) Game theory analyzing, in a novel mathematica! framework, rational competition between two or more antagonists for maximum gain and minimum loss. (4) Decision theory, similarly analyzing rational choices, within human organizations, based upon examination of a given situation and its possible outcomes. (5) Topology or relational mathematics, including non-metrical fields such as network and graph theory. (6) Factor analysis, i.e., isolation, by way of mathematica! analysis, of factors in multivariable phenomena in psychology and other fields. Advances m General System Theory 91 (7) General system theory in the narrower sense (G.S.T.), trying to derive, from a general definition of "system" as a complex of interacting components, concepts characteristic of organized wholes such as interaction, sum, mechanization, centralization, competition, finality, etc., and to apply them to concrete phenomena. While systems theory in the braad sense has the character of a basic science, it has its correlate in applied science, sametimes subsumed under the general name of Systems Science. This development is closely connected with modern automation. Broadly speaking, the following fields can be distinguished (Ackoff, 1960; A.D. Hall, 1962): Systems Engineering, i.e., scientific planning, design, evaluation, and construction of man-machine systems; Operations research, i.e., scientific control of existing systems of men, machines, materials, money, etc.; Human Engineering, i.e., scientific adaptation of systems and especially machines in order to obtain maximum efficiency with minimum cost in money and other expenses. A very simple example for the necessity of study of "manmachine systems" is air traveL Anybody crossing continents by jet with incredible speed and having to spend endless hours waiting, queuing, being herded in airports, can easily realize that the physical techniques in air travel are at their best, while "organizational" techniques still are on a most primitive level. Although there is considerable overlapping, different conceptual tools are predominant in the individual fields. In systems engineering, cybernetics and information theory and also general system theory in the narrower sense are used. Operations research uses tools such as linear programming and game theory. Human engineering, concerned with the abilities, physiological limitations and variahilities of human beings, includes biomechanics, engineering psychology, human factors, etc., among its tools. The present survey is not concerned with applied systems science; the reader is referred to Hall's hook as an excellent textbook of systems engineering (1962). However it is well to keep in mind that the systems approach as a navel concept in science has a close parallel in technology. The motives leading to the postulate of a general theory of systems can be summarized under a few headings. (1) Up to recent times the field of science as a nomothetic en- 92 GENERAL SYSTEM THEORY deavor, i.e., trying to establish an explanatory and predictive system of laws, was practically identical with theoretica! physics. Consequently, physical reality appeared to be the only one vouchsafed by science. The consequence was the postulate of reductionism, i.e. the principle that biology, behavior and the social sciences are to be handled according to the paragon of physics, and eventually should be reduced to concepts and entities of the physical level. Owing to developments in physics itself, the physicalistic and reductionist theses became problematic, and indeed appeared as metaphysical prejudices. The entities about which physics is talking-atoms, elementary particles and the like -have turned out to be much more ambiguous than previously supposed: not metaphysical building blocks of the universe, but rather complicated conceptual models invented to take account of certain phenomena of observation. On the other hand, the biologica!, behaviaral and social sciences have come into their own. Owing to the concern with these fields on the one hand, and the exigencies of a new technology, a generalization of scientific concepts and models became necessary which resulted in the em.ergenee of new fields beyond the traditional system of physics. (2) In the biologica!, behaviaral and sociological fields, there exist predominant problems which were neglected in classica! science or rather which did not enter its considerations. If we look at a living organism, we abserve an amazing order, organization, maintenance in continuous change, regulation and apparent teleology. Similarly, in human behavior goal-seeking and purposiveness cannot be overlooked, even if we accept a strictly behavioristic standpoint. However, concepts like organization, directiveness, teleology, etc., just do not appear in the classic system of science. As a matter of fact, in the so-called mechanistic world view based upon classica! physics, they were considered as illusory or metaphysical. This means, for example, to the biologist that just the specific problems of living nature appeared to lie beyond the legitimate field of science. The appearance of models-conceptual and in some cases even material-representing such aspects of multivariable interaction, organization, selfmaintenance, directiveness, etc., implies introduetion of new categories in scientific thought and research. (3) Classica! science was essentially concerned with two-variable problems, linear causal trains, one cause and one effect, or with Advances zn General System Theory 93 few variables at the most. The classica! example is mechanics. It gives perfect solutions for the attraction between two celestial bodies, a sun and a planet, and hence permits exact prediction of future constellations and even the existence of still undetected planets. However, already the three-body problem of mechanics is insoluble in principle and can only be approached by approximations. A similar situation exists in the more modern field of atomie physics (Zacharias, 1957). Here also two-body probIerus such as that of one proton and electron are solvable, but trouble arises with the many-body problem. Many problems, particularly in biology and the behaviaral and social sciences, are essentially multivariable problems for which new conceptual tools are needed. Warren Weaver (1948), co-founder of information theory, has expressed this in an often-quoted statement. Classica! science, he stated, was concerned either with linear causal trains, that is, two-variable problems; or else with unorganized complexity. The latter can be handled with statistica! methods and ultimately sterns from the second principle of thermodynamics. However, in modern physics and biology, problems of organized complexity, i.e., interaction of a large but not infinite number of variables, are popping up everywhere and demand new conceptual tools. (4) What has been said are not metaphysical or philosophic contentions. We are not erecting a harrier between inorganic and living nature which obviously would be inappropriate in view of intermediates such as viruses, nucleo-proteins and self-duplicating units. Nor do we protest that biology is in principle "irreducible to physics" which also would be out of place in view of the tremenclous advances of physical and chemica! explanation of life processes. Similarly, no harrier between biology and the behavioral and social sciences is intended. This, however, does not obviate the fact that in the fields mentioned we do not have appropriate conceptual tools serving for explanation and prediction as we have in physics and its various fields of application. (5) It therefore appears that an expansion of science is required to deal with those aspects which are left out in physics and happen to concern the specific characteristics of biologica!, behavioral, and social phenomena. This amounts to new conceptual models to be introduced. (6) These expanded and generalized theoretica! constructs or 94 GENERAL SYSTEM THEORy models are interdisciplinary-i.e., they transeend the conventional departments of science, and are applicable to phenomena in various fields. This results in the isomorphism of models, general principles and even special laws appearing in various fields. In summary: Inclusion of the biologica!, behaviaral and social sciences and modern technology necessitate generalization of basi~ concepts in science; this implies new categories of scientific thinking compared to those in traditional physics; and models introduced for such purpose are of an interdisciplinary nature. An important consideration is that the various approaches enumerated are not, and should not be considered to be monopolistic. One of the important aspects of the modern changes in scientific thought is that there is no unique and all-embracing "wor~d system." All scientific constructs are models representing eertam aspects or perspectives of reality. This even applies to theoretica! physics: far from being a metaphysical presentation of ultimate reality (as the materialism of the past proclaimed and modern positivism still implies), it is but one of these models and, as recent developments show, neither exhaustive nor unique. The various "systems theories" also are models that mirror different aspects. They are not mutually exclusive and are aften combined in application. For example, certain phenomena may be amenable to scientific exploration by way of cybernetics, others by way of general system theory in the narrower sense; or even in the same phenomenon, certain aspects may be describable in the one or the other way. This, of course, does not preclude but rather implies the hope for further synthesis in which the various approaches of the present toward a theory of "wholeness" and "organization" may be integrated and unified. Actually, such further syntheses, e.g., between irreversible thermodynamics and information theory, are slowly developing. Methods in General Systems Research Ashby (1958a) has admirably outlined two possible ways or general methods in systems study: Two main lines are readily distinguished. One, already well developed in the hands of von Bertalanffy and his co-workers, takes the world as we find it, examines the various systems that occur in it-zoological, physiological, and so on-and then Advances zn General System Theory 95 draws up statements about the regularities that have been observed to hold. This method is essentially ~~P!!'i~!'!-1. The second methad is to start at the other end. Instead of studying first one system, then a second, then a third, and so on, it goes to the other extreme, considers the set of all conceivable systems and then reduces the set to a more reasanabie size. This is the method I have recently followed. It will easily be seen that all systems studies follow one or the other of these methods or a combination of both. Each of the approaches has its advantages as well as shortcomings. (1) The first method is empirico-intuitive; it has the advantage that it remains rather close to reality and can easily be illustrated and even verified by examples taken from the individual fields of science. On the other hand, the approach Jacks mathematica! elegance and deductive strength and, to the mathematically minded, will appear naive and unsystematic. Nevertheless, the merits of this empirico-intuitive procedure should not be minimized. The present writer has stated a number of "system principles," partly in the context of biologica! theory and without explicit reference to G.S.T. (von Bertalanffy, 1960a, pp. 37-54), partly in what emphatically was entitled an "Outline" of this theory (Chapter 3). This was meant in the literal sense: It was intended to call attention to the desirability of such a field, and the presentation was in the way of a sketch or blueprint, illustrating the approach by simple examples. However, it turned out that this intuitive survey appears to be remarkab1y complete. The main principles affered such as wholeness, sum, centralization, differentiation, leading part, closed and open system, finality, equifinality, growth in time, relative growth, competition, have been used in manifo1d ways (e.g., general definition of system: Hall and Fagen, 1956; types of growth: Keiter, 1951-52; systems engineering: A.D. Hall, 1962; social work: Hearn, 1958). Excepting minor variations in terminology intended for clarification or due to the subject matter, no principles of similar significanee were added-even though this would be highly desirable. It is perhaps even more significant that this also applies to considerations which do not refer to the present writer's work and hence cannot be said to be unduly influenced by it. Perusal 96 GENERAL SYSTEM THEORY of studies such as those by Beer (1960) and Kremyanskiy (1960) on princip1es, Brad1ey and Calvin (1956) on the network of chemica! reactions, Haire (1959) on growth of organizations, etc., will easi1y show that they are also using the "Bertalanffy principles." (2) The way of deductive systems theory was foliowed by Ashby (1958b). A more informal presentation which summarizes Ashby's reasoning (1962) lends itself particularly well to analysis. Ashby asks about the "fundamental concept of machine" and answers the question by stating "that its internal state, and the state of its surroundings, defines uniquely the next state it will go to." If the variables are continuous, this definition corresponds to the description of a dynamic system by a set of ordinary differential equations with time as the independent variable. However, such representation by differential equations is too restricted for a theory to include biologica! systems and calculating machines where discontinuities are ubiquitous. Therefore the modern definition is the "machine with input": It is defined by a set S of internal states, a set I of input and a mapping f of the product set I X S into S. "Organization," then, is defined by specifying the machine's states S and its conditions I. If S is a product set S = 1T; T., with i as the parts and T specified by the mapping f, a "self-organizing" system, according to Ashby, can have two meanings, namely: (1) The system starts with its parts separate, and these parts then change toward forming connections (example: cells of the embryo, first having little or no effect on one another, join by formation of dendrites and synapses to form the highly interdependent nervous system). This first meaning is "changing from unorganized to organized." (2) The second meaning is "changing from a bad organization to a good one" (examples: a child whose brain organization makes it fire-seeking at first, while a new brain organization makes him fire-avoiding; an automatic pilot and plane coupled first by deleterious positive feedback and then improved). "There the organization is bad. The system would be 'self-organizing' if a change were automatically made" (changing positive into negative feedback). But "no machine can be self-organizing in this sense" (author's italics). For adaptation (e.g., of the homeostat or in a self-programming computer) means that we start with a set S of states, and that f changes into g, so that organization is a variable, e.g., a function of time a (t) which has first the value f and later the value g. Advances in General System Theory 97 However, this change "cannot be ascribed to any cause in the set S)· so it must come from some outside agent) acting on the system S as input" (our italics). In other terms, to be "selforganizing" the machine S must be coupled to another machine. This concise statement permits observation of the limitations of this approach. We completely agree that description by differential equations is not only a clumsy but, in principle, inadequate way to deal with many problems of organization. The author was well aware of this, emphasizing that a system of simultaneous differential equations is by no means the most general fotmulation and is chosen only for illustrative purposes (Chapter 3). However, in overcoming this limitation, Ashby introduced another one. His "modern definition" of system as a "machine with input" as reproduced above, supplants the general system model by another rather special one: the cybernetic model-i.e., a system open to information but closed with respect to entropy transfer. This becomes apparent when the definition is applied to "self-organizing systems." Characteristically, the most important kind of these has no place in Ashby's model, namely systems organizing themselves by way of progressive differentiation, evolving from states of lower to states of higher complexity. This is, of course, the most obvious form of "self-organization," apparent in ontogenesis, probable in phylogenesis, and certainly also va1id in many social organizations. We have here not a question of "good" (i.e., useful, adaptive) or "bad" organization which, as Ashby correctly emphasizes, is relative to circumstances; increase in differentiation and complexity-whether useful or not-is a criterion that is objective and at least in principle amenable to measurement (e.g., in termsof decreasing entropy, of information). Ashby's contention that "no machine can oe self-organizing," more explicitly, that the "change cannot be ascribed to any cause in the set S" but "must come from some outside agent, an input" amounts to exclusion of self-differentiating systems. The reason that such systems are not permitted as "Ashby machines" is patent. Self-differentiating systems that evolve toward higher complexity (decreasing entropy) are, for thermodynamic reasons, possible only as open systems-e.g., systems importing matter containing free energy to an amount overcompensating the increase in entropy due to irreversible processes within the system ("im- 98 GENERAL SYSTEM THEORY port of negative entropy" in Schrödinger's expression). However, we cannot say that "this change comes from some outside agent, an input"; the differentiation within a developing embryo and organism is due to its internal laws of organization, and the input (e.g., oxygen supply which may vary quantitatively, or nutrition which can vary qualitatively within a broad spectrum) makes it only possible energetically. The above is further illustrated by additional examples given by Ashby. Suppose a digital computer is carrying through multiplications at random; then the machine will "evolve" toward showing even numbers (because products even X even as well as even X odd give numbers even), and eventually only zeros will he "surviving." In still another version Ashby quotes Shannon's Tenth Theorem, stating that if a correction channel has capacity H, equivocation of the amount H can be removed, but no more. Both examples illustrate the working of closed systems: The "evolution" of the computer is one toward disappearance of differentiation and establishment of maximum homogeneity (analog to the second principle in closed systems); Shannon's Theorem similarly concerns closed systems where no negative entropy is fed in. Compared to the information content (organization) of a living system, the imported matter (nutrition, etc.) carries not information but "noise." Nevertheless, its negative entropy is used to maintain or even to increase the information content of the system. This is a state of affairs apparently not provided for in Shannon's Tenth Theorem, and understandably so as he is not treating information transfer in open systems with transformation of matter. In both respects, the living organism (and other behavioral and social systems) is not an Ashby machine because it evolves toward increasing differentiation and inhomogeneity, and can correct "noise" to a higher degree than an inanimate communieation channel. Both, however, are consequences of the organism's character as an open system. Incidentally, it is for similar reasons that we cannot replace the concept of "system" by the generalized "machine" concept of Ashby. Even though the latter is more liberal compared to the classic one (machines defined as systems with fixed arrangement of parts and processes), the objections against a "machine theory" of life (von Bertalanffy, 1960, pp. 16-20 and elsewhere) remain valid. Advances in General System Theory 99 These remarks are not intended as adverse criticism of Ashby's or the deductive approach in general; they only emphasize that there is no royal road to general systems theory. As every other scientific field, it will have to develop by an interplay of empirica!, intuitive and deductive procedures. If the intuitive approach leaves much to be desired in logical rigor and completeness, the deductive approach faces the difficulty of whether the fundamental terms are correctly chosen. This is not a particular fault of the theory or of the workers concerned but a rather common phenomenon in the history of science; one may, for example, remember the long debate as to what magnitude-force or energy -is to be considered as constant in physical transformations until the issue was decided in favor of mv2;2. In the present writer's mind, G.S.T. was conceived as a working hypothesis; being apracticing scientist, he sees the main function of theoretica! models in the explanation, prediction and control of hitherto unexplored phenomena. Others may, with equal right, emphasize the importance of axiomatic approach and quote to this effect examples like the theory of probability, non-Eueliclean geometries, more recently information and game theory, which were first developed as deductive mathematica! fields and later applied in physics or other sciences. There should be no quarrel about this point. The danger, in both approaches, is to consider too early the theoretica! model as being closed and definitive-a danger particularly important in a field like general systems which is still groping to find its correct foundations. Advances of General System Theory The decisive question is that of the explanatory and predictive value of the "new theories" attacking the host of problems around wholeness, teleology, etc. Of course, the change in intellectual elimate which allows one to see new problems which were overlooked previously, or to see problems in a new light, is in a way more important than any single and special application. The "Copernican Revolution" was more than the possibility somewhat better to calculate the movement of the planets; general relativity more than an explanation of a very small number of recalcitrant phenomena in physics; Darwinism more than a hypothetical answer to zoological problems; it was the changes 100 GENERAL SYSTEM THEORY in the general frame of reference that mattered (d. Rapoport, 1959a). Nevertheless, the justification of such change ultimately is in specific achievements which would not have been obtained without the new theory. There is no question that new horizons have been opened up but the relations to empirica! facts often remain tenuous. Thus, information theory has been hailed as a "major breakthrough," but outside the original technological field, contributions have remained scarce. In psychology, they are so far limited to rather trivia! applications such as rote learning, etc. (Rapoport, 1956, Attneave, 1959). When, in biology, DNA is spoken of as "coded information" and of "breaking the code" when the structure of nucleic acids is elucidated, use of the term information is a façon de parler rather than application of information theory in the technica! sense as developed by Shannon and Weaver (1949). "Information theory, although useful for computer design and network analysis, has so far not found a significant place in biology" (Bell, 1962). Game theory, too, is a novel mathematica! development which was considered to he comparab1e in scope to Newtonian mechanics and the introduetion of calculus; again, "the applications are meager and faltering" (Rapoport, 1959a; the reader is urgently referred to Rapoport's discussions on information and game theory which admirably analyze the probIeros here mentioned). The same is seen in decision theory from which considerable gain in applied systems science was expected; but as regards the much-advertised military and business games, "there has been no controlled evaluation of their performance in training, persounel selection, and demonstration" (Ackoff, 1959). A danger in recent developments should not remain unmentioned. Science of the past (and partly still the present) was dominated by one-sided empiricism. Only collection of data and experiments were considered as being "scientific" in biology (and psychology); "theory" was equated with "speculation" or "philosophy," forgetting that a mere accumulation of data, although steadily piling up, does not make a "science." Lack of recognition and support for development of the necessary theoretica! framework and unfavorable influence on experimental research itself (which largely became an at-random, hit-or-miss endeavor) was the consequence (cf. Weiss, 1962a). This has, in certain fields, changed to the contrary in recent years. Enthusiasm for the new Advances in General System Theory 101 mathematica! and logica! tools available has led to feverish "model building" as a purpose in itself and often without regard to empirica! fact. However, conceptual experimentation at random has no greater chances of success than at-random experimentation in the laboratory. In the words of Ackoff (1959), there is the fundamental misconception in game (and other) theory to mistake for a "problem" what actually is only a mathematica! "exercise." One would do well to remember the old Kantian maxim that experience without theory is blind but theory without experience a mere intellectual play. The case is somewhat different with cybernetics. The model here applied is not new; although the enormous development in the field dates from the introduetion of the name, Cybernetics (Wiener, 1948), application of the feedback principle to physiological processes goes back to R. Wagner's work nearly 40 years ago (d. Kment, 1959). The feedback and borneostasis model has since been applied to innumerable biologica! phenomena andsomewhat less persuasively-in psychology and the social sciences. The reason for the latter fact is, in Rapoport's words (1956) that usually, there is a well-marked correlation between the scope and the soundness of the writings .... The sound work is confined either to engineering or to rather trivia1 applications; ambitious formulations remain vague. This, of course, is an ever-present danger in all approaches to general systems theory: doubtless, there is a new compass of thought but it is difficult to steer between the Scylla of the trivia! and the Charybdis of mistaking neologisms for explanation. The following survey is limited to "classica!" general system theory-"classical" not in the sense that it claims any priority or excellence, but that the models used remain in the framework of "classica!" mathernaties in contradistinction to the "new" rnathematics in game, network, information theory, etc. This does not imply that the theory is merely application of conventional mathematics. On the contrary, the system concept poses problems which are partly far from being answered. In the past, system problems have led to important mathematica! developments such as Volterra's theory of integro-differential equations, of systems with "memory" whose behavior depends not only on actual conditions but also on previous history. Presently important prob- 102 GENERAL SYSTEM THEORY 1ems are waiting for further developments, e.g., a general theory of non-linear differential equations, of steady states and rhythmic phenomena, a generalized principle of least action, the thermadynamie definition of steady states, etc. It is, of course, irrelevant whether or not research was explicitly labeled as "genera1 system theory." No complete or exhaustive review is intended. The aim of this unpretentious survey will be fulfilled if it can serve as a sort of guide to research done in the field, and to areas that are promising for future work. ÜPEN SYSTEMS i. The theory of open systems is an important generalization of physical theory, kinetics and thermodynamics. It has led to new principles and insight, such as the principle of equifinality, the generalization of the second thermadynamie principle, the possibie increase of order in open systems, the occurrence of periodic phenomena of overshoot and false start, etc. The extensive work in biology and related fields is partly reviewed in Chapters 5-7. (For further discussion also cf. Bray and White, 1957; Jung, 1956; Morchio, 1956; Netter, 1953, 1959). Beyond the individual organism, systems principles are also used in population dynamics and ecologie theory (review: J. R. Bray, 1958). Dynamic ecology, i.e., the succession and climax of plant populations, is a much-cultivated field which, however, shows a tendency to slide into verbalism and terminological debate. The systems approach seems to offer a new viewpoint. Whittacker (1953) has described the sequence of plant communities toward a climax formation in terms of open systems and equifinality. According to this author, the fact that similar climax formations may develop from different initia! vegetations is a striking example of equifinality, and one where the degree of independenee of starting conditions and the course development has taken appear even greater than in the individual organism. A quantitative analysis on the basis of open systems in terms of production of biomass, with climax as steady state attained, was given by Patten (1959). The open-system concept has also found application in the earth sciences, geomorphology (Chorley, 1964) and meteorology (Thompson, 1961) drawing a detailed comparison of modern meteoro1ogical concepts and Bertalanffy's organismic concept in Advances in General System Theory 103 biology. It may be remembered that a1ready Prigogine in his classic (1947) mentioned meteorology as one possible field of application of open systems. GROWTH-IN-TIME The simplest forms of growth which, for this reason, are particularly apt to show the isomorphism of 1aw in different fields are the exponential and the logistic. Examples are, among many others, the increase of knowledge of number of animal species (Gessner, 1952), publications on drosophila (Hersh, 1942), of manufacturing companies (Haire, 1959). Boulding (1956a) and Keiter (1951-52) have emphasized a general theory of growth. The theory of animal growth after Bertalanffy (and others)which, in virtue of using overall physiological parameters ("anabolism," "catabolism") may be subsumed under the heading of G.S.T. as well as under that of biophysics-has been surveyed in its various applications (Bertalanffy, 1960b). RELATIVE GROWTH A principle which is also of great simplicity and generality concerns the relative growth of components within a system. The simple relationship of allometric increase applies to many growth phenomena in biology (morphology, biochemistry, physiology, evolution). A similar relationship obtains in social phenomena. Social differentiation and division of labor in primitive societies as well as the process of urbanization (i.e., growth of cities in comparison to rural population) follow the allometric equation. Application of the latter offers a quantitative measure of socia1 organization and deve1opment, apt to replace the usual, intuitive judgments (Naroll and Bertalanffy, 1956). The same principle apparently applies to the growth of staff compared to total number of employees in manufacturing companies (Haire, 1959). CoMPETITION AND RELATEn PHENOMENA The work in population dynamics by Volterra, Lotka, Gause and others belongs to the classics of G.S.T., having first shown that it is possible to develop conceptual models for phenomena 104 GENERA L SYSTEM THEORY such as the "struggl e for existenc e" that can be submitt ed. to empiric a! test. Populat ion dynamic s an~ re~ated. populau on genetics have since become importa nt fields m bwl?g1~al research . It is importa nt to note that investig ation of th1s ~m~ belongs not only to basic but also to applied biology. Th1s IS true .of fishery biology where theoreti ca! models are used to estabhs h optimu m conditio ns for the exploita tion of the sea (survey of the more importa nt models: Watt, 1958). The most elabor~te dynamic model is by Beverto n and Holt (1957;. shor~ survey. H~lt, w.y.) develop ed for fish populat ions. explm:e d m comme~Cial fishery but certainl y of wider applicat i.on .. ~h1s m~del takes mto account reeruitm ent (i.e., entering of md1v1duals mto the population), growth (assume d to follow the growth equatio ns af.ter Bertalan ffy), capture (by exploita tion), and natura! mortaht y. The practica l value of this model is illustrat ed by the fact th~t it has been adopted for routine purpose s by the F~o~ and. ~gn­ culture Organiz ation of the United Nations , ~he Bnt1s~ Mm1str y of Agricul ture and Fisherie s and other official agenCies. Richard son's studies on armame nts races (cf. Rapopo rt, 1957, 1960), notwith standin g their shortcom ings, dramati cally s~ow the possible impact of the systems conc:pt ~pon th: mos: vital concerns of our time. If rational and sCienufic cons1derat~on.s matter at all, this is one way to refute such catchwo rds as Sz vzs pacem para bellum. . . . The expressi ons used m populat wn dyna.mic~ and the bioIogical "struggl e for existenc e," in econom etncs, m the stu.dy of armame nt races (and others) all belong to the same far:uly of equatio ns (the system discussed in Chapter 3). A sy~tema:rc comparison and study of these parallel isms would be hrgbly mteresting andrew arding (cf. also Rapopo rt, 1957, p. 88). One may, for example , suspect that the laws gover~ing business cycles and those of populat ion fluctuat ions accordm g to ~olte~ra stem from similar conditio ns of competi tion and interact iOn m the system. In a non-ma themati ca! way, Bouldin g (1953) has discusse d w~at he calls the "Iron Laws" of social organiza tions: the Malthus ran law, the law of optimu m size of organiza tions, existenc e of cycles, the law of oligopo ly, etc. SYSTEMS ENGINEE RING The theoreti ca! interest of systems enginee ring and operatio ns research is in the fact that entities whose compon ents are most il I Advanc es in General System Theory 105 heterog eneous- men, machine s, building s, monetar y and other values, inflow of raw materia l, outflow of product s and many other items-c an successfully be submitt ed to systems analysis. As already mention ed, systems enginee ring employs the methodology of cyberne tics, informa tion theory, network analysis, flow and block diagram s, etc. Conside rations of G.S.T. also enter (A.D. Hall, 1962). The first approac hes are concern ed with structured, machine -like aspects (yes-or-no decision s in the case of informa tion theory); one would suspect that G.S.T. aspects will win increase d importa nce with dynami c aspects, flexible organizations, etc. PERSONA LITY THEORY Althoug h there is an enormo us amount of theorizi ng on neural and psychol ogical function in the cyberne tic line based upon the brain-co mputer compari son, few attempt s have been made to apply G.S.T. in the narrowe r sense to the theory of human behavio r (e.g., Krech, 1956; Mennin ger, 1957). For the present purpose s, the latter may be nearly equated with persona lity theory. We have to realize at the start that persona lity theory is at present a battlefie ld of contrast ing and cantrov ersial theories . Hall and Lindzey (1957, p. 71) have justly stated: "All theories of behavio r are pretty poor theories and all of them leave much to be desired in the way of scientific proof"- this being said in a textboo k of nearly 600 pages on "Theori es of Persona lity." We can therefor e not well expect that G.S.T. can present solution s where persona lity theorist s from Freud and Jung to a host of modern writers were unable to do so. The theory will have shown its value if it opens new perspect ives and viewpoi nts capable of experim ental and practica l applicat ion. This appears to be the case. There is quite a group of psychol ogists who are commit ted to an organism ic theory of persona lity, Goldste in and Maslow being well-kn own represen tatives. There is, of course, the fundam ental question whether , first, G.S.T. is not essentia lly a physical istic simile, inapplic able to psychic phenom ena; and secondl y whether such model has explanato ry value when the pertine nt variable s cannot he defined quantita tively as is in general the case with psychol ogical phenomena . (1) The answer to the first questio n appears to be that the 106 GENERAL SYSTEM THEORY system concept is abstract and general enough to permit application to entities of whatever denominatio n. The notions of "equilibrium ," "homeostasi s," "feedback," "stress," etc., are no less of technologie or physiologica l origin but more or less successfully applied to psychologica l phenomena. System theorists agree that the concept of "system" is not limited to material entities but can be applied to any "whole" consisting of interacting "component s." (2) If quantization is impossible, and even if the components of a system are ill-defined, it can at least be expected that certain principles will qualitatively apply to the whole qua system. At least "explanatio n in principle" (see below) may be possible. Rearing in mind these limitations, one concept which may prove to be of a key nature is the organismic notion of the organism as a spontaneous ly active system. In the present author's words, Even under constant external conditions and in the absence of external stimuli the organism is not a passive but a basically active system. This applies in particular to the function of the nervous system and to behavior. It appears that internal activity rather than reaction to stimuli is fundamenta L This can be shown with respect both to evolution in lower animals a,nd to developmen t, for example, in the first movements of embryos and fetuses (von Bertalanffy, 1960a). This agrees with what von Holst has called the "new conception" of the nervous system, based upon the fact that primitive locomotor activities are caused by central automatisms that do not need external stimuli. Therefore, such movements persist, for example, even after the conneetion of motoric to sensory nerves had been severed. Hence the reflex in the classic sense is not the basic unit of behavior but rather a regulatory mechanism superposed upon primitive, automatic activities. A similar concept is basic in the theory of instinct. According to Lorenz, innate releasing mechanisms (I.R.M.) play a dominant role, which sometimes go off without an external stimulus (in vacuo or running-idle reactions): A bird which has no material to build a nest may perform the movements of nest building in the air. These consideratio ns are in the frameworko f what Hebb (1955) called the "conceptual C.N.S. of 1930-1950." The more recent Advances in General System Theory 107 insight. into activating systems of the brain emphasizes differently, and With a wealth of experimenta l evidence, the same basic concept of the autonomous activity of the C.N.S. T~e significanee of these concepts becomes apparent when we consider that they are in fundamenta l contrast to the conventiona l stimulus-res ponse scheme which assumes that the organism is an essentially reactive system answering, like an automaton, to external stimuli. The dominanee of the S-R scheme in contempora ry psychology needs no emphasis, and is obviously connected with the. ze!tgeist of a ~ighly mechanized society. This principle is basic .m psychologica l theories which in all other respects are opposite, for example, in behavioristic psychology as well as in psychoanalys~s. Accordin~ to Freud it is the supreme tendency of the orgamsm to get nd of tensions and drives and come to rest. i~ ,~ st~te of equilibrium governed by the "principle of stability which .Freud borrowed from the German philosopher, Fechner. Neurotic and psychotic behavior, then, is a more or less effective or abortive defense mechanism tending to restore some sort of equilibrium (according to D. Rapaport's analysis (1960) of the structure of psychoanaly tic theory: "economie" and "adaptive points of view"). Charl~tte ~ühler (1959), the well-known child psychologist , has aptly epitomiZed the theoretica! situation: In .the fundamenta l psychoanaly tic model, there is only one basic tendency, that is toward need gratification or tension reduction. . . . Present-day biologie theories emphasize the "spontaneity " of the organism's activity which is due to its ~ui~t-in energy. The organism's autonomous functioning, its dnve to perform certain movements" is emphasized by Bertal.ai_Iffy. · .. These concepts represent a complete revision of the orzgznal homeostasis principle which emphasized exclusively th: t~ndenc~ toward equilibrium . It is the original borneostasis p~mCiple With which psychoanaly sis identified its theory of discharge of tensions as the only primary tendency (italics partly ours). In brief, we may define our viewpoint as "Beyond the Romeostatie Principle": . ~~~ The S-~ .scheme misses the realms of play, exploratory actlvities, creativity, self-realizati on, etc.; 108 GENERAL SYSTEM THEORY (2) The economie scheme misses just specific, human achievements-the most of what loosely is termed "human culture"; (3) The equilibriu m principle misses the fact that psychologi cal and behaviara l activities are more than relaxation of tensions; far from establishin g an optima! state, the latter may entail psychosis-like disturbanc es as, e.g., in sensory-de privation experiments. It appears that the S-R and psychoana lytic model is a highly unrealistic picture of human nature and, in its con~equences, a rather dangerous one. Just what we consider to be specific human achieveme nts can hardly be brought under the utilidrian , homeostasis, and stimulus-r esponse scheme. One may call mountain climbing, composing of sonatas or lyrica! poems "psycholog ical homeostas is"-as has been done-but at the risk that this physiologically well-define d concept loses all meaning. Furthermo re, if the principle of borneostat ic maintenan ce is taken as a golden rule of behavior, the so-called well-adjus ted individual will be the ultimate goal, that is a well-oiled robot maintaini ng itself in optima! biologica!, psychologi cal and social homeostas is. This is Brave New World-no t, for some at least, the ideal state of humanity. Furthermo re, that precarious mental equilibriu m must not be disturbed: Hence, in what rather ironically is called progressive education, the anxiety not to overload the child, not to impose constraint s and to minimize all directing influences with the result of a previously unheard-o f erop of illiterates and juvenile delinquen ts. In contrast to conventio nal theory, it can safely be maintaine d that not only stresses and tensions but equally complete release from stimuli and the consequen t mental void may be neurosogenic or even psychosogenic. Experimen tally this is verified by the experimen ts with sensory deprivatio n when subjects, insulated from all incoming stimuli, after a few hours develop a so-called model psychosis with hallucinat ions, unbearabl e anxiety, etc. Clinically it amounts to the same when insulation leads to prisoners' psychosis and to exacerbati on of mental disease by isolation of patients in the ward. In contrast, maximal stress need not necessarily produce mental disturbanc e. If conventio nal theory were correct, Europe during and after the war, with extreme physiologi cal as well as psychologi cal stresses, should have been a gigantic lunatic asylum. As a matter of fact, there was Advances in General System Theory 109 statisticall y no increase either in neurotic or psychotic disturbances, apart from easily explained acute disturbanc es such as combat neurosis (see Chapter 9). So we arrive at the conception that a great deal of biologica! and human behavior is beyond the principles of utility, homeastasis and stimulus-re sponse, and that it is just this which is characteris tic of human and cultmal activities. Such a new look opens new perspectiv es not only in theory but in practical implications with respect to mental hygiene, education, and society in generaL (See Chapter 9). What has been said can also be couched in philosophi cal terms. If existential ists speak of the emptiness and meaningle ssness of life, if they see in it a souree not only of anxiety but of actual mental illness, it is essentially the same viewpoint: that behavior is not merely a matter of satisfactio n of biologica! drives and of maintenan ce in psycholog ical and social equilibriu m but that something more is involved. If life becomes unbearabl y empty in an industriali zed society, what can a person do but develop a neurosis? The principle, which may loosely be called s12o~: taneous activity of the psychophy sical organism, is a more realistk formula.tio n of what the existential ists want to say in their often obscure language. And if personalit y theorists like Maslow or Gardner Murphy speak of self-realiza tion as human goal, it is again a somewhat pompous expression of the same. THEORETIC AL HlSTORY We eventually come to those highest and ill-defined ent1t1es that are called human cultures and civilizations. It is the field often called "philosoph y of history." We may perhaps better speak of "theoretic a! history," admittedly in its very first beginnings. This name expresses the aim to form a connecting link between "science" and the "humaniti es"; more in particular , between the social sciences and history. It is understoo d, of course, that the techniques in sociology and history are entirely different (polls, statistica! analysis against archival studies, internal evidence of historie relics, etc.). However, the object of study is essentially the same. Sociology is essentially concerned with a temporal cross-section as human societies are; history with the "longitudi nal" study how societies 110 GENERAL SYSTEM THEORY become and develop. The object and techniques of study certainly justify practical differentiation; it is less clear, however, that they justify fundamentally different philosophies. The last statement already implies the question of constructs in history, as they were presented, in grand form, from Vico to Regel, Marx, Spengler, and Toynbee. Professional historians regard them at best as poetry, at worst as fantasies pressing-with paranoic obsession-the facts of history into a theoretica! bed of Procrustes. It seems history can learn from the system theorists not ultimate solutions but a sounder methodological outlook. Problems hitherto considered to be philosophical or metaphysical can well be defined in their scientific meaning, with some interesting outlook at recent developments (e.g., game theory) thrown into the bargain. Empirica! criticism is outside the scope of the present study. For example, Geyl (1958) and many others have analyzed obvious misrepresentations of historica! events in Toynbee's work, and even the non-specialist reader can easily draw a list of fallacies especially in the later, Holy Ghost-inspired volumes of Toynbee's magnum opus. The problem, however, is larger than errors in fact or interpretation or even the question of the merits of Marx's, Spengler's or Toynbee's theories; it is whether, in principle, models and laws are admissible in history. A widely held contention says that they are not. This is the concept of "nomothetic" method in science and "idiographic" metbod in history. While science to a greater or less extent can establish "laws" for natural events, history, concerned with human events of enormous complexity in causes and outcome and presumably determined by free decisions of individuals, can only describe, more or less satisfactorily, what has happened in the past. Here the methodologist has his first comment. In the attitude just outlined, academie history condemns constructs of history as "intuitive," "contrary to fact," "arbitrary," etc. And, no doubt, the criticism is pungent enough vis-à-vis Spengler or Toynbee. It is, however, somewhat less convincing if we look at the work of conventional historiography. For example, the Dutch historian, Peter Geyl, who made a strong argument against Toynbee from such methodological considerations, also wrote a brilliant book about Napoleon (1949), amounting to the result that there are a dozen or so different interpretations-we may safely say, models Advances in General System Theory 111 -of Napoleon's character and career within academie history, all based upon "fact" (the Napoleonic period happens to be one of the best documented) and all flatly contradicting each other. Roughly speaking, they range from Napoleon as the brutal tyrant and egotistic enemy of human freedom to Napoleon the wise planner of a unified Europe; and if one is a Napoleonic student (as the present writer happens to be in a small way), one can easily produ.ce some original documents refuting misconceptions occurring even in generally accepted, standard histories. You cannot have it both ways. If even a figure like Napoleon, not very remote in time and with the best of historica! documentation, can be interpreted contrarily, you cannot well blame the "philosophers of history" for their intuitive procedure, subjective bias, etc., when they deal with the enormous phenomenon of universa! history. What you have in both cases is a conceptual model which always will represent certain aspects only, and for this reason will be one-sided or even lopsided. Hence the construction of conceptual models in history is not only permissible but, as a matter of fact, is at the basis of any historica! interpretation as distinguished from mere enumeration of data-i.e., chronicle or annals. If this is granted, the antithesis between idiographic and nomothetic procedure reduces to what psychologists are wont to call the "molecular" and "molar" approach. One can analyze events within a complex whole-individual chemica} reactions in an organism, perceptions in the psyche, for example; or one can look for overall laws covering the whole such as growth and development in the first or personality in the second instance. In terms of history, this means detailed study of individuals, treaties, works of art, singular causes and effects, etc., or else overall phenomena with the hope of detecting grand laws. There are, of course, all transitions between the first and second considerations; the extremes may be illustrated by Carlyle and his hero worship at one pole and Tolstoy (a far greater "theoretica! historian" than commonly admitted) at the other. The question of a "theoretica! history" therefore is essentially that of "molar" models in the field; and this is what the constmets of history amount to when divested of their philosophical embroidery. The evaluation of such models must follow the general rules ll2 GENERAL SYSTEM THEORY for verification or falsification. First, there is the consideration of empirica! bases. In this particular instance, it amounts to the question whether or not a limited number of civilizations-some 20 at the best-provide a sufficient and representative sample to establish justified generalizations. This question and that of the value of proposed models will be answered by the general criterion: whether or not the model has explanatory and predictive value, i.e., throws new light upon known facts and correctly foretells facts of the past or future not previously known. Although elementary, these considerations nevertheless are apt to remave much misunderstanding and philosophical fog which has clouded the issue. (1) As has been emphasized, the evaluation of models should be simply pragmatic in terms of their explanatory and predictive merits (or lack thereof); a priori considerations as to their desirability or moral consequences do not enter. Here we encounter a somewhat unique situation. There is little objection against so-called "synchronie" laws-i.e., supposed regularities governing societies at a certain point in time; as a matter of fact, beside empirica! study this is the aim of sociology. Also certain "diachronie" laws-i.e., regularities of development in time-are undisputed such as, e.g., Grimm's law stating rules for the changes of consonants in the evolution of Indo-Germanic languages. It is commonplace that there is a sort of "life cycle" -stages of primitivity, maturity, baroque dissalution of form and eventual decay for which no particular external causes can be indicated-in individual fieldsof culture, such as Greek sculpture, Renaissance painting or German music. Indeed, this even has its counterpart in certain phenomena of biologica! evolution showing, as in ammonites or dinosaurs, a first explosive phase of formation of new types, foliowed by a phase of speciation and eventually of decadence. Violent criticism comes in when this model is applied to civilization as a whole. It is a legitimate question-why often rather unrealistic models in the social sciences remain matters of academie discussion, while models of history encounter passionate resistance? Granting all factual criticism raised against Spengler or Toynbee, it seems rather obvious that emotional factors are involved. The highway of science is strewn with corpses of deceased theories which just decay or are preserved as mummies A dvances in General System T heory ll3 in the museum of history of science. In contrast, bistorical constructs and especially theories of bistorical cycles appear to touch a raw nerve, and so opposition is much more than usual criticism of a scientific theory. (2) This emotional involvement is connected with the question of "Historica! Inevitability" and a supposed degradation of human "freedom." Befare turning to it, discussion of rnathematical and non-mathematica! models is in order. Advantages and shortcomings of mathematica! models in the social sciences are well known (Arrow; 1956; Rapoport, 1957). Every mathematica! model is an oversimplification, and it remains questionable whether it strips actual events to the bones or cuts away vital parts of their anatomy. On the other hand, so far as it goes, it .permits necessary deduction with of ten unexpected results which would not be obtained by ordinary "common sense." In particular, Rashevsky has shown in several studies how mathematica! models of bistorical processes can be constructed (Rashevsky, 1951, 1952). On the other hand, the value of purely qualitative models should not be underestimated. For example, the concept of "ecologie equilibrium" was developed long before Volterra and others introduced mathematica! models; the theory of selection belongs to the stock-in-trade of biology, but the mathematica! theory of the "struggle for existence" is comparatively recent, and far from being verified under wildlife conditions. In complex. ph:nomena, ":xplanation in principle" (Hayek, 1955) ~y .quahtatlve models IS preferabie to no explanation at ~11. Th~s Is ~y no means limited to the social sciences and history; It apphes ahke to fields like meteorology or evolution. (3) "Historica! inevitability"-subje ct of a well-known study by Si.r Isaiah Berlin (1955) -dreaded as a consequence of "theoretica! history,". supposedl~ c~ntradicting our direct experience of having free chmces and ehmmating all moral judgment and values-is a phantasmagoria based upon a world view which does not exist any more. As in fact Berlin emphasizes, it is founded upon the concept of the Laplacean spirit who is able completely to predict the future from the past by means of deterministic laws. This has no resemblance to the modern concept of "laws of nature." All "laws of nature" have a statistica! character. They do not predict 114 GENERAL SYSTEM THEORY an inexorably determined future but probabilities which, depending on the nature of events and on the laws available, may approach certainty or else remain far below it. It is nonsensical to ask for or fear more "inevitability" in bistorical theory than is found in sciences with relatively high sophistication like meteorology or economics. Paradoxically, while the cause of free will rests with the testimony of intuition or rather immediate experience and can never he proved objectively ("Was it Napoleon's free will that led him to the Russian Campaign?"), determinism (in the statistica! sense) can he proved, at least in smali-scale models. Certainly business depends on personal "initiative," the individual "decision" and "responsibility" of the entrepreneur; the manager's choice whether or not to expand business by employing new appointees is "free" in precisely the sense as Napoleon's choice of whether or not to accept battle at the Moskwa. However, when the growth curve of industrial companies is analyzed, it is found that "arbitrary" deviations are foliowed by speedy return to the normal curve, as if invisible forces were active. Haire (1959, p. 283) states that "the return to the pattern predicted by earlier growth suggests the operadon of inexorable farces operating on the social organism" (our italics). It is characteristic that one of Berlin's points is "the fallacy of bistorical determinism (appearing) from its utter inconsistency with the common sense and everyday life of looking at human affairs." This characteristic argument is of the same nature as the advice not to adopt the Copernican system because everybody can see that the sun and not the earth moves from morning to evening. (4) Recent developments in rnathematics even allow to submit "free will"-apparently the philosophical problem most resistant to scientific analysis-to mathematica! examination. In the light of modern systems theory, the alternative between molar and molecular, nomothetic and idiographic approach can he given a precise meaning. For mass behavior, system laws would apply which, if they can he mathematized, would take the form of differential equations of the sort of those used by Richardson (cf. Rapoport, 1957) mentioned above. In contrast, free choice of the individual would he described by formulations of the nature of game and decision theory. Advances in General System Theory 115 Axiomatically, game and decision theory are concerned with "rational" choice. This means a choice which "maximizes the individuars utility or satisfaction," that "the individual is free to choose among several possible courses of action and decides among them at the basis of their consequences," that he "selects, being informed of all conceivable consequences of his actions, what stands highest on his list," he "prefers more of a commodity to less, other things being equal," etc. (Arrow, 1956). Instead of economical gain, any higher value may he inserted without changing the mathematica! formalism. The above definition of "rational choice" includes everything that can he meant by "free will." If we do not wish to equate "free will" with complete arbitrariness, lack of any value judgment and therefore completely inconsequential actions (like the philosopher's favorite example: It is my free will whether or not to wiggle my left little finger), it is a fair definition of those actions with which the moralist, priest or historian is concerned: free decision between alternatives based upon insight into the situation and its consequences and guided by values. . The difficulty to apply theory even to simple, actual situations IS of course enormous; so is the difficulty in establishing overall laws. However, without explicit formulation, both approaches can he evaluated in principle-leading to an unexpected paradox. ~he "principle of rationality" fits-not the majority of human acuons but rather the "unreasoning" behavior of animals. Animals and organisms in general do function in a "ratiomorphic" way, maxiruizing such values as maintenance, satisfaction, survival, etc.; they select, in genera!, what is biologically good for them, and prefer more of a commodity (e.g., food) to less. H uman behavior, on the other hand, falls far short of the principle of rationality. It is not even necessary to quote Freud to show how small is the compass of rational behavior in man. Women in a supermarket, in genera!, do not maximize utility but are susceptible to the tricks of the advertiser and packer; they do not make a rational choice surveying all possibilities and consequences; and do not even prefer more of the commodity packed in an inconspicuous way to less when packed in a big :ed box. with attractive design. In our society, it is the job of an mfluenual specialty-advertiser s, motivation researchers, etc.-to make choices irrational which essentially is done by coupling 116 GENERAL SYSTEM THEOR Y biologica! factors-conditi oned reflex, unconscious drives-with symbolic values (cf. von Bertalanffy, 1956a). And there is no refuge by saying that this irrationality of human behavior concerns only trivia! actions of daily life; the same principle applies to "historica!" decisions. That wise old bird Oxenstierna, Sweden's ChanceHor during the Thirty Years' War, expressed this perfectly by saying: Nescis) mi fili) quantilla ratione mundus regatur-you don't know, my dear boy, with what little reason the world is governed. Reading newspapers or listening to the radio readily shows that this applies perhaps even more to the 20th than the 17th century. Methodological ly, this leads to a remarkable conclusion. If one of the two models is to be applied, and if the "actuality principle" basic in bistorical fields like geology and evolution is adopted (i.e., the hypothesis that no other principlesof explanation should be used than can be observed as operative in the present)-then it is the statistica! or mass model which is backed by empirica! evidence. The business of the motivation and apinion researcher, statistica! psychologist, etc., is based upon the premise that statistica! laws obtain in human behavior; and that, for this reason, a small but well-chosen sample allows for extrapolation to the total population under consideration. The generally good working of a Gallup poll and prediction verifies the premise-with some incidental failure like the well-known example of the Truman election thrown in, as is to be expected with statistica! predictions. The opposite contention-tha t history is governed by "free will" in the philosophical sense (i.e., rational decision for the better, the higher moral value or even enlightened selfinterest) is hardly supported by fact. That here and there the statisticallaw is broken by "rugged individualists" is in its character. Nor does the role played in history by "great men" contradiet the system concept in history; they can be conceived as acting Iike "leading parts," "triggers" or "catalyzers" in the bistorical process -a phenomenon well accounted for in the general theory of systems. (5) A further question is the "organismic analogy" unanimously condemned by historians. They combat untiringly the "metaphysical," "poetical," "mythical" and thoroughly unscientific nature of Spengler's assertion that civilizations are a sort of Advances in General System Theory 117 "organisms," being bom, developing according to their internal Iaws and eventually dying. Toynbee (e.g., 1961) takes great pains .to emphasize that he did not fall into Spengler's trap-even though it is somewhat difficult to see that his civilizations, connected by the biologica! relations of "affiliation" and "apparentation," even with a rather strict time span of development, are not conceived organismically. Nobody should know better than the biologist that civilizations are not "organisms." It is trivia! to the extreme that a biologica! organism, a material entity and unity in space and time, is something different from a social group consisting of distinct individuals, and even more from a civilization consisting of generations of human beings, of material products, institutions, ideas, values, and what not. It implies a serious underestimate of Vico's, Spengler's (or any normal individual's) intelligence to suppose that they did not realize the obvious. Nevertheless, it is interesting to note that, in contrast to the historians' scruples, sociologists do not abhor the "organismic analogy" but rather take it for granted. For example, in the words of Rapopart and Horvath (1959): There is some sense in considering a real organization as an organism, that is, there is reason to believe that this comparison need not be a sterile metaphorical analogy, such as was common in schalastic speculation about the body politie. Quasibiologica! functions are demonstrabie in organizations. They maintain themselves; they sametimes reproduce or metastasize; they respond to stresses; they age, and they die. Organizations have discernible anatomies and those at least which transfarm material inputs (like industries) have physiologies. Or Sir Geoffrey Vickers (1957): Institutions grow, repair themselves, reproduce themselves, decay, dissolve. In their external relations they show many characteristics of organic life. Some think that in their internal relations also human institutions are destined to become increasingly organic, that human cooperation will approach ever more closely to the integration of cells in a body. I find this 118 GENERAL SYSTEM THEORY prospect unconvincing (and) unpleasant. (N.B., so does the present author.) And Haire (1959, p. 272): The biologica! model for social organizations-and here, particularly for industrial organizations-means taking as a model the living organism and the processes and principles that regulate its growth and development. It means looking for lawful processes in organizational growth. The fact that simple growth laws apply to social entities such as manufacturing companies, to urbanization, division of labor, etc., proves that in these respects the "organismic analogy" is correct. In spite of the historians' protests, the application of theoreticalmodels, in particular, the model of dynamic, open and adaptive systems (McClelland, 1958) to the historica! process certainly makes sense. This does not imply "biologism," i.e., reduction of social to biologica! concepts, but indicates system principles applying in both fields. (6) Taking all objections for granted-poor method, errors in fact, the enormous complexity of the historica! process-we have nevertheless reluctantly to admit that the cyclic roodels of history pass the most important test of scientific theory. The prediedons made by Spengler in The Decline of the West, by Toynbee when forecasting a time of trouble and contending states, by Ortega y Gasset in Revolt of the Masses-we may as well add Brave New World and 1984-have been verified to a disquieting extent and considerably better than many respectable roodels of the social scientists. Does this imply "historie inevitability" and inexorable dissolution? Again, the simple answer was missed by moralizing and philosophizing historians. By extrapolation from the life cycles of previous civilizations nobody could have predicted the Industrial Revolution, the Population Explosion, the development of atmnic energy, the emergence of underdeveloped nations, and the expansion of Western civilization over the whole globe. Does this refute the alleged model and "law" of history? No, it only says that this model-as every one in science-mirrors only certain aspects or facets of reality. Every model becomes dangerous only when it commits the "Nothing-but" fallacy which mars not only Advances in General System Theory 119 theoretica! history, but the roodels of the mechanistic world picture, of psychoanalysis and many others as well. . We have hoped to show in this survey that General System Theory has contributed toward the expansion of scientific theory; has led to new insights and principles; and has opened up new probieros that are "researchable," i.e., are amenable to further study, experimental or mathematica!. The limitations of the theory and its applications in their present status are obvious; but the principles appear to be essentially sound as shown by their application in different fields. The Organism Considered as Physical System 5 The Organism Considered as Physical System The Organism as Open System Physical chemistry presents the theory of kinetics and equilibria in chemica! systems. As example, consider the reversible reaction in ester formation: C 2 H 5 0H + CH 3 ·COOH +==± CH3COO·CzH5 + H20, in which always a certain quantitative ratio between alcohol and acetic acid on the one hand, and between ester and water on the other, is established. Application of physico-chemical equilibrium principles, especially of chemical kinetics and the law of mass action, has proved to be of fundamental importance for the explanation of physiological processes. An example is the function of blood, to transport oxygen from the lung to the tissues of the body and, conversely, carbon dioxide formed in the tissues to the lungs for exhalation; the process results from the equilibria between hemoglobin, oxyhemoglobin and oxygen according to the law of mass action, and quantitative formulations can be stated not only for the simple conditions in hemoglobin solution, but also for the more complicated ones in the blood of vertebrates. The importance of kinetic consideration of enzyme reactions, of respiration, fermentation, etc., is well known. Similarly, other physico-chemical equilibria (distribution, diffusion, adsorption, electrastatic equi- 121 libria) are of fundamental physiological significanee (cf. Moser and Moser-Egg, 1934). . Consiclering the organism as a whole, it shows characteristics similar to those of systems in equilibrium (cf. Zwaardemaker, 1906, 1927). We find, in the celland in the multicellular organism, a certain composition, a constant ratio of the components, which at first resembles the distribution of components in a chemical system in equilibrium and which, to a large extent, is maintained under different conditions, after disturbances, at different body size, etc.: an independenee of composition of the absolute quantity of components, regulative capacity after disturbances, constancy of composition under changing conditions and with changing nutrition, etc. (cf. von Bertalanffy, 1932, pp. 190ff.; 1937, pp. 80ff.). We realize at once, however, that there may be systems in equilibrium in the organism, but that the organism as such cannot be considered as an equilibrium system. The organism is not a closed, but an open system. We term a system "closed" if no material enters or leaves it; it is called "open" if there is import and export of materiaL There is, therefore, a fundamental contrast between chemical equilibria and the metabolizing organisms. The organism is not a static system closed to the outside and always containing the identical components; it is an open system in a (quasi-)steady state, maintained constant in its mass relations in a continuous change of component material and energies, in which material continually enters from, and leaves into, the outside environment. The character of the organism as a system in steady (or rather quasi-steady) state is one of its primary criteria. In a general way, the fundamental phenomena of life can be considered as consequences of this fact. Consiclering the organism over a shorter span of time, it appears as a configuration maintained in a steady state by the exchange of components. This corresponds to the first main field of general physiology-i.e., physiology of metabolism in its chemica! and energetic aspects. Superimposed on the steady state are smaller process waves, basically of two kinds. First there are periodic processes originating in the system itself and hence autonomie (e.g., automatic movements of the organs of respiration, circulation and digestion; automatic-rhythmic, electrical activities of nerve centers and the brain supposedly resulting from rhythmic chemica! discharges; automatic move- 122 GENERAL SYSTEM THEORY ments of the organism as a whole). Secondly, the organism reacts to temporary changes in environment, to "stimuli," with reversible fluctuations of its steady state. This is the group of processes caused by changes of external conditions and hence heteronomie subsumed in physio1ogy of excitation. They can be considered as temporary disturbances of the steady state from which the organism returns to "equilibrium," to the equal flow of the steady state. Such consideration has proved to be usefu1 and leading to quantitative formulations (cf. p. 137). Finally, the definition of the state of the organism as steady state is va1id only in first approximation, insofar as we envisage shorter periods of time in an "adult" organism, as we do, for examp1e, in investigating metabolism. If we take the total life cycle, the process is not stationary but on1y quasi-stationary, subject to changes slow enough to abstract from them for certain research purposes, and comprising embryonic development, growth, aging, death, etc. These phenomena, not quite exhaustively encompassed under the term of morphogenesis, represent the third large complex of problems in general physiology. Such consideration proves especially useful in areas accessible to quantitative formulation. . In genera!, physical chemistry is limited almost exclusively to consideration of processes in closed systems. To these refer the well-known formulations of physical chemistry; the law of mass action, in particular, is used only for definition of true chemical equilibria in closed systems. The applicability of chemica! equilibria to, e.g., transfer reactions is based on the fact that these are fast ionic reactions attaining equilibrium. Open chemica! systems are hardly taken into consideration in physical chemistry. This restrietion of kinetics to closed systems is understandable; for open systems are more difficult to establish technically, and not of major importance in the purely physical consideration. Nevertheless, such arrangements are easily visualizable-e.g., when in a reaction a p b the product b of the left-to-right reaction is continually removed from the system by suitable means (precipitation, dialysis through a membrane permeable only for b but not for a, etc.) while a is continually introduced into the system. Systems of this kind occasionally occur in technological chemistry; continuous fermentation in the production of acetic acid is an example for what is herecalled "open chemica! system." However, such systems are of great importance to the biologist. The Organism Considered as Physical System 123 For open chemica! systems are iudeed realized in nature in the form of living organisms, maintaining themselves in a continuous exchange of their components. "Life is a dynamic equilibrium in a polyphasic system" (Hopkins). We therefore need a definition of the so-called stationary equilibrium, the constancy of composition in the change of components, similarly as well-known expressionsof physical chemistry define true chemica! equilibria in closed systems. Obviously, the reaction system and reaction conditions are infinitely more complicated in organisms than in the systems usually dealt with in physical chemistry. These are reactions among an extraordinarily high number of components. Moreover, the cell and organism are not homogeneaus systems (a true solution), but represent highly heterogeneous, colloidal systems so that reactions depend not only on mass action but on many physico-chemical factors of adsorption, diffusion, etc. Even enzyme reactions in the test tube do not, in genera!, simply follow the law of mass action. This being the case, it is clear that reactions even in simple organismic systems cannot be written in a closed system of equations; this is possible only for isolated partial systems. It is, however, possible, first, to state certain general principles for open systems, irrespective of the special nature of the system. Secondly, although in view of the enormous number of reactions in the organism and even the individual cell, it is impossible to follow individual reactions, expressions can be used that represent statistica! averages of a multitude of incalculable or even unknown processes. Such a procedure is already applied in chemistry by using overall formulas for reactions consisting of numerous steps. Similarly, balance equations in physiology of metabolism and bioenergetics are based on statistica! averages resulting from numerous and largely unknown processes in intermediary metabolism. We may, for instance, summarize anabolic and catabolie processes as "assimilation" and "dissimilation," respectively, and consider, as a first approximation, the steady state as balance of "assimilation" and "dissimilation." Such magnitudes, representing statistica! averages of a multitude of inextricable processes, can be used for calculation in a way similar to that conventionally used in physical chemistry for individual compounds and reactions. The maintenance of the system in a continuous flow and ex- 124 GENERAL SYSTEM THEORY change of material and energy, the order of innumerable physicochemical reactions in a cell or organism in a way granting the first, the maintenance of a constant ratio of the components even under different conditions, after disturbances, at different sizes, etc., are the central problems of organic metabolism. The doublefaeed change of living systems in assimilation and dissimilation manifests-in the wordsof vonTschermaks (1916)-a trend toward maintenance of a certain state, regeneration compensating the disturbance caused by degeneration. How is it that what has been lost in the process is rebuilt from the materials offered in nutrition, that building blocks liberated by enzymes find the right place in the organismic system so that it maintains itself in metabolism? What is the principle of "automatic self-regulation" of metabolism? We are possessed of a vast knowledge of physicochemical processes in the cell and in the organism; but we must not overlook the fact "that even after complete explanation of individual processes, we are worlds away from fully understanding the total metabolism of a cell" (M. Hartmann, 1927, p. 258). Extremely Iittle is known about the principles cantrolling the individual processes in the way indicated above. No wonder that again and again the problem led to vitalistic conclusions (e.g. Kottje, 1927). Obviously, general principles as those we are going to develop cannot provide a detailed explanation of those problems; they can, however, indicate the general physical fóÛndations of that essential characteristic of life, self-regulation of metabolism and maintenance in change of components. The special way in which these are realized in individual metabolic processes can be determined only by experimental investigation. It can be hoped, however, that the general consideration alerts to possibilities hitherto hardly envisaged, and that the formulations proposed, or similar equations, he apt to describe concrete individual phenomena. General Characteristics of Open Chemica[ Systems True equilibria in closed systems and stationary "equilibria" in open systems show a certain similarity, inasmuch as the system, taken as a whole and in view of its components, remains constant in both systems. But the physical situation in both cases is fundamentally different. Chemica! equilibria in closed systems The Organism Considered as Physical System 125 are based on reversible reactions; they are a consequence of the second principle of thermodynamics and are defined by min~mum ·free energy. In open systems, in contrast, the steady state IS not reversible as a whole nor in many individual reactions. Furthermore, the second principle applies, by definition, to closed systems only and does not define the steady state. . . A closed system must, according to the second prmCiple, eventually attain a time-independent state of equilibrium, defi_n~d by maximum entropy and minimum free energy (heat e~mhb­ rium, thermadynamie derivation of the law of mass actiOn _by van't Hoff, etc.), where the ratio between the phases rema1ns constant. An open chemica! system may attain (certain conditions presupposed) a time-independent st~ad~ state, where ~he system remains constant as a whole and m 1ts (macroscopie) phases, though there is a continuous flow of component materials. . A closed system in equilibrium does not need energy for lts preservation, nor can energy be obtained from it. F~r example, a closed reservoir contains a large amount of (potenual) energy; but it cannot drive a motor. The same is true of a chemica! system in equilibrium. It is not a state of chemica! rest; rather reactions are continually going on, so regulated by the law of mass action that as much is formed of every species of molecules or ions as disappears. Nevertheless, the chemica! equilibrium is incapable of performing work. For maintaining the p~ocesses going on, no work is required nor can work be won from It. The algebraic sum of work obtained from and used by the elementary reactions equals zero. In order to perform work, it is necessary that the system be not in a state of equilibrium but ten~ t? attain it; only then can energy he won. In order that th1s 1s achieved continually, the hydrodynamic as well as chemica! system must be arranged as stationary-i.e., a steady flow of water or chemica! substances must be maintained whose energy content is transformed into work. Continuous working capacity is, therefore, not possible in a closed system which tends to attain equilibrium as soon as possible, but only in an open system. The apparent "equilibrium" found in an organism ~s. not a tr~e equilibrium incapable of performing work; rather 1t IS a dynam1c pseudo-equilibrium, kept constant at a certain distance from true equilibrium; so being capable of performing work but, ?n the other hand, requiring continuous import of energy for mamtaining the distance from true equilibrium. 126 GENERAL SYSTEM THEORY For the maintenance of "dynamic equilibrium," it is necessary that the rates of processes be exactly harmonized. Only in this way is it possible that eertaio components can be brok~n down, so Iiberating usabie energy while, on the other hand, Im~ort prevents the system from attaining equilibrium. Fast reactwns, al~o in the organism, lead to chemica! equilibrium (e.g. of hemoglobm and oxygen); slow reactions do not reach equilibrium b.ut are kept in a steady state. Therefore, the condition for the ex1stence of a chemica! system in a steady state is a eertaio slowness of reactions. Momentary reactions, like those between ions, lead to equilibrium in "infinitely short" time. The mai~te.nance of a steady state in the organism is due to the fact that It IS compo~ed of complex carbon compounds; these are, on the one hand, nch in energy but chemically inert, so that the maintenance of co~­ siderable chemica! potential is possible; on the other hand, rap1d and regulated release of this amount of energy is performed by enzyme actions, so that a steady state is maintained. For deriving conditions and characteristics of steady states we may use a general transport equation. Let Q, be a measure of the i-th element of the system, e.g. a concentration or energy in a system of simultaneous equations. lts variation may be expressed by: óQi = T. • ót + P.• (5.1) T, represents the velocity of transport of the element Q, in a volume element at a eertaio point of space, while P, is the rate of production. Many equations appearing in physics, biology and even sociology, eau be considered as special cases of (5.1). For example, in molecular magnitude, the P, are functions indicating the rate of reactions by which the substances Q, are formed and destroyed; the T. will have different forms depending on the system concerned. If, for example, no outer forces influence the masses, the T, will be expressed by Fick's diffusion equation. In case T, disappears, we have the usual equations for a set of reactions in a closed system; if P, disappears, we have the simple diffusion equation where T, has the form: T, = D,v·2 Qv the Laplacian symbol \72 representing the sum of the partial derivatives in x) y) z, the The Organism Considered as Physical System 127 D. the diffusion coefficients. In biology, equations of this type a;e found, e.g., in growth; and they appear in sociology and . population dynamics. In general, the rate of cha»:ge of ~ popul~­ tion equals the population movement (immigratwn mmus emigration) plus rate of reproduetion (birth minus death rate) .. In general, we therefore have a set of simultaneous partlal differential equations. P, as well as T, will, in general, be nonlinear functions of Q, and other system variables Q, and furthermore functions of the space coordinates x) y) z and timet. For solving the equation, we must know the special form of the . equations, and the initial and limiting conditions. For our purpose, two considerations are important, wh1ch we may call temporal cross and longitudinal sections. The first problem is the maintenance in a steady state which, biologically, is the fundamental problem of metabolism. The secoud concerns changes of the system with respect to time, biologically expressed, e.g. as growth. Briefly we shall also mention a third problemi.e., periodic changes as, in the organismic realm, are characteristic of autonomie processes such as automatic-rhythmical movements, etc. These three aspects correspond to the general problems of the three main fields of physiology (cf. pp. l2lf.). The problem of "longitudinal temporal section," of the changes of the system in time, will be answered by solution of differential equation of type (5.1). As a simple example, consider an open chemica! system, consisting of only one component Q, reaction material being continually imported and resulting reaction products removed. Let E be the amount of imported reaction material per time unit; k, the reaction constant according to the law of mass action; kQ, therefore, the amount of change per time unit; then, presupposed the amount imported at the beginning is greater than that transformed, the concentration of the system will increase according to the equation: dQ = E- kQ. (5.2) dt As is easily seen, this is a special case of the general equation (5.1). Since inflow was assumed to be constant and outflow equal to the chemica! reaction, hence diffusion and concentration 128 GENERAL SYSTEM THEORY gradients were neglected (or, as may be said, a complete "shaking" of the system was assumed), the space co-ordinates in (5.1) disappear; instead of a partial, we have an ordinary differential equation. Concentration at time t then is: The Organism Considered as Physical System For eliminating the constant in the first equation, equate it to 0; x 1 *, x 2 * ... be the roots of these equations. We introduce · as new variables: XI 1 (5.3) Q0 being the initial concentration at t = 0. Concentration there- fore asymptotically increases to a eertaio limit where turnover equals inflow (assumed to be constant). This maximal concentration is Qro = E/k. A system more approaching biologica} conditions is as follows. Let there be transport of material a 1 into the system proportional to the difference between its concentration outside and inside of the system (X-x 1 ). Biologically, we may here think of simple sugars or amino acids. The imported material a 1 may form, in a monomolecular and reversible reaction, a compound a 2 of concentration x 2 (e.g. monosaccharids transformed into polysaccharids, amino acids into proteins). On the other hand, the substance a 1 may be catabolized in an irreversible reaction (e.g. oxidation, desamination) into a3 ; and a3 may be removed from the system, proportional to its concentration. Then we have the following system of reactions: = X1 * - X1 ... (5.5) and reformulate (5.4) accordingly. The general type of such equations is: 1 1 aux 11 + a12X z + ... + dX = dt anx 1 1 + az2X + dX = dt I 1 2 ! 2 ... + (5.6) with the general solution (cf. p. 58): + C12eXzt + ... C1neXnt ~'. . ~- ~~ .e~1.t. ~- ~~ 2 ~~2: .~ ....... ~2-<n: x' 1 = 2 x'n = CueX 1 t 1 Cn1ex 11 an - À a 12 a22 - À ••. k1 x~ x1 Px2 aln • • • Gnn- kal xa Kd Outflow and equations: dx dt 1 dx2 dt = K 1(X- x 1) - k1x1 + k2x2 - kax1 = X1 (- K 1 - k1 - ka) k2x2 = k1x1 - + kzxz + K 1X (5.4) (5.7) + Cn2ex 21 + ... Cnnexnt = 0. K1 kz } The À's are given by the characteristic equation: a21 I 129 (5.8) À We now consider the temporal cross-section, i.e. the distribution of components in the time-independent steady state. In genera}, a system defined by equation (5.1) can have three different solutions. First, there can be unlimited increase of the Q;; secondly, a time-independent steady state may be attained; thirdly, there may be periodic solutions. It is difficult to prove the existence of a steady state for the general system (5.1), yet it can be shown in eertaio cases. Suppose that both terms are linear in the Q; and independent of t. Then the solution can be found by standard methods of integration and is of the form: Qi = Qi1(x,y, z) + Qi2 (x,_y, z, t), (5.9) where Q, 2 is a function of t which with increasing time is decreas- 130 GENERAL SYSTEM THEORY ing to zero for certain relations between constauts and Iimiting conditions. If, on the other hand, there is a time-independent steady state expressed by Q, 1 in (5.9), Q, 1 must suffice for the time-independent equation: T, + P, = 0 The Organism Considered as Physical System ratio of the components is maintained in changing inflow, chang· ing absolute size, etc. Furthermore we find: X1 (5.10) From this we see: (I) If there is a stationary solution, the composition of the system in the steady state remains constant with respect to the components Q, although the reactions continue and do not reach equilibrium as in a closed system, and although there is inflow and outflow of material; the situation so highly characteristic of organismic systems. (2) In the steady state the number of elements entering state Q, (x, y, z, t) by transport and chemica! reaction per time unit equals the number leaving it. Similar considerations can be made with respect to periadie solutions. It is true that the above derivation presupposes rather special assumptions on the nature of the equations. However, although no general criterion is known for the existence of stationary and periadie solutions in system (5.1), these conditions can be indicated for certain types of linear and even non-linear cases. Important to us is the fact that the existence of stationary, dynamic "equilibria" in open systems, or as we may also say, the existence of a certain order of processes guaranteed by dynamic rather than structural-mechanical principles, can be derived from general considerations. Solving equations (5.4) for the steady state we obtain: 131 *= K1+ka In case an external disturbance ("stimulus") leads to increased catabolism-e.g., increase of the reaction constant k 3 while the other constauts remain unaltered-x 1 decreases. Since, however, inflow is proportional to the concentration difference X-xv with increase of the latter intake is increased. If, after cessation of the "stimulus," the constant of catabolism returns to its normal value, the system will return to its original state. If, however, the disturbance and hence the change of rate of catabolism persists, a new steady state will be established. Thus the system develops farces directed against the disturbance, tending to compensate increased catabolism by increased intake. It therefore shows "adaptation" to the new situation. These, too, are "self-regulative" characteristics of the system. It can, therefore, be seen that the properties indicated as characteristic of organismic systems, are consequences of the nature of open systems: maintenance in "dynamic equilibrium," independenee of composition of the absolute quantity of components, maintenance of the composition under changing conditions and nutrition, reestablishment of dynamic equilibrium after normal catabolism or catabolism increased by a stimulus, dynamic order of processes, etc. "Self-regulation of metabolism" can be made understandable on the basis of physical principles. Equifinality X1 : X2 : Xa = 1 : kl : ka k2 K • 2 We therefore see that in the steady state a constant ratio between the components is established although it is not, as in a closed system, based on an equilibrium of reversible reactions, but the reactions are partly irreversible. Moreover, the ratio of components in the steady state depends only on the reaction constants, not on the amount of the inflow; the system thus shows "self-regulation," camparabie to organismic systems, where the One important characteristic of biologica! systems is circumscribed by terms like "purposiveness," "finality," "goal-seeking," etc. Let us see whether physical considerations can contribute to a clarification of these terms. It has aften been emphasized that every system attaining an equilibrium shows, in a certain way, "finalistic" behavior as was discussed previously (pp. 75f.). More important is the following consideration. Frequent attempts have been made to understand organic regulations as 132 I.,, GENERAL SYSTEM THEORY establishment of an "equilibrium" (of course, of extremely complicated nature) (e.g., Köhler, 1927), to apply LeChatelier's and similar principles. We are not in a position to define such "equilibrium state" in complicated organic processes, but we can easily see that such a conception is, in principle, inadequate. For, apart from certain individual processes, living systems are not closed systems in true equilibrium but open systems in a steady state. Nevertheless, steady states in open systems have remarkable characteristics. An aspect very characteristic of the dynamic order in organismic processes can be termed as equifinality. Processes occurring in machine-like structures follow a fixed pathway. Therefore the final state will be changed if the initia! conditions or the course of processes is altered. In contrast, the same final state, the same "goal," may be reached from different initia! conditions and in different pathways in organismic processes. Examples are the development of a normal organism from a whole, a divided or two fused ova, or from any pieces as in hydroids or planarians, or the reaching of a definite final size from different initia! sizes and after a different course of growth, etc. We may define: A system of elements Q, (x, y, z, t) is equifinal in any subsystem of elements QF if the initia! conditions Q,. (x, y, z) can be changed without changing the value of Q; (x, y, z, oo ). We can stipulate two interesting theorems: I. If there exists a solution of form (5.9), initia! conditions do not enter into the solution for the steady state. This means: lf open systems (of the kind discussed) attain a steady state, this has a value equifinal ar independent of initial conditions. A general proof is difficult because of the lack of general criteria for the existence of steady states; but it can be given for special cases. 2. In a closed system, some function of the elements-e.g., total mass or energy-is by definition a constant. Consider such an integral of the system, M(QJ If the initia! conditions of Q, are given as Q,., we must have: M(Qi) = M(Q,o) = M, (5.11) independent of t. If the Q., tend toward an asympotic value, Q,v The Organism Considered as Physical System M(Qil) = M 133 (5.12) M, however, cannot be entirely independent of Q,.; with change of Q,., also M and therefore M(Q;1) are altered. If this integral changes its value, at least some of the Qil must also change. This, however, is contrary to the definition of equifinality. We may therefore stipulate the theorem: A closed system cannot be equifinal with regard to all Q,. For example, in the simplest case of an open chemica! system according to equation (5.2), concentration at time t is given by (5.3); fort =ro, Q = Efk, i.e. it is independent of the initia! concentration Q. and dependent only on the system constauts E and k. A derivation of equifinality-i.e., the reaching of a steady state independent of time and initia! conditions-in ditfusion systems can be found in Rashevsky (1938, Chapter 1). The general consideration, of course, does not provide an explanation for specific phenomena if we do not know the special conditions. Yet, the general formulation is not without interest. We see, first, that it is possible to give a physical formulation to the apparently metaphysical or vitalistic concept of finality; as is well known, the phenomenon of equifinality is the basis of the so-called "proofs" of vitalism of Driesch. Secondly, we see the close relation between one fundamental characteristic of the organism, i.e. the fact that it is not a closed system in thermadynamie equilibrium but an open system in a (quasi-)stationary state with another one, equifinality. 1 A problem not here considered is the dependenee of a system not only on actual conditions, but also on past conditions and the course taken in the past. These are the phenomena known as "after-effect," "hereditary" (in mathematica! sense: E. Picard) or "historie" (Volterra) (cf. D'Ancona, 1939, Chapter XXII). In this category belong phenomena of hysteresis in elasticity, elec1 The limitations of organismic regulation are based on the fact that the organism (ontogenetically as wel! as phylogenetically) passes from the state of a system of dynamically interacting elements to the state of structural "mechanisms" and individual causa! ebains (cf. pp. 68ff.). lf the components become independent of each other, the change in each one depends only on the conditions within this component. Change or removal of a component must cause a final state different from the normal state; regulation is impossible in a completely "mechanized" system disintegrated into mutually independent causa! chains (except for control by feedback mechanisms cf. p. 42fl. and elsewhere) . \ I 134 GENERAL SYSTEM THEORY tricity, magnetism, etc. Taking dependenee on the past into consideration, our equations would become integro-differen tial equations as discussed by Volterra (cf. D'Ancona) and Donnan (1937). Biologica[ A pplications It should have become evident by now that many characteristics of organismic systems, often considered vitalistic or mystica!, can be derived from the system concept and the characteristics of certain, rather general system equations, in conneetion with thermadynamie and statistical-mech anical considerations. lf the organism is an open system, the principles generally applying to systems of this kind must apply to it (maintenance in change, dynamic order of processes, equifinality, etc.) quite irrespective of the nature of the obviously extremely complicated relations and processes between the components. Naturally, such a general consideration does not give an explanation for particular life phenomena. The principles discussed should, however, provide a general frame or scheme within which quantitative theories of specific life phenomena should be possible. In other terms, theories of individual biologica! phenomena should turn out as special cases of our general equations. Without striving for completeness, a few examples may show that and how the conception of organism as open chemica! system and steady state has proved an efficient working hypothesis in various fields. Rashevsky (1938) investigated, as a highly simplified theoretica! model of a cell, the behavior of a metabolizing droplet into which substances diffuse from outside, in which they undergo chemica! reactions, and from which reaction products flow out. This consideration of a simple case of open system (whose equations are special cases of our equation [5.1]) allows mathematica! deduction of a number of characteristics always considered as essential life phenomena. There results an order of magnitude for such systems conesponding to that of actual cells, growth and periadie division, the impossibility of spontaneous generation (omnis cellula e cellula), general characteristics of cell division, etc. Osterhout (1932-33) applied, and quantitatively elaborated, the open-system consideration to phenomena of permeability. He The Organism Considered as Physical System 135 stuclied permeation in cell models consisting of a non-aqueous Iayer surrounded by an aqueous outer and inner fluid (the latter conesponding to cell sap). An accumulation of penetrating s~b­ stances takes place within this cell, explained by salt formatiOn of the penetrating substance. The result is not an equilibrium but a steady state, in which the composition of the cell sap remains constant under increase of volume. This model is similar to that mentioned on p. 126. Mathematica! expressions were derived, and the kinetics of this model is similar to that in living cells. Open systems and steady states generally play a fundamental role in metabolism although mathematica! formulation has been possible only in simple cases or models. For example, t~e continuation of digestion is only possible because of the contmuous resorption of the products of enzymatic action by the intestine; it therefore never reaches a state of equilibrium. In other cases, accumulation of reaction products may lead to stopping the reaction which explains some regulatory processes (cf. von Bertalanffy, 1932, p. 191). This is true of the use of depot materials: Decomposition of starch stored in the endosperm of many plant seeds into soluble products is regulated by the need of the growing plant for carbohydrates; if development is experimentally inhibited, the use of starch in the endosperm stops. Pfeffer and Hansteen (quoted from Höber, 1926, p. 870) made it probable that the accumulation of sugar originating from digestion of starch and not used up by the inhibited seedling is the cause for the stopping of starch breakdown in the endosperm. If the endosperm is isolated and connected with a small plaster column, the breakdown of starch continues in the endosperm if the sugar diffuses through the plaster column into a quantity of water, but is inhibited if the column is placed in a small quantity of water only so that the concentration of sugar inhibits hydrolysis. One field where processes can already be formulated in the form of equations, is the theory of growth. It can be assurr:ed (von Bertalanffy, 1934), that growth is based on a counteractiOn of anabolic and catabolie processes: The organism grows when building-up surpasses breaking-down , and becomes stationary, when both processes are balanced. It can further be assumed that, in many organisms, catabolism is proportional to volume (weight), anabolism is proportional to resorption, i.e., a surface. 136 GENERAL SYSTEM THEORY This hypothesis can he supported by a number of morphological and physiological arguments and in simple cases, such as planarians, can he partly verified by measurement of intestinal surface (von Bertalanffy, 1940b). If K is a constant for catabolism per unit mass, total catabolism will he KW (w = weight); similar, with TJ as constant per unit surface, anabolism will he TJS, and weight increase defined by the dl.fference of these magnitudes: dw - dt = TJS- KW. (5.13) From this basic equation, expressions can he derived which quantitatively represent empirica! growth curves and explain a considerable number of growth phenomena. In simpler cases these growth laws are realized with the exactness of physical experiments. Moreover, the rate of catabolism can he calculated from growth curves and comparing values so calculated with those directly determined in physiological experiment, an excellent agreement is found. This tends to show, first, that the parameters of the equations are not mathematically constructed entities but physiological realities; secondly, that basic processes of growth are rendered by the theory (cf. Chapter 7). This example well illustrates the principle of equifinality discussed previously. From (5.13) follows for weight increase: (5.14) where E and k are constants related to TJ and K, and where w. is the initia! weight. The stationary final weight is given by w* (Ejk) 3 ; it is thus independent of the initia! weight. This can also he shown experimentally since the same final weight, defined by the species-specific constauts E and k, may he reached after a growth curve entirely different from the normal one (cf. von Bertalanffy, 1934). Obviously, this growth theory follows the conceptions of kinetics of open systems; equation (5.13) is a special case of the general equation (5.1). The basic characteristic of the organism, its representing an open system, is claimed to he the principle of organismic growth. = The Organism Considered as Physical System 137 Another field where this concept has proved itself fruitful is the phenomenon of excitation. Hering first considered the phenomena of irritability as reversible disturbances of the stationary flow of organismic processes. In the state of rest, assimilation and dissimilation are balanced; a stimulus causes increased dissimilation; but then the quantity of decomposable substances is decreased, the counteracting assimilation process is accelerated, until a new steady state between assimilation and dissimilation is reached. This theory has proved to he extremely fruitful. The theory of Pütter (1918-1920), further developed by Hecht (1931), considers the formation of excitatory substances from sensitive substances (e.g., visual purple in the rods of the vertebrate eye) and their disappearance as the basis of excitation. From the counteraction of these processes, production and remaval of excitatory substances, the quantitative relations of sensory excitation can he derived on the basis of chemica! kinetics and the law of mass action: threshold phenomena, adaptation to light and darkness, intensity discrimination, Weber's law and its limitations, etc. A similar hypothesis of excitatory and inhibitory substances and of a dissimilation mechanism under the influence of stimuli forms the basis of Rashevsky's theory (1938) of nervous excitation by electric stimuli, formally identical with the theory of excitation by Hili (1936). The theory of excitatory substances is not limited to sense organs and the peripheral nervous system, but applicable also to the transmission of excitation from one neuron to another at the synapses. Without entering the still unsettled question of a chemica! or electrical theory of transmission in the central nervous system, the first explains many of the basic features of the central nervous system compared with the peripheral nerve, such as irreciprocity of conduction, retardation of transmission in the central nervous system, summation and inhibition; here, too, is the possibility of quantitative formulations. Lapicque, e.g., developed a mathematica! theory of summation in the central nervous system; according to Umrath, it can he interpreted by the production and disappearance of excitatory substances. We may therefore say, first, that the large areasof metabolism, growth, excitation, etc., begin to fuse into an integrated theoreti- 138 GENERAL SYSTEM THEORY cal field, under the guidance of the concept of open systems; secondly, that a large number of problems and possible quantitative formulations result from this concept. In conneetion with the phenomena of excitation, it should be mentioned that this conception also is significant in pharmacological problems. Loewe (1928) applied the concept of the organism as open system in quantitative analysis of pharmacological effects and derived the quantitative relations {or the action mechanism of eertaio drugs ("put-in," "drop-in," "blockout" systems). Finally, problems similar to those discussed with respect to the individual organism also occur with respect to supra-individual entities which, in the continua! death and birth, immigration and emigration of individuals, represent open systems of a higher nature. As a matter of fact, the equations developed by Volterra for population dynamics, biocoenoses, etc. (cf. D'Ancona, 1939) belong to the general type discussed above. In conclusion, it may be said that consideration of organismic phenomena under the conception discussed, a few general principles of which have been developed, has already proved its importance for explanation of specific phenomena of life. 6 The Model of Open System The Living Machine and lts Limitations The present discussion may be started with one of those trivia! questions which are often only too difficult to answer scientifically. What is the difference between a normal, a sick and a dead organism? From the standpoint of physics and chemistry the answer is bound to be that the difference is not definable on the basis of so-called mechanistic theory. Speaking in termsof physics and chemistry, a living organism is an aggregate of a great number of processes which, suflident work and knowledge presupposed, can be defined by means of chemica! formulas, mathematica! equations, and laws of nature. These processes, it is true, are different in a living, sickor dead dog; but the laws of physics do not tell a difference, they are not interested in whether dogs are alive or dead. This remains the same even if we take into consideration the latest results of molecular biology. One DNA molecule, protein, enzyme or hormonal process is as good as another; each is determined by physical and chemica! laws, none is better, healthier or more normal than the other. Nevertheless, there is a fundamental difference between a live and a dead organism; usually, we do not have any difficulty in distinguishing between a living organism and a dead object. In a living being innumerable chemica! and physical processes are so "ordered" as to allow the living system to persist, to grow, to develop, to reproduce, etc. What, however, does this notion of "order" mean, for which we would look in vain in a textbook of 140 GENERAL SYSTEM THEORY physics? In order to define and exp1ain it we need a model, a conceptua1 construct. One such model was used since the beginnings of modern science. This was the model of the living machine. Depending on the state of the art, the model found different interpretations. When, in the seventeenth century, Descartes introduced the concept of the animal as a machine, only mechanica! machines existed. Hence the animal was a complicated clockwork. Borelli, Harvey and other so-called iatrophysicists explained the functions of muscles, of the heart, etc., by mechanica! principles of levers, pumps and the like. One can still see this in the opera, when in the Tales of Hoffmann the beautiful Olympia turns out to he an artfully constructed doll, an autornaton as it was called at the time. Later, the steam engine and thermodynamics were introduced, which led to the organism being conceived as a heat engine, a notion which lead to calorie calculations and other things. However, the organism is not a heat engine, transforming the energy of fuel into heat and then into mechanica! energy. Rather it is a chemodynamic machine, directly transforming the energy of fuel into effective work, a fact on which, for example, the theory of muscle action is based. Lately, self-regulating machines came to the fore, such as thermostats, missiles aiming at a target and the servomechanisms of modern technology. So the organism became a cybernetic machine, explanatory of many borneostatic and related phenomena. The most recent development is in terms of molecular machines. When one talks about the "mill" of the Krebs cycle of oxidation or about the mitochondria as "power plant" of the cell, it means that machinelike structures at the molecular level determine the order of enzyme reactions; similarly, it is a micromachine which transforms or translates the genetic code of DNA of the chromosomes into specific proteins and eventually into a complex organism. Notwithstanding its success, the machine model of the organism has its difficulties and limitations. First, there is the problem of the origin of the machine. Old Descartes did not have a problem because his animal machine was the creation of a divine watchmaker. But how do machines come about in a universe of undirected physico-chemical events? Clocks, steam engines and transistors do not grow by themselves in nature. Where do the infinitely more complicated living ma- The Model of Open System 141 chines come from? We know, of course, the Darwinistic explanation; but a doubt remains, particularly in the physically minded; there remain questions not usually posed or answered in textbooks on evolution. Secondly, thete is the problem of regulation. To he sure, selfrepairing machines are conceivable in terms of the modern theory of automata. The problem comes in with regulation and repair after arbitrary disturbances. Can a machine, say, an embryo or a brain, he programmed for regulation not after a certain disturbanee or finite set of disturbances, but after disturbances of an indefinite number? The so-called Turing machine can, in principle, resolve even the most complex process into steps which, if their number is finite, can he reproduced by an automaton. However, the number of steps may he neither finite nor infinite, but "immense," i.e., transeending the number of particles or possible events in the universe. Where does this leave the organism as machine or automaton? It is well-known that organic regulations of such sort were used by vitalists as proof that the organic machine is controlled and repaired by superphysical agents, socalled entelechies. Even more important is a third question. The living organism is maintained in a continuous exchange of components; metabolism is a basic characteristic of living systems. We have, as it were, a machine composed of fuel spending itself continually and yet maintaining itself. Such machines do not exist in present-day technology. In other words: A machinelike structure of the organism cannot he the ultimate reason for the order of life processes because the machine itself is maintained in an ordered flow of processes. The primary order, therefore, must lie in the process itself. Same Characteristics of Open Systems We express this by saying that living systems are basically~()pçn s~s (Burton, 1939; von Bertalanffy, 1940a; Chapter 5). An open system is defined as a system in exchange of matter with its environment, presenting import and export, building-up and breaking-down of its material components. Up to comparatively recent times physical chemistry, in kinetics and thermodynamics, was restricted to closed systems; the theory of open systems is relatively new and leaves many problems unsolved. The devel- 142 GENERAL SYSTEM THEORY opment of kinetic theory of open systems derives from two sources: first the biophysics of the living organism, secondly developments in industrial chemistry which, besides reactions in closed containers or batch processes, increasingly uses continuous reaction systems because of higher efficiency and other advantages. The thermadyna mie theory of open systems is the so-called irreversible thermodynam ics (Meixner & Reik, 1959); it became an important generalizatio n of physical theory through the work of Meixner, Onsager, Prigogine and others. Even simple open systems show remarkable characteristi cs (Chapter 5). Under certain conditions, open systems approach a time-indepe ndent state, the so-called steady state (Fliessgleichgewicht after von Bertalanffy, 1942). The steady state is maintained in distance from true equilibrium and therefore is capable of doing work; as it is the case in living systems, in contrast to systems in equilibrium . The system remains constant in its composition, in spite of continuous irreversible processes, import and export, building-up and breaking-do wn, taking place. The steady state shows remarkable regulatory characteristi cs which become evident particularly in its equifinality. If a steady state is reached in an open system, it is independen t of the initia! conditions, and determined only by the system parameters, i.e., rates of reaction and transport. This is called equifinality as found in many organISmic processes, e.g., in growth (FIG. 6.1). In contrast to closed The Model of Open System 143 physico-chemical systems, the same final state can therefore be reached equifinally from different initia! conditions and after disturbances of the process. Furthermore , the state of chemica! equilibrium is independen t of catalyzers accelerating the processes. The steady state, in contrast, depends on catalyzers present and their reaction constants. In open systems, phenomena of overshaat and false start (FIG. 6.2) may occur, with the system 200 150 V / 50 I/ 0 ./ -- '/ - ~ . /:-- ~ / ... i". -- -... "' / _...... , __ ............ I .... ....... ... ....,I / I ~ 25 50 75 100 125 150 175 200 225 250 Time in doys 275 300 Fig. 6.1. Equifinality of growth. Heavy curve: normal growth of rats. Broken curve: at the 50th day, growth was stopped by vitamin deficiency. After reestablishmen t of normal regime, the animals reached the normal final weight. (After Höber from von Bertalanffy, 1960b). Fig. 6.2. Asymptotic approach to steady state (a) , false start (b) , and overshoot (c), in open systems. Schematic. proceeding first in a direction opposite to that eventually leading to the steady state. Conversely, phenomena of overshoot and false start, as frequently found in physiology, may indicate that we are dealing with processes in open systems. From the viewpoint of thermodynam ics, open systems can maintain themselves in a state of high statistica! improbabilit y, of order and organization . According to the second principle of thermodynam ics, the general trend of physical processes is toward increasing entropy, i.e., states of increasing probability and decreasing order. Living systems maintain themselves in a state of high order and im- 144 GENERAL SYSTEM THEORY probability, or may even evolve toward increasing differentiation and organization as is the case in organismic development and evolution. The reason is given in the expanded entropy function of Prigogine. In a closed system, entropy always increases according to the Clausius equation: dS~O (6.1) In an open system, in contrast, the total change of entropy can he written according to Prigogine: dS = d.S + d,S, (6.2) d.S denoting the change of entropy by import, d,S the production of entropy due to irreversible processes in the system, such as chemical reactions, diffusion, heat transport, etc. The term d,S is always positive, according to the secoud principle; d.S, entropy transport, may he positive or negative, the latter, e.g., by import of matter as potendal carrier of free energy or "negative entropy." This is the basis of the negentropie trend in organismic systems and of Schrödinger's statement that "the organism feeds on negative entropy." More complex open-system models, approximating biologica! problems, have been developed and analyzed by Burton, Rashevsky, Hearon, Reiner, Denhigh and other authors. In recent years, computerization has been widely applied for the solution of sets of numerous simultaneous equations (frequently nonlinear) (e.g., Franks, 1967; B. Hess and others) and for the simulation of complex open-system processes in physiological problems (e.g., Zerbst and coworkers; 1963 ff.). Gompartment theory (Rescigno and Segre, 1967; Locker, 1966b) provides sophisticated methods for cases where reactions take place not in a homogenous space but in subsystems partly permeable to the reactants, as is the case in industrial systems and obviously many processes in the cell. As can he seen, open systems compared with conventional closed systems show characteristics which seem to contradiet the usual physicallaws, and which were often considered as vitalistic characteristics of life, i.e., as a vialation of physical laws, explainable only by introducing soul-like or entelechial factors into the organic happening. This is true of the equifinality of organic regulations, if, for example, the same "goal," a normal organism, is produced by a normal, a divided, two fused ova, etc. In fact, 145 The Model of Open System this was the most important "proof of vitalism" according to Driesch. Similarly, the apparent contradiction of the trend toward increase of entropy and disorder in physical nature, and the negentropie trend in development and evolution were often used as vitalistic arguments. The apparent contradictions disappear with the expansion and generalization of physical theory to open systems. Open Systems in Biology The model of open systems is applicable to many problems and fieldsof biology (Beier, 1962, 1965; Locker et al., 1964, 1966a). A survey of the biophysics of open systems, including theoretica! foundations and applications, was given some years ago (von Bertalanffy, l953a); a revised edition (with W. Beier, R. Laue and A. Locker) is presently in preparation. The present survey is restricted to some representative examples. There is, first, the large field of Goethe's Stirb und werde, the continuous decay and regeneration, the dynamic structure of living systems at all levels of organization (Tables 6.1-6.3). GenTable 6.1 Turnover rates of intermediates of cellular metabolism. (After B. HEss 196!S) structure mitod10ndria hemoglobin aldolase pseudodtolinesterase cholesterin fibrinogen glucose methionine ATP glycolysis ATP glycolysis + respiration ATP glycolysis + respiration citrate cycle intermediates glycolytic intermediates fla voproteinrcti.I fla voprotcinux. Fe2+/Fel+- cytodtrome a Fe2+/Fel+- cytochrome a:l species organ man rabbit man man man rat man man man !iver erythrocytes musde serum serum serum total organism total organism erythrocytes thrombocytes mouse ascites tumor mou~e rat kidney mouse mouse ascites tumor ascites tumor grasshopper wing muscle mouse ascites tumor turnover time in seconds 1.3X 101 1.5 x 107 1.7X10' 1.2X 10' 9.5X10' 4.8X 10' 4.4X 10' 2.2X10' 1.6X 10' 4.8X1o• 4.0X10 1 1 -10 0.1- 8.5 4.6X10"' 1o·• 1.9X 1o·• 146 GENERAL SYSTEM THEORY Table 6.2 Protein turnover determined by introduetion of glycine labelled with 15N. (After SPRINSON & RITTENBERG (l949b) turnov.er rate (r) RAT: total protein proteins of liver, plasma and internat organs rest of body 0.04 0.12 0.033 total protein proteins of liver and serum protein of musculature and other organs 0.0087 0.0693 0.0044 MAN: Table 6.3 Rate of mitosis in rat tissues. (After F. D. BERTALANFFY 1960) daily rate of mitosis (per cent) Organs without mitosis nerve cells, neuroepithelium, neurilemma, retina, adrenal medulla . . . . . . . . . 0 Organs with occasional mitosis but no cell renewal liver parenchyma, renal cortex and medulla, most glandular tissue, urethra, epididymis, vas deferens, muscle, vascular endothelium, cartilage, bone . . . . . . . less than 1 Organs with cel! renewal upper digestive tract . large intestine and anus stomach and pylorus small intestiite . . trachea and bronchus ureter and bladder . epidermis . . . sebaceous glands cornea . . . . . . . lymph node . . . . . pulmonar.y alvcolar cells . seminiferous epithelium . 7 -24 10 -23 11 -54 64 -79 2 - 4 1.6- 3 3 - 5 13 14 14 15 renewal time (days) 4.3-14.7 4.3-10 1.9- 9.1 1.3- 1.6 26.7-47.6 33 ~2.5 19.1-3H 8 6.9 6.9 6.4 16 The Model of Open System 147 erally it may be said that this regeneration takes place at far higher turnover rates than was anticipated. For example, it is certainly surprising that calculation on the basis of open system revealed that the proteins of the human body have a turnover time of not much more than a hundred days. Essentially the same is true for cells and tissues. Many tissues of the adult organism are maintained in a steady state, cells being continuously lost by desquamation and replaced by mitosis (F. D. Bertalanffy and Lau, 1962). Techniques such as the application of colchicine that arrests mitosis and thus permits counting of dividing cells over certain periods, as well as labelling with tritiated thymidine, have revealed a sametimes surprisingly high renewal rate. Prior to such investigations, it was hardly expected that cells in the digestive tract or respiratory system have a life span of only a few days. After the exploration of the paths of individual metabolic reactions, in biochemistry, it has now become an important task to understand integrated metabolic systems as functional units (Chance et al., 1965). The way is through physical chemistry of enzyme reactions as applied in open systems. The complex network and interplay of scores of reactions was clarified in functions such as photosynthesis (Bradley and Calvin, 1956), respiration (B. Hess and Chance, 1959; B. Hess, 1963) and glysolysis, the latter investigated by a computer model of some hundred nonlinear differential equations (B. Hess, 1969). From a more general viewpoint, we begin to understand that besides visible morphologic organization, as observed by the electron microscope, light microscope and macroscopically , there is another, invisible, organization resulting from interplay of processes determined by rates of reaction and transport and defending itself against environmental disturbances. Hydrodynamic (Burton, 1939; Garavaglia et al., 1958; Rescigno, 1960) and particularly dectronie analogs provide another approach besides physiological experiment, especially permitting solutions of multivariable problems which otherwise exceed time limits and available mathematica! techniques. In this way Zerbst et al. (1963ff.) arrived at important results on temperature adaptation of heart frequency, action potentials of sensory cells (amending the Hodgkin-Huxle y feedback theory), etc. Furthermore, energetic conditions have to be taken into ac- ) 148 GENERAL SYSTEM THEORY count. The concentration, say, of proteins in an organism does not correspond to chemica! equilibrium; energy expense is necessary for the maintenance of the steady state. Thermadynamie consideration permits an estimate of energy expense and comparison with the energy balance of the organism (Schulz, 19!?0; von Bertalanffy, 1953a). Another field of investigation is active transport in the cellular processes of import and export, kidney function, etc. This is connected with bioelectrical potentials. Treatment requires application of irreversible thermodynamics. In the human organism, the prototype of open system is the blood with its various levels of concentradons maintained constant. Concentrations and removal of both metabolites and administered test substances follow open-systems kinetics. Valuable clinical tests have been developed on this basis (Dost, 1953-1962). In a broader context, pharmacodynamic action in general represeuts processes taking place when a drug is introduced into the open system of the living organism. The model of the open system can serve as foundation of the laws of pharmacodynamic effects and dose-effect relations (Loewe, 1928; Druckery and Kuepfmüller, 1949; G. Werner, 1947). Furthermore, the organism responds to external stimuli. This can be conceived of as disturbance and subsequent reestablishment of a steady state. Consequently, quantitative laws in sensory physiology, such as the Weber-Fechner law, belong to open systems kinetics. Hecht (1931), long before the forma! introduetion of open systems, expressed the theory of photoreceptors and existing laws in the form of "open" reaction kinetics of sensitive materiaL The greatest of biologica! problems, remote from exact theory, is that of morphogenesis, the mysterious process whereby a nearly undifferentiated droplet of protoplasm, the fertilized ovum, becomes eventually transformed into the marvelous architecture of the multicellular organism. At least a theory of growth as quantitative increase can be developed (cf. pp. 17lff.). This has become a routine method in international fisheries (e.g., Beverton and Holt, 1957). This theory integrates physiology of metabolism and of growth by demonstrating that various types of growth, as encountered in certain groups of animals, depend on roetabolie constants. It renders intelligible the equifinality of growth The Model of Open System 149 whereby a species-specific final size is attained, even when starting conditions were different or the growth process was interrupted. At least part of morphogenesis is effectuated by so-called relative growth Q. Huxley, 1932), i.e., different growth rates of the various organs. This is a consequence of the competition of these components in the organism for available resources, as can be derived from open system theory (Chapter 7). Not only the cell, organism, etc., may be considered as open system, but also higher integrations, such as biocoenoses, etc. (d. Beier, 1962, 1965). The open-system model is particularly evident (and of practical importance) in continuous cell culture as applied in certain technological processes (Malek, 1958, 1964; Brunner, 1967). These few examples may suffice to indicate briefl.y the large fields of application of the open-system model. Years ago it was pointed out that the fundamental characteristics of life, m~tab~­ lism, growth, development, self-regulation, response to stlmuh, spontaneous activity, etc., ultimately may be considered as consequences of the fact that the organism is an open system. The theory of such systems, therefore, would be a unifying principle capable of combining diverse and heterogeneaus phenomena under the same general concept, and of deriving quantitative laws. I believe this prediction has on a whole proved to be correct and has been testified by numerous investigations. Bebind these facts we may trace the outlines of an even wider generalization. The theory ~fcop~n systems is part of a general system theory. This doctrine is concerned with principles that ~pply to systems in genera!, irrespective of the nature of their components and the forces governing them. With general system theory we reach a level where we no longer talk about physical and chemica! entities, but discuss wholes of a completely general nature. Yet, certain principles of open systems still hold true and may be applied successfully to wider fields, from ecology, the competition and equilibrium among species, to human economy and other sociological fields. Open Systems and Cybernetics Here the important question of the relation of general system theory and cybernetics, of open systems and regulatory mecha- 150 GENERAL SYSTEM THEORY nisrus appears (cf. pp. 160ff.). In the present context a few remarks will suffice. The basis of the open-system model is the dynamic interaction of its components. The basis of the cybernetic model is the feedback cycle (FIG. I.l) in which, by way of feedback of information, a desired value (Sollwert) is maintained, a target is reached, etc. The theory of open systems is a generalized kinetics and thermodynamics. Cybernetic theory is based on feedback and information. Both models have, in respective fields, been successfully applied. However, one has to be aware of their differences and limitations. The open-system model in kinetic and thermadynamie farmulation does not talk about information. On the other hand, a feedback system is closed thermodynamically and kinetically; it has no metabolism. In an open system increase of order and decrease of entropy is thermodynamically possible. The magnitude, "informatiön," is defined by an expression formally identical with negative entropy. However, in a closed feedback mechanism information can only decrease, never increase, i.e., information can be transformed into "noise," but notvice versa. An open system may "actively" tend toward a state of higher organization, i.e., it may pass from a lower to a higher state of order owing to conditions in the system. A feedback mechanism eau "reactively" reach a state of higher organization owing to "learning," i.e., information fed into the system. In summary, the feedback model is preeminently applicable to "secondary" regulations, i.e., regulations based on structural arrangements in the wide sense of the word. Since, however, the structures of the organism are maintained in metabolism and exchange of components, "primary" regulations must evolve from the dynamics in an open system. Increasingly, the organism becomes "mechanized" in the course of development; hence later regu1ations particularly correspond to feedback mechanisms ,(homeostasis, goal-directed behavior, etc.). The open-system model thus represents a fertile working hypothesis permitting new insights, quantitative statements and experimental verification. I would like, however, to mention some important unsolved problems. The Model of Open System 151 Unsolved Problems At present, we do not have a thermadynamie criterion that would define the steady state in open systems in a similar way as maximum entropy defines equilibrium in closed systems. It was believed for some time that such criterion was provided by minimum entropy production, a statement known as "Prigogine's Theorem." Although it is still taken for granted by some biologists (e.g., Stoward, 1962), it shou1d be emphasized that Prigogine's Theorem, as was well known to its author, applies only under rather restrictive conditions. In particular, it does not define the steady state of chemica! reaction systems (Denbigh, 1952; von Bertalanffy, 1953a, 1960b; Foster et al., 1957). A more recent generalization of the theorem of minimum entropy production (Glansdorff and Prigogine, 1964; Prigogine, 1965) encompassing kinetic considerations has still to be evaluated in its consequences. Another unsolved problem of a fundamental nature originates in a basic paradox of thermodynamics. Eddington called entropy "the arrow of time." As a matter of fact, it is the irreversibility of physical events, expressed by the entropy function, which gives time its direction. Without entropy, i.e., in a universe of completely reversible processes, there would be no difference between past and future. However, the entropy functions do not contain time explicitly. This is true of both the classica! entropy function for closed systems by Clausius, and of the generalized function for open systems and irreversible thermodynamics by Prigogine. The only attempt I know of to fill this gap is a further generalization of irreversible thermodynamics by Reik (1953), who attempted to introduce time explicitly into the equations of thermodynamics. A third problem to be envisaged is the relation between irreversible thermodynamics and information theory. Order is the basis of organization and therefore the most fundamental problem in biology. In a way, order can be measured by negative entropy in the conventional Boltzmann sense. This was shown, e.g., by Schulz (1951) for the nonrandom arrangement of amino acids within a protein chain. Their organization in contrast to hazard arrangement can be measured by a term called chain entropy (Kettenentropie). However, there exists a different ap- 152 GENERAL SYSTEM THEORY proach to the problem, i.e., by measurement in terms of yes-or-no decisions, so-called bits, within the framework of information theory. As is well-known, information is defined by a term formally identical with negative entropy, thus indicating a correspondence between the two different theoretica! systems of thermodynamics and of information theory. Elaboration 'of a dictionary, as it were, for translating the language of thermodynamics into that of information theory and vice versa, would seem to be the next step. Obviously, generalized irreversible thermodynamics will have to be employed for this purpose because it is only in open systems that maintenance and elaboration of order do not run contrary to the basic entropy principle. The Russian biophysicist Trincher (1965) came to the condusion that the state function, entropy, is not applicable to living systems; he contrasts the entropy principle of physics with biologica! "principles of adaptation and evolution," expressing an increase of information. Here we have to take into consideration that the entropy principle has a physical basis in the Boltzmann derivation, in statistkal mechanics and in the transition toward more probable distributions as is necessary in chance processes; presently, no physical explanation can be given for Triucher's phenomenological principles. Here we are dealing with fundamental problems which, I believe, "are swept under the carpet" in the present biologica! creed. Today's synthetic theory of evolution considers evolution to be the result of chance mutations, after a well-known simile (Beadle, 1963), of "typing errors" in the reduplication of the genetic code, which are directed by selection, i.e., the survival of those populations or genotypes that produce the highest number of offspring under existing external conditions. Similarly, the origin of life is explained by a chance appearance of organic compounds (amino acids, nucleic acids, enzymes, ATP, etc.) in a primeval ocean which, by way of selection, formed reproducing units, viruslike forms, protoorganisms, cells, etc. In contrast to this it should be pointed out that selection, competition and "survival of the fittest" already presuppose the existence of self-maintaining systems; they therefore cannot be the result of selection. At present we know no physical law which would prescribe that, in a "soup" of organic compounds, open systems, self-maintaining in a state of highest improbability, are The Model of Open System 153 formed. And even if such systems are accepted as being "given," there is no law in physics stating that their evolution, on the whole, would proceed in the direction of increasing organization, i.e., improbability. Selection of genotypes with maximum offspring helps little in this respect. It is hard to understand why, owing to differential reproduction, evolution ever should have gone beyond rabbits, herring or even bacteria, which are unrivaled in their reproduetion rate. Production of local conditions of higher order (and improbability) is physically possible only if "organizational forces" of some kind enter the scene; this is the case in the formation of crystals, where "organizational forces" are represented by valencies, lattice forces, etc. Such organizational forces, however, are explicitly denied when the genome is considered as an accumulation of "typing errors." Future research will probably have to take into consideration irreversible thermodynamics, the accumulation of information in the genetic code and "organizational laws" in the latter. Presently the genetic code represents the vocabulary of hereditary substance, i.e., the nucleotide triplets which "spell" the amino acids of the proteins of an organism. Obviously, there must also exist a grammar of the code; the latter cannot, to use a psychiatrie expression, be a word salad, a chance series of unrelated words (nucleotide triplets and corresponding amino acids in the protein molecules). Without such "grammar" the code could at best produce a pile of proteins, but not an organized organism. Certain experiences in genetic regulation indicate the existence of such organization of the hereditary substratum; their effects will have to be studied also in macroscopie laws of evolution (von Bertalanffy, 1949a; Rensch, 1961). I therefore believe that the presently generally accepted "synthetic theory of evolution" is at best a partial truth, not a complete theory. Apart from additional biologica! research, physical considerations have to be taken into account, in the theory of open systems and its present borderline problems. Condusion The model of the organism as open system has proved useful in the explanation and mathematica! formulation of numerous life phenomena; it also leads, as is to be expected in a scientific 154 GENERAL SYSTEM THEORY working hypothesis , to further problems, partly of a fundamen tal nature. This implies that it is not only of scientific but also of "meta-s~ientific" importanc e. The mechanist ic concept of nature ~redommant so far emphasize d the resolution of happening s into hnear causal chains; a conception of the world as ,a result of chance events, and a physical and Darwinisti c "play of dice" (Einstein); the reduction of biologica! processes to laws known from inanimate nature. In contrast to this, in the theory of open sys_te~s (and its further generaliza tion in general system theory), prmoples of multivaria ble interactio n (e.g., reaction kinetics, fluxes and forces in irreversibl e thermodyn amics) become apparent, a dynamic organizati on of processes and a possible expansion of physical laws under considerat ion of the biologica! realm. Therefore , these developme nts form part of a new farmulation of the scientific world view. 7 Some Aspects of System Theor y in Biology Introducin g the present symposium on Quantitativ e Biology of Metabolism , the speaker's task, it would seem, is to outline the conceptual framework of the field, mustrating its leading ideas, theories, or-as we may preferably say-the conceptual constructs or models applied. According to widesprea d opinion, there is a fundamen tal distinetion between "observed facts" on the one hand-whi ch are the unquestio nable rock bottorn of science and should be collected in the greatest possible number and printed in scientific joumals -and "mere theory" on the other hand, which is the product of speculatio n and more or less suspect. I think the first point I should emphasize is that such antithesis does not exist. As a matter of fact, when you take supposedl y simple data in our field-say, determina tion of Qo 2 , basal roetabolie rates or temperature coefficien ts-it would take hours to unravel the enormous amount of theoretica ! presuppos itions which are necessary to form these concepts, to arrange suitable experimen tal designs, to create machines doing the job-and this all is implied in your supposedl y raw data of observatio n. If you have obtained a series of such values, the most "empirica! " thing you can do is to present them in a table of mean values and standard deviations . This presuppos es the model of a binomial distributi on-and with this, the whole theory of probabilit y, a profound and to a large extent unsolved problem of mathemati cs, philosoph y and even metaphysic s. If you are lucky, your data can be plotted in a simple fashion, obtaining the graph of a straight line. But considering the unconceiv able complexit y of processes even in a simple cell, it is little short of a miracle that the simplest possible 156 GENERAL SYSTEM THEORY model-na mely, a linear equation between two variables- actually applies in quite a number of cases. Thus even supposedly unadulter ated facts of observatio n already are interfused with all sorts of conceptua l pictures, model concepts, theories or whatever expression you choose. The choice is not whether to remain in the field of data or to theorize; the choice is only between models that are more or less abstract, generalize d, near or more remote from direct observatio n, more or less suitable to represent observed phenomen a. On the other hand, one should not take scientific models too seriously. Kroeber (1952), the great American anthropolo gist, once made a learned study of ladies' fashions. You know, sametimes skirts go down until they impede the lady in walking; again, up they go to the other possible extreme. Quantitati ve analysis revealed to Kroeber a secular trend as well as short-perio d fluctuation s in the length of ladies' skirts. This is a perfectly good little law of nature; however, it has little to do with the ultimate reality of nature. I believe a certain amount of intellectua l humility, lack of dogmatism , and good humor may go a long way to facilitate otherwise embittered debates about scientific theories and models. It is in this vein that I am going to discuss four models which are rather fundamen tal in the field of quantitati ve metabolism . The models I chose are those of the organism as open system and steady state, of homeostasis, of allometry, and the so-called Bertalanff y model of growth. This is not to say that these models are the most important ones in our field; but they are used rather widely and can illustrate the conceptua l framework as well as others. Open Systems and Steady States Any modern investigat ion of metabolism and growth has to take into account that the living organism as well as its components are so-called open systems, i.e., systems maintaini ng themselves in a continuou s exchange of matter with environme nt (FIG. 7.1). The essential point is that open systems are beyond the limits of conventio nal physical chemistry in its two main branches, kinetics and thermodyn amics. In other terms, conventional kinetics and thermodyn amics are not applicable to many Same Aspects of System Theory in Biology b ' ' ...... ___ 157 ~-- Fig. 7.1. a: Model of a simple open system, showing maintenance of constant concentratio ns in the steady state, equifinality, adaptation and stimulus·res ponse, etc. The model can be interpreted as a simplified schema for protein synthesis (A: amino acids, B: protein, C: deamination products; k 1 : polymerizat ion of amino acids into protein, k 2 : depolymerization, k 3 : deamination ; k 2 « k 1 , energy supply for protein synthesis not indicated) . In somewhat modilied form, the model is Sprinson & Rittenherg's (1949) for calculation of protein turnover from isotope experiments. (After von Bertalanffy, l953a) . b: The open system of reaction cycles of photosynthe sis in algae. (After Bradley & Calvin, 1957) 158 GENERAL SYSTEM THEORY processes in the living organism; for biophysics-the application of physics to the living organism-an expansion of theory is necessary. The living cell and organism is not a static pattem or machinelike structure consisting of more or less permanent "building materials" in which "energy-yielding materials" from nutrition are broken down to provide the energy requirements for life processes. It is a continuous process in which both so-called building materials as well as energy-yielding substances (Bau- and Betriebsstoffe of classica! physiology) are broken down and regenerated. But this continuous decay and synthesis is so regulated that the cell and organism are maintained approximately constant in a so-called steady state ( Fliessgleichgewicht, von Bertalanffy). This is one fundamental mystery of living systems; all other characteristics such as metabolism, growth, development, self-regulation, reproduction, stimulus-response, autonomous activity, etc., are ultimately consequences of this basic fact. The organism's being an "open system" is now acknowledged as one of the most fundamental criteria of living systems, at least so far as German science is concerned (e.g:, von Bertalanffy, 1942; Zeiger, 1955; Butenandt 1955, 1959). Before going further, I wish to apologize to the German colleagues for dwelling on matters which are familiar to them, and which I myself have often presented. As Dost (1962a) stated in a recent paper, "our sons already in their premedical examination take account of this matter," i.e., of the theory of open systems in their kinetic and thermadynamie formulations. Rememberto ~uote but two examples-the presentation of the topic by Blasms (1962) in the new editions of our classic LandoisRosemann textbook, and Netter in his manurnental Theoretica! Biochemistry (1959). I am sorry to say that the same does not apply to biophysics and physiology in the United States. I have looked in vain into leading American texts even to find the terms, "open system," "steady state" and "irreversible thermodynamics." That is to say, precisely that criterion which fundamentally distinguishes living systems from conventional inorganic ones is generally ignored or bypassed. Consideration of the living organisms as an open system exchanging matter with environment comprises two questions: first, their staties, i.e., maintenance of the system in a time-independent state; secondly, their dynamics, i.e., changes of the system in time. SameAspectsof System Theory in Biology 159 The problem can be considered from the viewpoints of kinetics and of thermodynamics. Detailed discussion of the theory of open systems can be found in the literature (extensive bibliographies in von Bertalanffy 1953a, 1960b). So I shall restriet myself to saying that such systems have remarkable features of which I will mention only a few. One fundamental difference is that closed systems must eventually attain a time-independent state of chemica! and thermadynamie equilibrium; in contrast, open systems may attain, under certain conditions, a time-independent state which is called a steady state, Fliessgleichgewicht, using a term which I introduced some twenty years ago. In the steady state, the composition of the system remains constant in spite of continuous exchange of components. Steady states or Fliessgleichgewichte are equifinal (FIG. 6.1); i.e., the same time-independent state may be reached from different initia! conditions and in different ways-much in contrast to conventional physical systems where the equilibrium state is determined by the initia! conditions. Thus even the simplest open reaction systems show that characteristic which defines biologica! restitution, regeneration, etc. Furthermore, classica! thermodynamics, by definition, is only concerned with closed systems, which do not exchange matter with environment. In order to deal with open systems, an expansion and generalization was necessary which is known as i?Teversible thermodynamics. One of its consequences is elucidation of an old vitalistic puzzle. According to the secoud principle of thermodynamics, the general direction of physical events is toward statesof maximum entropy, probability and molecular disorder, levelling down existing differentiations. In contrast and "violent contradiction" to the second principle (Adams, 1920), living organisms maintain themselves in a fantastically improbable state, preserve their order in spite of continuous irreversible processes and even proceed, in embryonic development and evolution, toward ever higher differentiations. This apparent riddle disappears by the consideration that the classic second principle by definition pertains only to closed systems. In open systems with intake of matter rich in high energy, maintenance of a high degree of order and even advancement toward higher order is thermodynamically permitted. Living systems are maintained in a more or less rapid exchange, degeneration and regeneration, catabolism and anabolism of their 160 GENERAL SYSTEM THEORY components. The living organism is a hierarchical order of open systems. What imposes as an enduring structure at a certain level, in fact, is maintained by continuous exchange of components of the next lower level. Thus, the multicellular organism maintains itself in and by the exchange of cells, the cell in the exchange of cell structures, these in the exchange of composing chemica! èompounds, etc. As a general rule, turnover rates are the faster the smaller the components envisaged (Tables 6.1-3). This is a good illustration for the Heraclitean flow in and by which the living organism is maintained. So much about the statics of open systems. If we take a look at changes of open systems in time, we also find remarkable characteristics. Such changes may occur because the living system initially is in an unstable state and tends toward a steady state; such are, roughly speaking, the phenomena of growth and development. Or else, the steady state may be disturbed by a change in external conditions, a so-called stimulus; and this-again roughly speaking-comprises adaptation and stimulus-response. Here too characteristic differences to closed systems obtain. Closed systems generally tend toward equilibrium states in an asymptotic approach. In contrast, in open systems, phenomena of false start and overshoot may occur (FIG. 6.2). In other terms: If we find overshoot or false start-as is the case in many physiological phenomena-we may expect this to be a process in an open system with certain predictabie mathematica! characteristics. As a review of recent work (Chapter 6) shows, the theory of the organism as an open system is a vividly developing field as it should he, consictering the basic nature of biologica! Fliessgleichgewicht. The above examples are given because, after the basic investigations by Schönheimer (1947) and his group into the "Dynamic State of Body Constituents" by way of isotope tracers, the field is strangely neglected in American biology which, under the inftuence of cybernetic concepts, rather has returned to the machine concept of the cell and organism, thereby neglecting the important principles offered by the theory of open systems. Feedback and Romeostasis Instead of the theory of open systems, another model construct I! Same Aspects of System Theory in Biology 161 is more familiar to the American school. It is the concept of feedback regulation, which is basic in cybernetics and was biologically formulated inCannon's concept of borneostasis (e.g., Wiener, 1948; Wagner, 1954; Mittelstaedt, 1954, 1956; Kment, 1957). We can give it only a brief consideration. As is generally known, the bas1c model is a circular process where part of the output is monitored back, as information on the preliminary outcome of the response, into the input (FIG. 7.2a), thus making the system self-regulating; he it in the sense of maintenance of certain variables or of steering toward a desired goal. The first is the case, e.g., in a simple thermostat and in the maintenance of constant temperature and many other parameters in the living organism; the second, in self-steering missiles and proprioceptive control of voluntary movements. More elaborate feedback arrangements in technology and physiology (e.g., FIG. 7.2b) are variations or aggregates of the basic scheme. Phenomena of regulation following the feedback scheme are of widest distribution in all fields of physiology. Furthermore, the concept appeals to a time when control engineering and automation are ftourishing, computers, servomechanisms, etc., are in the center of interest, and the model of the "organism as servomechanism" appeals to the Zeitgeist of a mechanized society. Thus the feedback concept sametimes has assumed a monopoly suppressing other equally necessary and fruitful viewpoints: The feedback model is equated with "systems theory" in general (Grodin, 1963; Jones and Gray, 1963; Casey, 1962), or "biophysics" is nearly identified with "computer design and information theory" (Elsasser, 1958, p. 9). It is therefore important to emphasize that feedback systems and "homeostatic" control are a significant but special class of self-regulating systems and phenomena of adaptation (cf. Chapter 6). The following appear to he the essential criteria of feedback control systems: (1) Regulation is based upon preestablished arrangements ("structures" in a broad sense). This is well expressed by the German term Regelmechanismen which makes it clear that the systems envisaged are of the nature of "mechanisms"-in contrast to regulations of a "dynamic" nature resulting from free interplay of forces ahd mutual interaction between components and tending toward equilibrium or steady states. (2) Causal trains within the feedback system are linear and uni- 162 GENERAL SYSTEM THEORY STIMULUS ---+ IRECEPTOR ,__..... ~ . RESPONSE MESSAGE MESSAGE Same Aspects of System Theory in Biology CON'IROL APPARATUS I ® FEEDBACK Cerebral cortex I Governit;tg value ,.. Regulation device Central switching mechanisms ~ _N_,_ ya_g_u~ _.,. Dieneephalon rr=.:E ~ t " lpancreo tropie H. Hypophysis ' ILrenotropi: ~!"i ACTH corticotro~ thvreotropic H. i __., B-cells Pancreas is lands A-cells Medulla Ad renals Cortex Insulin ~M;Q!L__ Adrenalin Glucocorticoids Thyroid Thyroxin Somatotrooin Cor ticos teroids Adrenalin Insulin ,...___ Feedback Regulation value - - Glycosensible recepters in pancreas, C,N,S, (hypothetical Blood sugar Liver storage TnrrP•<P Re:=on ( Blood sugar level mg% )~oc<oo Muscle energy consumption Kidney overflow Blood sug:~ valve Decrease Gevernor system t_______Disturbance factor r-- 1--....- . . I I I I I I Fig. 7.2. a: Simple feedback scheme. b: Romeostatic regulation of the blood sugar level. (After Mittelstaedt, 1954.) directional. The basic feedback scheme (FIG. 7.2) is still the classica! stimulus-response (S-R) scheme, only the feedback loop being added so that causality becomes circular. 163 (3) Typical feedback or homeostatic phenomena are "open" with respect to incoming information, but "closed" with respect to matter and energy. The concepts of information theoryparticularly in the equiva1ence of information and negative entropy-correspond therefore to "closed" thermodynamics (thermostatics) rather than irreversible thermodynamics of open systems. However, the latter is presupposed if the system (like the living organism) is to he "self-organizing" (Foerster and Zopf, 1962), i.e" is to go toward higher differentiation. As was mentioned above, no synthesis is reached as yet. The cybernetic scheme permits, by way of block diagrams, clarification of many important phenomena of self-regulation in physiology and lends itself to information-theoretical analysis. The open-system scheme permits kinetic and thermadynamie analysis. Comparison of flow diagrams of feedback (FIG. 7.2) and open systems (FIG. 7.1) intuitively shows the difference. Thus dynamics in open systems and feedback mechanisms are two different model concepts, each in its right in its proper sphere. The open-system model is basically nonmechanistic, and transcends not only conventional thermodynamics, but also one-way causality as is basic in conventional physical theory (cf. Chapter 4). The cybernetic approach retains the Cartesian machine model of the organism, unidirectional causality and closed systems; its novelty lies in the introduetion of concepts transeending conventional physics, especially those of information theory. Ultimately, the pair is a modern expression of the ancient antithesis of "process" and "structure"; it will eventually have to he resolved dialectically in some new synthesis. Physiologically speaking, the feedback model accounts for what may he called "secondary regulations" in metabolism and other fields, i.e., regulations by way of preestablished mechanisms and fixed pathways, as in neurohormonal controL lts mechanistic character makes it particularly applicable in the physiology of organs and organ systems. On the other hand, dynamic interplay of reactions in open systems applies to "primary regulations" such as in cell metabolism (cf. Hess and Chance, 1959) where the more general and primitive open-system regulation obtains. Allometry and the Surface Rule Let us now proceed to the third model which ts the so-called 164 GENERAL SYSTEM ·THEORY principle of allometry. As is well known, many phenomena of metabolism, and of biochemistry, morphogenesis, evolution, etc., follow a simple equation: Some Aspectsof System Theory in Biology 165 Table 7.1 Metabolism in dogs. (After RUBNER around 1880) (7.1) ! , I i.e., if a .variable y is plotted logarithmically against another variabie x, a straight Iine results. There are so many cases where this equation applies that examples are unnecessary. Therefore let us look instead at fundamentals. The so-called allometric equation is, in fact, the simplest possible law of relative growth, the term taken in the broadest sense; i.e., increase of one variable, y, with respect to another variabie x. We see this immediately by writing the equation in a somewhat different form: dy . _!_ : dx . _.!_ = Rel. Gr. Rate (y, x) = a. x dt y dt (7 .2) As can easily he seen, the allometric equation is a solution of this function which states that the ratio of the relative increase of variabie y to that of x is constant. We arrive at the allometric relation in a simple way by consirlering that any relative growth -only presupposed it is continuous-ca n generally he expressed by: R. G. R. (y,x) = F, (7.3) where F is some undefined function of the variables concerned. The simplest hypothesis is that F he a constant, rz, and this is the principle of allometry. However, it is well known that historically the principle of allometry came into physiology in a way very different from the derivation given. It appeared in a much more special form when Sarrus and Rameaux found around 1840 that metabolic rate in animals of different body weight does not increase in proportion to weight, but rather in proportion to surface. This is the origin of the famous surface law of metabolism or law of Rubner, and it is worthwhile to take a look at Rubner's original data of about 1880 (Table 7.1). In dogs of varying weight, metabolic rate decreases if calculated per unit of weight; it remains approximately constant per unit surface, with a daily rate of about 1000 kcal. per square meter. As is well known, the so-called surface law has caused an enormous debate and literature. In fact, Rubner's law is a very special case of the allametrie function, y representing ' ~ , !! I weight in kg 3.1 6.5 11.0 17.7 19.2 23.7 30.4 caL production per kg 85.8 61.2 57.3 45.3 44.6 40.2 34.8 caL production per sq. m body surface 1909 1073 1191 1047 1141 . 1082 984 basal metabolic rate, x body weight, and the exponent rz amounting to 2/3. I believe ~hat the general derivation just mentioned puts the surface law mto correct perspective. Endless discussions of some 80 years are overcome when we consider it a special case of allom:try, a~d t~ke the allometric equation for what it really is: a h1g?I~ s1mphfied, approximate formula which applies to an astomshmgly broad range of phenomena, but is neither a dogma nor an explanation for everything. Then we shall expect all sorts of allometric relationships of metabolic measures and body s~ze-with ~ ce~tain preponderance of surface or 2/3-power functwns, cons1dermg the fact that many metabolic processes are controlled by surfaces. This is precisely what we find (Table 7.2). In Qther words, 2/3 is not a magie number; nor is there anything sacr:d about the 3/4 power which more recently (Brody, 1945; Kle1ber, 1961) has been preferred to the classica! surface Iaw. Even the expression: Gesetz der fortschreitende n Stoffwechselreduktion (Lehmann, 1956)-law of progressive reduction of metabolie rate-is not in place because there are metabolic processes which do not regress with increasing size. Furthermore, from this it follows that the dependenee of metabolic rates on body size is not invariable as was presupposed by t~e surface law.. It rather can vary, and indeed does vary, espeCially as a functwn of (1) the organism or tissue in question; (2) physiological conditions; and (3) experimental factors. As to the variation of metabolic ra te depending on the organism 166 GENERAL SYSTEM THEORY Table 7.2 Equations relating quantitative properties with body weights among mammals. (After AnoLPH 1949; modified) intake of water (ml!hr) urine output (ml!hr) urea clearance (ml/hr) inulin clearance (ml!hr) creatinine clearance (ml/hr) diodrast clearance (ml/hr) hippurace clearance (m!Jhr) Q., consum. basal (mi STP/hr) he7mbeat duration (hr) breath duration (hr) ventilation ra te (ml!hr) tidal volume (mi) gut beat duration (hr) N total output (g/hr) N endogenous output (g/hr) creatinine N output (g/hr) sulphur output (g/hr) 0• consum. !i ver slices -(mi STP/hr) hemoglobin wt (g) .82 .72 1.31 .62 .62 myoglobin wt (g) cytoduome wt (g) nepbra number .77 .69 .89 .80 .734 .27 .28 .74 1.01 .31 .735 .72 .90 .74 .77 .99 .08 diameter renal corp. (cm) kidneys wt (g) brain wt (g) he art wt (g) lungs wt (g) liver wt (g) thyroids wt (g) adrenals wt {g) pituitary wt (g) stom. + intes. wt (g) blood wc (g) .85 .70 .98 .99 .87 .80 .92 .76 .94 .99 Surface /a7p: a == .66 relacive ~o absolu~e weight (y = bw•);- .33 relattve to untt weight ( ~ 167 15t;:-_ -------------------------------------lK~ney ~1=--------------- regression a regression a - .88 SameAspectsof System Theory in Biology 101-- er- ····-::-.-:- ~ --- --- _________ ••••••••• -· Brom Liver -,- --. ---- -- ~~;~~US ·-------------- Diophrogm :: 3 I I 8 10 -- ·····-~-~-:::-.:::::_~----... ~~ I I 20 I 30 I I 40 50 60 ' 11 I I I I 200 80 100 300 400 Body weight in g Fig. 7.3. Qo2 (1110 2 jmg dry wt.jhr.) of several rat tissues. On1y regression lines are shown in this and the following figures; for complete data see originals. (After von Bertalanffy & Pirozynski, 1953.) Table 7.3 = bw• ) Intraspecific and interspecific allometry (constants "') in organs of mammals. (After VON BERTALANFFY & PIROZYNSKI 1952) or tissue concerned, I shall give later on examples with respect to total metabolism. Differences in size dependenee of Qo 2 in various tissues are shown in Figure 7.3. A similar example is presented in Table 7.3 with respect to comparison of intra- and interspecHic allometries. Variations of size-dependence of metabolie rate with physiological conditions are demonstrated by data obtained in our laboratory in an impörtant aspect which has been little investigated. The size-dependence of metabolism as expressed in the allometry exponent a varies, depending on whether basal metabolic rate (B.M.R.), resting metabolism, or metabolism in muscular activity is measured. Figure 7.4 shows such variation in rats, comparing basal and nonbasal metabolic rates. Figure 7.5 gives a more extensive comparison in mice, including different degrees of muscular activity. These data confirm Locker's statement (l96la) that with increasing intensity of metabolic rate, a tends to decrease. Variations in the slope of the regression lines are also found in invertebrates when metabolic rates of fasting and nonfasting animals are compared (FIG. 7.6). Variations of a with experimental conditions .deser~e much more attention than usually given. Often the attitude IS rat B. & P. BRODY bra in 0.20 0.17 heart 0.82 0.80 cat ~ 0.92 0.82 lungs !i ver kidneys 0.73 0.75 dog monkey various authors cattie horse adult mammals jnterspecific 0.24 0.66 0.69 0.58 0.54 0.83 0.82 0.85 0.84 0.98 0.98 0.99 0.25 0.62 0.30 1.00 0:86 0.93 0.69 0.93 0.82 0.92 0.58 1. Cycle: 1. Cvcle: 1.26 1.'14 2. Cycle: 2. c,·cle 0.67 0.'68 0.80 0.82 0.71 ~ 0.65 0.61 0.70 0.70 0.61 0.87 0.88 0.92 0.66 0.85 0.87 0.76 taken as if Qo 2 were a constant characteristic of the tissue under consideration. This is by no means the case. Variations appear, for exampk, with different bases of reference, such as fresh weight, dry weight, N-content, etc. (Locker, 1961 b). The simplest Ba1al (Su~m~èr) ·~ Same Aspects of System Theory in Biology GENERAL SYSTEM THEORY 168 l"o a 1 30~""'40--60e-:-·--ioïLoo---,,"'ooc---~d·o ;----------------:1.1'),) ~'00 r Weight in Gum• Non Basal Condltlonll ••• + / : I J~:o I n..ul (Winter) -·· • Bual (Surroner) --- + JO b 40 60 80 100 W~lght 200 60 400 iD Gr&mt Fig. 7.4. Size dependenee of metabolic rates in rat under basal and nonbasal conditions. Animals fasted for 18 hrs. prior to experiment (small animals less); determinations at 29°-30oC; conditions of muscular rest. A break in the regression lines is assumed at a body weight of 110 gm., corresponding with many physiological changes (cf. Fig. 7.11) . "Basal Summer" determinations were made with a climatization period of 15-18 hours at thermoneutrality preceding experiment; "Basal Winter" without climatization; "Nonbasal conditions" with 10 hours fasting, foliowed by a meal 45-60 minutes prior to experiment. a<! , b ~ (Unpublished data by Racine & von Bertalanffy.) I I I i . I lfi :i,': 169 demonstration is change of the medium. Not on1y-as every experimenter knows-does the absolute 'magnitude of Qo 2 vary greatly depending, e.g., on whether saline or medium with metabolites is used; the same is true of size dependenee or the parameter a (FIG. 7.7). Locker's rule, as mentioned previously, again is verified; its confirmations by the experiments summarized in Figures 7.4, 7.5 and 7.7 are particularly impressive because they were obtained independent of and prior to statement of the rule. The variation of Qo 2 in different media indicates that different partial processes in respiration are measured. This is the reasou why I doubt that total metabolism or B.M.R. can be obtained by so-called summated tissue respiration (Martin and Fuhrmann, 1955). Which Qo 2 of the individual tissues 15 20 3ody :.:t in 25 30 ~ Fig. 7.5. Size dependenee of metabolic rates in mice. Determinations at 2~o and 21 oe: p~e~ious fasting and climatization. In the experiments wlth muscular act1v1ty, the scattering of va1ues is considerable owing to the ~i~culty in keeping the performed work constant. Therefore the quahtatlve . statement that the slope of the regression lines decreases is well estab~1shed, but no particular significanee should be attached to the numencal va1ues of u.. (Unpublished data by Racine & von Berta1anffy.) s?ould he summated? The Qo 2 as obtained, say, in Ringer solutiOn or that obtained with metabolites which may be twice as high? How do the different a's of the various tissues add up to the 2/3 or 3/4 observed in B.M.R. of the entire animal? Simi1arly, Locker (1962) has shown that also the component processes of Qo2, such as carbohydrate and fat respiration, may have different regressions. Before leaving this topic, I would like to make another remark on principle. We have to agree that the allametrie equation is, at best, a simplified approximation. Nevertheless, it is more than a convenient way of platting data. Notwithstanding its simplified 170 GENERAL SYSTEM THEORY mm~o. hr. 200 100 a 80 20 10 10 20 30 40 50 100 200 300 Fig. 7.6. o consumption of larvae of T_~ne~rio molit~r _(2?°C). a: larvae 2 fed; b: starved for two days. In b, Muller s and Teissier s values combined. (After von Bertalanffy & Müller, 1943.) SameAspec tsof System Theory in Biology 171 character and mathematica ! shortcoming s, the principle of allometry is an expression of the interdepende nce, organization and harmonizati on of physiologica l processes. Only because processes are harmonized, the organism remains alive and in a steady state. The fact that many processes follow simple allometry, indicates that this is a general rule of the harmonizati on of processes (Adolph, 1949): "Since so many properties have been found to be adequately interrelated by equations of one form, it seems very unlikely that other properties would be related according to a radically different type of equation. For if they were, they would be incompatibl e with the properties reviewed." Furthermore , although we encounter a wide range of values of allometry constants, these certainly are not accidental. At least to a wide extent, they depend on biotechnical principles. It is a truism in engineering that any machine requires changes in proportion to remain functional if it is built in different size, e.g., if a smali-scale model is increased to the · desired working size. To an extent, it can be understood why certain types of allometry, such as dependenee on surface, body mass, etc., obtain in particular cases. The studies by Günther and Guerra (1955) and Guerra and Günther (1957) on biologica! similarity, the relations of birds' wings (Meunier, 1951), pulse rate (von Bertalanffy, l960b) and brain weight (von Bertalanffy and Pirozynski, 1952) to body size are examples of functional analysis of allometry which, I believe, will become an important field for further research. Theory of Animal Growth Body Weight in Gra::ts Fig. 7.7. Size dependenee of ~o of diaphragm _in different media .. a: 2 Krebs-Ringer phosphate soluuon; b: Krebs medmm I!, type A, with glucose; c: Same medium, with glucose and metabohtes. (After von Bertalanffy & Estwick, 1953.) The last model I wish to discuss is the model of growth, honorifically called the Bertalanffy equations (von Bertalanffy, 1957b, l960b); basic ideas go back to the great German physiologist Pütter (1920). Here, too, I am not primarily concerned with details or even the merits and shortcoming s of the model; I rather wish to use it to make clear some principles in quantitative metabolism research. We all know, firstly, that the process of growth is of utmost complexity; and secondly, that there is a large number of formulas on the market which claim satisfactorily to represent observed growth data and curves. The general procedure was that some 172 GENERAL SYSTEM THEORY more or 1ess complex and more or less plausible equation was proposed. Then the investigator sat down to calculate a number of growth curves with that formula, and was satisfied if a sufficient approximati on of empirica! data was obtained. Here is a first illusion we have to destroy. It is a mathematica ! rule of thumb that almost every curve can be approximate d if three or more free parameters are permitted-i. e., if an equation contains three or more so-called constants that cannot be verified otherwise. This is true quite irrespective of the particular form of the equation chosen; the simplest equation to be applied is a power series (y = a. 0 + a.1 x + a. 2 x 2 + ...) developed to, say, the cubic term. Such calculation is a mere mathematica ! exercise. Closer approximati on can always be obtained by permitting further terms. The consequence is that curve-fitting may be an indoor sport and useful for purposes of interpolatio n and extrapolatio n. However, approximati on of empirica! data is not a verification of particular mathematica ! expressions used. We can speak of verification and of equations representing a theory only if (l) the parameters occurring can be confirmed by independen t experiment; and if (2) predictions of yet unobserved facts can be derived from the theory. It is in this sense that I am going to discuss the so-called Bertalanffy growth equations because, to the best of my knowledge, they are the only ones in the field which try to meet the specifications just mentioned. The argument is very simple. If an organism is an open system, its increase or growth rate (G.R.) may, quite generally, be expressed by a balance equation of the form: dw = G.R. dt = Synth. - Deg. +. (7 .4) i.e., growth in weight is represented by the difference between processes of synthesis and degeneration of its building materials, plus any number of indetermina te factors that may influence the process. Without loss of generality, we may further assume that the terms are some undefined functions of the variables concerned: + .. . . G.R. = j 1(w, t) - fz (w, t) (7.5) Now we see immediately that time t should not enter into the equation. For at least some growth processes are equifinal, i.e., Same Aspects of System Theory in Biology 173 the same final values can be reached at different times (FIG. 6.1). Even without strict mathe~natical proof, we can see intuitively that this would not be possible if growth rate directly depends on time; for if this were the case, different growth rates could not occur at given times as is sometimes the case. Consequentl y, the terros envisaged will be functions of body mass present: (7.6) if we tentatively limit the consideratio n to the simplest opensystem scheme. The simplest assumption we can make is that the terros are power functions of body mass. And, indeed, we know empirically that quite generally the size dependenee of physiologica l processes can well be approximate d by allometric expressions. Then we have: (7.7) where 77 and K are constants of anabolism and catabolism, respectively, conespondin g to the general structure of allometric equations. Mathematic a! consideratio ns show furthermore that smaller deviations of the exponent m from unity do not much influence the shape of the curves obtained. Thus, for further simplificatio n let us put m = 1. This makes things much easier mathematica lly, and appears to be justified physiologically, since physiologica l experience- limited it is true-seems to show that catabolism of building materials, especially proteins, is roughly proportiona l to body mass present. Now let us make a big leap. Synthesis of building materials needs energy which, in aerobic animals, is provided by processes of cell respiration and ultimately the ATP system. Let us assume there are correlations between energy metabolism of an animal and its anabolic proce~~ès. This is plausible insofar as energy metabolism must, in one way or the other, provide the energies that are required for synthesis of body components . We therefore insert for size dependenee of anabolism that of roetabolie rates (n = a.) and arrive at the simple equation: dw - dt = '17Wa- KW. (7.8) GENERAL SYSTEM THEORY 174 SameAspe ctsof System Theory in Biolog;y 175 The salution of this equation is: w = { 'Y/ K ( 'Y/ --Wo (1-a)) e-(1-a)Kt } 1/1 -a (7 .9) K with w 0 = weight at time t = 0. Empiricall y, we find that resting metabolism of many anima~s is surface-de pendent, i.e., that they follow Rubner's ~ul_e. I? th1s case, we set cz = 2j3. There are other animals where 1t 1s d1rectly dependent on body mass, and then cz = 1. Finally, cases are found where metabolic rate is in between surface and mass proportionality, that is 2/3 < cz < 1. Let us ten~atively ref;; to the~e differences in size-depen dence of metabohc rate as metabohc types." . . Now if we insert the different values for cz mto our bas1c equation, we easily see that they yield very different curves of growth. Let us refer to them as "growth types." T_hese are ~um­ marized in Table 7.4; conespond ing graphs, showmg the dlfferences in metabolic behavior and concomita nt differences of growth curves, are presented in Figure 7.8. Detailed discussion s of the theory have been given elsewhere. lt has been shown that the above derivation s apply in many cases; no less than fomteen different arguments in verificatio n of the theory can b~ pres_ented (Table 7.5, FIGs. 7.9, 7.10). We shalllimit the present d1scuss10n to a few remarks on principle. All parameter s of the growth equations are verifiable ex~eri­ mentally. cz, the size dependene e of metabolic rate, determme s the shape of the growth curve. This correlation has been confirmed in a wide range of cases, as seen in Table 7.4 K, constant of catabolism , can in first approxima tion be identified with turnover of total protein (r) as determine d by isotape tracers an_d other techniques . For example, from the growth curves catabohc rates of 0.045/day for the rat, and 1.165 g. proteinfkg . body wt.jday for man were calculated (von Bertalanffy , 1938). Determinatio ns of protein catabolism then available did not agree with these prediction s: protein loss determine d by minimum N-excretio n was 0.00282jd ay for the rat after Terroine, and some 0.4-0.6 g. proteinfkg . body wt.jday for man, according to the conception s then prevailing in physiology (von Bertalan~y, 1942, pp. 180ff., 186-188). It was therefore a striking confirmat1 0n Table 7.4 Metabolic types and growth types. w, l: Weight, length at time t; w , l : initia! weight, length; w*, 1*: final weight, length; 'lJ, k; constants0 of0 anabolism and catabolism. (After VON BERTALANFF Y 1942) Metabolic type I. Respiration surfaceproportional Growth type Growth equations Examples (a) Linear growth curve: du·/dt = "JW'Ia- "w Lamelliattaining without ina) l = l''-(l'"-lo)e-•t:'3 branchs, fish, f/exion a steady state, mammals 3 (b) Weight grom:h curve: bJ w= [~1 w'·-( 3 sigmoid, attaining, with wo)e-•<13]3 inflexion at c. 1/3 of final weight, a steady Vw.*- state U. Respiration weightproportional Linear and weight dcddt = >jW-XW growth curves exponen- a) l = loea/3 tial, no steady state b) w = woe<t = CW Insect larvae, attained, but growth intercepted by meta· morphosis or seasonal cycles UI. Respiration intermedia te between surfaceand u:eightproportion.1/ity (a) Linear growth curve: do::/dt = "JW•-xw; 1 attaining with infiexion ' a<n< 1 a steady state. (b) Weight growth curve: dl/dt = !J.' /ln-Z._ !../ 3 3 sigmoid, similar to I (b) Orthoptera, Helicidae Planorbidae of the theory when later on determîna tions using the isotape method (Sprinson and Rittenberg , 1949, Table 6.2) yielded turnover rates of total protein (r) of 0.04/day for the rat, and of 1.3 g. protein/kg . body wt.jday for man in an amazing agreement between predicted and experimen tal values. It may be noted in passing that an estimate of the turnover time of the human organism similar to that found in isotape experimen ts (r ""' 0.009, t ""' 110 days) can be obtained in different ways, e.g., also from calorie loss in starvation (t = 100 days: Dost, 1962a). 71, constant of anabolism , is dimension ally complex. It can, however, be checked by compariso n of growth curves of related organisms: according to theory, the ratio of metabolic rates should correspond to the ratio of 11 's of the animals concerned . This also has been confirmed (FIG. 7.10). GENERAL SYSTEM THEORY 176 SameAspec tsof System Theory in Biology 177 Table 7.5 .. • i• . 1/ 1 8 Ë ' eo á.l I I 30 100 200 300 Weight in mg 1 / 140 V 1 ' ~ 3040 eo eo1oo 200 300 1[711 40 la.. I ((o 8 Ti~ 10 20 12 inWMks 0 1..,- 1 J I i I !h, 11 20 60 40 Time- in I-tours • -•- .r I I ,ó ' fiI ". 80 :!00 I' " ' V 17 I :, I ~~ ' • "' I 8 12 Time 16 20 24 in WHks (Orosopl'lilo) I 21.1 32.0 42.3 51.4 60.1 68.0 75.3 82.3 89.0 95.3 101.6 107.6 112.7 117.7 122.2 126.5 130.9 135.3 140.2 145.0 148.6 152.0 5 • 8 I 3 2 10~ lifll '\ 70 100 200 observed 1 2 3 4 '' I "' !+ r1 4 V ö v. Ë I wr I .J.. ~ • Weighl in mg • time in years I' I: .. 8 (Tenebrio) 100 b y0.7~ 1...1 ' : 1 I ~ eoo . 2 :! Growth of Acipenser stellatus (After VON BERTALANFFY 1942) m Fig. 7.8. Metabolic and growth types. Type I: Lebistes reticulatus; type II: insect larvae; type lil: Plunorbis sp. a: dependenee of metabolic rate on body size; b: growth curves. (After von Bertalanffy, 1942.) 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 length in cm calculated 21.1 34.3 41.5 50.8 59.5 67.8 75.5 82.8 89.7 96.2 102.3 108.0 113.4 118.5 122.5 127.9 132.2 136.2 140.0 143.5 146.9 150.0 k 0.062 0.062· 0.061 0.061 0.061 0.060 0.060 0.059 0.059 0.059 0.060 0.059 0.059 0.058 0.059 0.059 0.059 0.060 0.061 0.061 0.061 = Growth. equation: l 201.1 (201.1 - 21.1) -o.o6•. Owing to the regulanty o.f growth curves, the BERTALANFFY equations are most suitable for calculatwn of growth in .fish. In this example, the growth constant k ( k(3) was. calculated m a way similar to calculation of reaction constant.s m chemica! reactions. Variations of this parameter are minima!, so showiUg the adequacy of the equation. = The theory, therefore, fulfills the first postulate indicated above, i.e., verification of calculated parameters in independen t experiments. As has been shown elsewhere, it also fulfills the secoud postulate: Predictions from the theory were made which came as "surprises," i.e., were unknown at the time, but later on confirmed. Discussion of some typical objections is in place because it may contribute to better understandi ng of mathematica ! models in gener al. (1) The main reproach against models and laws for physiological phenomena is that of "oversimplif ication." In a process such as animal growth there is, at the level of cells, a microcosm of innumerable processes of chemical and physical nature: all the reactions in intermediary metabolism as well as factors like cell permeability , diffusion, active transport and innumerable others. On the level of organs, each tissue behaves differently with respect to cell renewal and growth; besides multiplicati on of cells, formation of intercellular substances is included. The organism as a whole changes in composition , with alterations of the content in pr~tein, deposition of fat or simple intake of water; the specific ~e1ght ~f ~rgans changes, not to speak of morphogene sis and differentlatiO n which presently elude mathematica ! formulation . Is not any simple model and formula a sort of rape of nature, pressing reality into a Procrustean bed and recklessly cutting off what doesn't fit into the mold? The answer is that science in GENERAL SYSTEM THEORY 178 30 40 5eeo 200 100 lhdy weigtt in g 0 100 200 I--e 300 Tme in days 400 Fig. 7.9. Calculation of growth of the white rat. Many physiological processes in the rat show discontinuities at about 100 gm. body weight, i.e., in the prepubertal stage (a) . Such "cycle" also appears in metabolism (Fig. 7.4), metabolic rates in animals under 100 gm. increasing more, and in animals above this size much less than would correspond to the surface rule. However, if regression is calculated over the whole weight range, a value near 2/3 results as gross average. Hence, in the calculation of the growth curve (1) two "cycles" separated at ""' 100 gm. should appear, and (2) in first approximation, rat growth should be calculable with the equations of "Type I", i.e. a. "" 2j3. Calculation of growth data made previous to the physiological determinations (b) verifies both expectations. The catabolie constant (k) results, for the second (postpubertal) cycle, as k ••,.·""" 0.045jday, in close correspondence with protein turnover determined by isotope tracers (r=0.04jday). (After von Bertalanffy, 1960b.) l :I iI , I general consists to a large extent of oversimplificat ions in the models it uses. These are an aspect of the idealization taking place in every law and model of science. Already Galileo's student, Torricelli, bluntly stated that if halls of stone, of metal, etc., do not follow the law, it is just too bad for them. Bohr's model of the atom was one of the most arbitrary simplifications ever conceived-but nevertheless became a cornerstone of modern physics. Oversimplificat ions progressively corrected in subsequent development are the most potentor indeed the only means toward conceptual mastery of nature. In our particular case it is not quite correct to speak of oversimplificati on. What is involved are rather balance equations over many complex and partly unknown processes. The legitimacy of such balance expressions is established by routine practice. For example, if we speak of Same Aspects of System Theory in Biology !1"'-1) 179 in mm. Time in weeks 7.10. Growth of Lebistes reticulatus. Upper lines: c1, lower lines: ~ Fig. 0 weight, • length. In the Guppy, growth in females and rnales shows considerable difference, the females reaching a multiple of body weight of the m_ales. Data are logarithmically plotted according to the integral of Equatwn 7.8; the close fit shows that the growth curves are correctly reproduced. The growth equations so obtained give a ratio of 1:1.5 for the _anabolic_ constauts 'lJ in females and males. According to theory, metabolrc rates m females and rnales should stand in the same ratio 1:1.5 as is actually found (Fig. 7.8,1). (After von Bertalanffy, 1938, 1960b.), B.M.R.-and are, in fact, able to establish quantitative relationships such as the "surface law"-it is balances we express which n~verthe!ess are important both theoretically and practically (e.g., d1agnost1c use of B.M.R.). The regularities so observed cannot be refuted by "genera! considerations" of oversimplificati on, but only empirically and by offering better explanations. It would be easy to make the growth model seemingly more realistic and to improve fitting of data, by introducing a few more parameters. 180 GENERAL SYSTEM THEORY However, the gain is spurious as long as these parameters cannot he checked experimentally; and for the reasans mentioned, a closer fit of data tells nothing about the merits of a particular formula if the number of "free constants" is increased. (2) Another question is the choice of parameters. It has been noted above that metabolic rate under basal and nonbasal conditions changes not only in magnitude but also with respect to allometry expressing its relation to body size. What is the justification of taking "resting metabolism" as standard and to range various species into "metabolic" and "growth types" accordingly? The answer is that among available measures of metabolismnone of them ideal-resting metabolism appears to approach best those natural conditions which prevail during growth. The B.M.R. standard (i.e., thermoneutrality of environment, fasting and muscular rest) makes the values so determined a laboratory artifact, because at least the first condition is unnatural; although it is most useful because B.M.R. values show the least dispersion. In cold-blooded animals, B.M.R. cannot he used as standard because there is no condition of thermoneutrality, and the fasting condition often cannot he exactly established. Activity metabolism, on the other hand, changes with the amount of muscular action (FIG. 7.4), and the growing animal is not under conditions of hard muscular work all the time. Hence resting metabolic rate is comparatively the best approximation to the natmal state; and choice of this parameter leads to a useful theory. (3) The most important criticism becomes apparent from the above discussion. It was said that there appear to he so-called metabolic types and growth types and correlations between both. However, earlier it has been emphasized that the parameters implied, especially the relation of metabolic rate to body size expressed in the exponent a, can he altered and shifted with experimental conditions (FIGS. 7.4-7.7). Similarly, also growth curves are not fixed. Experiments on the rat have shown that the shape of the growth curve, including location and existence of a point of infiection, can he changed by different nutrition (L. Zucker et al., l94la, 1941b, 1942; T.F. Zucker et al., 1941; Dunn et al., 1947; Mayer, 1948). None of the characteristics is rigidand, incidentally, within my own bio1ogica1 concepts, I would he the last to presuppose rigidity in the dynamic order of physiological processes. According to my whole biological outlook, SameAspectsof System Theory in Biology 181 I am rather committed to the ancient Heraclitean concept that what is permanent is only the law and order of change. However, the apparent contradiction can well he resolved when we remain faithful to the spirit of the theory. What is really invariable is the organization of processes expressed by certain relationships. This is what the theory states and experiments show, namely, that there are functional relationships between certain metabolic and growth parameters. This does not imply that the parameters themselves are unchangeable-and the experiments show that they are not. Hence, without loss of generality, we may understand "metabolic" and "growth types" as ideal cases observable under certain conditions, rather than as rigid species characteristics. "Metabolic" and "growth types" appear in the respective groups of animals if certain standard conditions are met. However, it is clearly incorrect that "the reduction of metabolic rates is a fundamental magnitude, not changing in different external conditions" (Lehmann, 1956). Under natmal or experimental conditions, the relationships can he shifted, and then a conesponding alteration of growth curves should take place. There are indications that this is actually the case; it is a clear-cut problem for further investigation. A case to the point are seasonal changes. Berg (1959, 1961), while in general confirming previous data, found that the sizemetabolism relation varies seasonally in snails: "Thus the relation, oxygen consumption to body size, is not a fixed, unchangeable quantity characteristic of all species as supposed by Bertalanffy.... If (Bertalanffy's theory) were true, then the observed seasonal variation in metabolic type would imply a seasonal variation in the type of growth rate." As a matter of fact, precisely this has been found in our laboratory long ago (von Bertalanffy and Müller, 1943). Seasonal variations of metabolic rate in snails have been described (FIG. 7.lla). But correspondingly, also the growth curve (exponential in this case because these snails belong to "Type II") shows breaks and cycles (FIG. 7.llb). Therefore, this certainly is a problem deserving more detailed investigation; however, the data available are a hint toward confirmation rather than refutation of the theory. I would have been much surprised, indeed suspicious, if this first crude model would have provided a conclusive theory. Such 182 GENERAL SYSTEM THEORY ..... ... . .. .. WEIGHT .. 020 IUD 0.50 WEIGHT 2.0 lO MONTHS Fig. 7.11. Metabolism and growth in land snails. a: Seasonal variati?ns in metabolic rates. The regression lines show, from bottorn to top, restmg metabolism of Cepaea vindobonensis inactive shortly after hibernation at 20°C, same at 28°C, and in activity period at 20°C. (Weight in gm.) Other conditions being equal, resting metabolism is considerably higher in the active compared to the inactive season. b: Growth in a related species (Eulota fruticum). The growth curve is exponential (Type II with a """" 1) , but shows seasonal fluctuations. (After von Bertalanffy & Müller, 1943) things just do not happen, as is witnessed by many examples from history of science. Mendel's laws were the beginnings of genetics but-with linkage, crossing-over, position effect and what not-it is only a minute part of genetic experience that is described by the classica! laws. Galileo's law is the beginning of physics, but only highly idealized cases-such as boclies falling in vacuo-actually follow the simple law. It is a long way from Bohr's simple model of the hydrogen atom to present atomie physics, and so on. It would be fantastically improbable if this were different with a proposed model of growth. The most we Same Aspects of System Theory in Biology 183 can say about it is that it is backed by a considerable amount of experimental evidence, has proved to have explanatory and predictive capacities, and offers clear-cut problems for further research. It is obvious that the theory has been developed for a limited number of cases only, owing to the limited number of good data and the time-consumin g nature both of observation and calculation of growth. Hemmingsen (1960) has made this clear: "With n varying as much as the examples show, within any group with allegedly (or at least first allegedly) uniform growth type, it seems impossible to accept Bertalanffy's generalizations unless a statistically significant correlation between n and growth type can be demonstrated on a much larger number of examples than the few ones which Bertalanffy has repeatedly published." I entirely agree with this criticism; many more data would be desirable, although one should not cavalierly bypass those offered in confirmation of the theory, even if they are some 20 years old. I would amend Hemmingsen's criticism by suggesting reexamination on a broader basis. This should include at least the following items: analysis of a large number of growth data, now made possible by electronic computers; concurrent determination of size-dependence of resting metabolism (constant a.) in these cases; determinations of protein catabolism (constant K ); determination, in related species, of the ratios between allometry exponents of metabolic rates and the theoretically identical ratios of the anabolic constants ( 7J ). These are all interesting and somewhat neglected research problems; and if the model does no more than bring them to the fore, it has proved its usefulness. Such investigation may bring additional confirmation of the model; it may lead to its modification and elaboration by taking into account additional factors; or it may lead to abandoning the model altogether and replacing it with a better one. If the latter should happen, I would be in no way disappointed. This is exactly what models are for-to serve as working hypotheses for further research. What I have tried to show in the models discussed are general ways of analysis of quantitative data. I wanted to make clear both the usefulness and the limitations of such models. Any model should be investigated according to its merit with a view at the explanations and predictions it is able to provide. General 184 GENERAL SYSTEM THEORY criticism does not help, and the decision whether or not a model is suitable, exclusively rests with facts of observation and experiment. On the other hand, no model should be taken as conclusive; at best it is an approximation to be progressively worked out and corrected. In close interaction between experiment and conceptualization, but not in confinement to experimentation or construction of purely speculative models, lies the further development of a field like quantitative biology of metabolism. Summary I. The theories of open systems, feedback, allometry and growth according to Bertalanffy are reviewed with respect to their experimental applications. 2. The models of both open system and feedback apply to a wide range of phenomena in physiology, and represent essential expansions of physical theory. The two conceptions should be clearly distinguished; the feedback model (homeostasis) should not be considered a cover-all for physiological regulation in general or identified with "systems theory." 3. The allometric equation represents the simplest possible relation between body size and metabolic processes. It is of a wide applicability and expresses the harmonization of processes in living systems. Howevet, there is no "surface" or "3 j 4-power law" or "law of progressive reduction of metabolic rates." The allometric relationship greatly varies in physiological phenomena. . 4. Variations of the relation between body size and metabolic rate may occur (a) in different tissues or in different species; (b) due to changes of physiological conditions; (c) due to different experimental designs. Among the conditions altering this relation are such factors as physiological activities, sex, season, previous acclimation, etc. 5. The size-dependence of total metabolism in mammals is different under basal conditions, in a nonthermoneutral environment, and under conditions of muscular activity. The variations follow Locker's rule, i.e., with an absolute increase of metabolic rate (expressed by the constant b of the allometric equation), regression with respect to body size (expressed by the slope of the allometric line, a.) tends to decrease. 6. The growth equations after Bertalanffy represent a highly simplified model which, however, covers many phenomena and regularities found in the physiology of metabolism and growth. The parameters occuring in these equations have been verified by physiological experiments in many cases. 7. In view of the changes of the size-metabolism relation mentioned under (5) , Bertalanffy's so-called metabolic and growth types should Same Aspects of System Theory in Biology 185 be considered as ideal cases realizable under certain standard conditions, rather than as invariable characteristics of the species or group of species concerned. 8. Seasonal variations of metabolic rates and growth rates seem to show correspondence. 9. Urgent problems for further research with respect to each of the basic models are outlined. The System Concept in the Sciences of Man 8 The System Concept in the Sciences of Man The Organismic Revolution In a famous passage of his Critique of Practical Reason, Kant stated that there are two things that fill him with indescribabie awe-the starry sky above him and the moral law within him. Kant's time was the height of German classicism. Within a few decades before and after 1800 the great German poets, writers and philosophers were clustered, and Kant's philosophy was the culminating synthesis of physical science as it had developed since Galileo and Newton. Pondering Kant's statement, we wonder. Among the things he could have found objects of awe, he might well have included a third. Kant did not mention life-in its aspects both as the miraculous organization of the living organism and as the microcosm of mind which comprehends the physical universe. It is not difficult to understand Kant's omission. Physics was nearing one of its culminating points to which Kant himself, in his work on the origin of the solar system, had contributed; the morallaw had a long history in the Greek and Judeo-Christian tradition. In contrast, the development of the sciences of biology and psychology had scarcely begun. The 180 years or so since Kant's writing have seen the Indus- 187 . trial Revolution and, in the near past, the Atomie Revolution, the Revolution of Automation and the Conquest of Space. But there appears to be a break. The breathtaking technological development and the affiuent society, realized at least in some parts of the globe, have left us with anxiety and meaninglessness. Physics, with all its stupendous modern insights, is not the crystalclear structure Kant believed it to be. Kant's moral imperative, even if not eroded, would be much too simple for a complex world. Even apart from the menace of physical annihilation, there is the feeling that our world vision and our system of values are breaking down in the advent of Nihilism which Nietzsche prophetically forecast at the turn of our century. Considered in the light of history, our technology and even our society are based on a physicalistic world picture which found an early synthesis in Kant's work, Physics is still the paragon of science, the qasis of our idea of society and our image of man. In the meanwhile, however, new sciences have arisen-the life, behavioral, and social sciences. They demand their place in a modern world view, and should be able to contribute to a basic reorientation. Less advertised than the contemporary revolutions in technology but equally pregnant of future possibilities is a revolution based on modern developments in biologica! and behaviaral science. For short, it may be called the Orga[tjsmic Revolution. Its core is the notion of system-apparently a pale, abstract and empty concept which nevertheless is full of hidden meaning, ferment and explosive potentialities. The hearing of this new conception can be epitomized in a short statement. The 19th and first half of the 20th century conceived of the world as chaos. Chaos was the oft-quoted blind play of atoms which, in mechanistic and positivistic philosophy, appeared to represent ultimate reality, with life as an accidental product of physical processes, and mind as an epiphenomenon. It was chaos when, in the current theory of evolution, the living world appeared a product of chance, the outcome of random mutations and survival in the mill of natural selection. In the same sense, human personality, in the theories of behaviorism as well as of psychoanalysis, was considered .a chance product of nature and nurture, of a mixture of genes and an accidental sequence of events from early childhood to maturity. Now we are looking for another basic outlook on the world- 188 GENERAL SYSTEM THEORY t/te world as organization. Such a conception-if it can be substantiated-would iudeed change the basic categories upon which scientific thought rests, and profoundly influence practical attitudes. This trend is marked by the emergence of a bundie of new disciplines such as cybernetics, information theory, general system theory, theories of games, of decisions, of queuing and others; in practical application, systems analysis, systems engineering, operations research, etc. They are different in basic assumptions, mathematica! techniques and aims, and they are often unsatisfactory and sometimes contradictory. They agree, however, in being concerned, in one way or the other, with "systems," "wholes" or "organization"; and in their totality, they herald a new approach. The Image of Man in Contemporary Thought What can these developments contribute toward the Sciences of Man? The unsatisfactory status of contemporary psychological theory is common knowledge. It seems a hodgepodge of contradicting theories ranging from behaviorism, which sees no difference between human behavior and that of laboratory rats (and, more important, engineers pattern human behavior after the model of rat behavior), to existentialism, for which the human situation is beyoud scientific understanding. The variety of conceptions and approaches would be quite healthy, were it not for one disturbing fact. All these theories share one "image of man" which originated in the physical-technological universe; which is taken for granted by otherwise antagonistic theories such as those of behaviorism, computer models of cognitive processes and behavior, psychoanalysis and even existentialism; and which is demonstrably false. This is the robot model of human behavior. It is, of course, true that there are a considerable number of trends toward new conceptions, urged on by the insight that the robot model is theoretically inadequate in view of empirica! fact and is practically dangerous in its application to "behavioral engineering." Nevertheless, while robotic concepts are frequently denounced overtly and covertly, they remain dominant in psychological research, theory, and engineering. They therefore deserve brief consideration even now. One leading concept is the stimulus-response scheme, or S-R The System Concept in the Sciences of Man 189 scheme for short. Behavior, animal and human, is considered to be response to stimuli coming from outside. In part, stimulusresponse is based upon inherited neural mechanisms, as in reflexes and instinctive behavior. The more important part, so far as human behavior is concerned, are acquired or conditioned responses. This may be classica! conditioning by way of repetition of the sequence of conditional and unconditional stimuli according to Pavlov. It may be operant conditioning by reinforcement of successful responses according to Skinner. It may be early childhood experience according to Freud, beginning with toilet training and other procedures whereby socially acceptable behavior is reinforced, but psychopathological complexes may also be formed. This, then, dominates psychological engineering. Scholastic learning is best carried through by teaching machines constructed according to the Skinnerian principles. Conditioning with psychoanalytic background keeps the wheels of free enterprise going. Advertising, motivation research, radio and television are ways of conditioning or programming the human machine so that it buys what it should: the washing powder wrapped in the most brilliant color, the biggest refrigerator as symbol of the maternal womb, or the politica! candidate commanding the most efficient party machine. - . The point is that the rules found by learning theorists in animal experiments are supposed to cover the total of human behavior. To Skinner, for example, the "verba! behavior" of the child is supposedly acquired in the same process of operant conditioning as Skinner's rats and pigeons learn their little tricks by being gratified with small pareels of food for correct responses. As a witty critic (Chomsky, 1959) noted, pareuts supposedly teach their child to walk and to speak because their teaching behavior is reinforeed by gratification, probably so that the child later on may make some money by delivering newspapers, or can call his pareuts to the telephone. More sophisticated versions of the scheme do not alter its essence. A secoud principle is that of environmentalism which states, in accordance with the S-R scheme, that behavior and personality are shaped by outside influences. The famous expression is that by Watson: Give me a bunch of kids, (said the founder of behaviorism), taken as they come-and I will make them doctors, lawyers, merchant men, beggars and thieves, solely by the power 190 GENERAL SYSTEM THEORY of conditioning. It is the same principle when psychoanalysis says that personality is formed by early childhood experience, especially of a sexual nature. In more general formulation, the human brain is a computer that can be programmed at will. The practical consequence is that human beings are born not only with equal rights but with equal capabilities. Hence our almost pathological concern with the abnormal, the mentally ill and outright crimina! who, by suitable reconditioning, should be brought back into the flock-often to the detriment of consideration given the healthy, normal or superior. Hence also the belief that money buys everything: when the Russians build better space vehicles, a few more billions spent on education will produce the erop of young Einsteins needed for closing the gap. The third is the equilibrium principle. In Freudian formulation, this is the "principle of stability": the basic function of the mental apparatus consistsin maintaining borneostatic equilibrium. Behavior essentially is reduction of tensions, particularly those of a sexual nature. Hence, let them release their tensions by way of promiscuity and other tension reduction, and you will have normal and satisfied human beings. Fourthly, behavior is governed by the principle of economy. It is utilitarian and should be carried through in the most economie way, that is, at minimum expense of mental or vital energy. In practice, the economie principle amounts to the postulate of minimum demands: for example, reduce scholastic demands to the minimum necessary to become an executive, electranies engineer or plumber-otherwise you warp personality, create tensions, and make an unhappy being. The present crisis of psychology (which, however, has already 1 lasted for some 30 years) can be summarized as the slow erosion of the robot model of man which up to recent years dominated 'psychology, particularly in the United States. Two points deserve to be reemphasized. First, the model of man as robot was germane to all fields of psychology and psychopathology, and to theories and systems otherwise different or antagonistic: to the S-R theory of behavior; to cognitive theory in what has been called the "dogma of immaculate perception," i.e. the organism as a passive receptor of stimuli; to learning theories, Pavlovian, Skinnerian, or with intervening variables; to diverse personality theories; to behaviorism, psychoanalysis, The System Concept in the Sciences of Man çy!?~tic 191 concepts in neurophysiology and psychology, and so on. Furthermore, "man as robot" was both expression and motor force of the zeitgeist of a mechanized and commercialized society; it helped to make psychology the handmaiden of pecuniary and politica! interests. It is the goal of manipulating psychology to make humans ever more into robots or automata, this being engineered by mechanized learning, advertising techniques, mass media, motivation research and brainwashing. Nevertheless, these basic presuppositions are spurious. That is to say, conditioning and learning theories correctly describe an important part or aspect of human behavior, but taken as a not!J}!l:g:!~ut theory they!?~<:Ornegstensiblyfalse and self-defeating 1ntheir application. The image of man as robot is metaphysics or myth, and its persuasiveness rests only in the fact that it so closely corresponds to the mythology of mass society, the glorification of the machine, and the profit motive as sole motor of progress. Unbiased observation easily shows the spuriousness of these basic assumptions. The S-R scheme leaves out the large part of behavior which is expression of spontaneons activities such as play, exploratory behavior and any form of creativity. Environmentalism is refuted by the elementary fact that not even fruit flies or Pavlovian dogs are equal, as any student of heredity or behavior should know. J3iologically, life is not maintenance or restoration of equilibrium but is essentially maintenance of disequilibria, as the doctrine of the organism as open system reveals. Reaching equilibrium means death and consequent decay. Psychologically, behavior not only tends to release tensions but ~lso builds up tensions; if this stops, the patient is a decaying mental corpse in the same way a living organism becomes a body in decay when tensions and forces keeping it from equilibrium have stopped. Juvenile delinquents who commit crime for fun, a new psychopathology resulting from too much leisure, the fifty percent mental cases in our hospitals-all this is proof that the scheme of adaptation, adjustment, conformity, psychological and social equilibrium doesn't work. There is a wide range of behavior-and, presumably also of evolution-which cannot be reduced to utilitarian principles of adaptation of the individual and survival of the species.. Greek sculpture, Renaissance painting. German music-indeed, any aspect of culture- 192 GENERAL SYSTEM THEORY has nothing to do with utility, or with the better survival of individuals or nations. Mr. Babbitt is in every utilitarian respect better off than Beethoven or Michelangelo. Also the principle of stress, so often invoked in psychology, psychiatry and psychosomatics, needs some reevaluation. As everything in the world, stress too is an ambivalent thing. Stress is not only a danger to life to be controlled and neutralized by adaptive mechanisms; it also creates higher life. If life, after disturbance from outside, had simply returned to the so-called borneostatic equilibrium, it would never have progressed beyond the amoeba which, after all, is the best adapted creature in the world-it has survived billions of years from the primeval ocean to the present day. Michelangelo, implementing the precepts of psychology, should have foliowed his father's request and gone in the wool trade, thus sparing bimself lifelong anguish although leaving the Sistine Chapel unadorned. Selye wrote: "The secret of health and happiness lies in successful adaptation to the ever-ebanging conditions of the globe; the penalties for failure in this great process of adaptation are disease and unhappiness" (1956, p. VII). He speaks for the worldly-wise and in a sense he is correct. But, taken literally, he would negate all creative activity and culture which, to an extent, have made him more than the beasts of the jungle. Considered as adaptation, creativity is a failure, a disease and unhappiness; the Vienna historian of culture, Egon Friedell (1927-31) has a brilliant analysis of this point. The maxim of adjustment, equilibrium and borneostasis cannot be foliowed by anyone who brings one single idea to the earth, including Selye himself, who certainly has paid for doing so. Life is not comfortable setding down in pre-ordained grooves of being; at its best, it is élan vita!, inexorably driven towards higher form of existence. Admittedly, this is metaphysics and poetic simile; but so, after all, is any image we try to form of the driving forces in the universe. I i System- Theoretica! Re-orientation It is along such lines that a new model or image of man seems to be emerging. We may briefly characterize it as the model of man as active personality system. This, it appears, is the com- The System Concept in the Sciences of Man 193 mon denominator of many otherwise different currents such as developmental psychology after Piaget and Werner, various neoFreudian schools, ego psychology, the "new look" in perception, recent theory of cognition, personality theories such as those of G. Allport and Maslow, new approaches in education, existential psychology and others. This implies a holistic orientation in psychology. It used to be the general trend of psychology to reduce mental happenings and behavior into a bundie of sensations, drives, innate and learned reactions, or whatever ultimate elements are theoretically presupposed. In contrast, the system concept tries to bring the psychophysiological organism as a whole into the focus of the scientific endeavor. Thus a new "model of man" appears necessary and, in fact, is slowly emerging in recent trends of bumanistic and organismic psychology. Emphasis on the creative side of human beings, on the importance of individual differences, on aspects that are nonutilitarian and beyond the biologica! values of subsistenee and survival-this and more is implied in the model of the active organism. These notions are basic in the re-orientation of psychology which is going on presently; hence the increasing interest general system theory is encountering in psychology and especially psychiatry. In contrast to the model of the reactive organism expressed by the S-R scheme-behavior as gratification of needs, relaxation of tensions, reestablishment of borneostatic equilibrium, its utilitarian and environmentalistic interpretations, etc.-we come rather to consider the psychophysical organism as a primarily active system. I think human activities cannot be considered otherwise. I, for one, am unable to see how, for example, creative and cultural activities of all sorts can be regarded as "response to stimuli," "gratification of biologica! needs," "reestablishment of homeostasis" or the like. It does not look particularly "borneostatie" when a businessman follows his restless activities in spite of the ulcers he is developing; or when mankind goes on inventing super-bombs in order to satisfy "biologica! needs." The concept applies not only to behavioral, but also to the cognitional aspects. It will be correct to say that it is the general trend in modern psychology and psychiatry, supported by biologica! insight, to recognize the active part in the cognitive 194 GENERAL SYSTEM THEORY process. Man is not a passive receiver of stimuli coming from an external world, but in a very concrete sense creates his universe. This, again, can be expressed in many ways: in Freud's reconstruction of the building-up of the "world" in the child; in terms of developmental psychology according to Piaget, W erner or Schachtel; in terms of the "new look in perception" emphasizing attitudes, affective and motivational factors; in psychology of cognition by analysis of "meaningful learning" after Ausubel; in zoological context by referring to von Uexküll's species-specific umwélt; philosophically and linguistically, in Cassirer's "symbolic forms" and culture-dependent categories; in von Humboldt's and Whorf's evidence of linguistic (i.e. symbolic and cultural) factors in the formation of the experienced universe. "The world as we experience it is the product of perception, not the cause of it." (Cantril, 1962). Such a list, in no way complete, illustrates different approaches to throw light on various aspects or facets which eventually should be synthesized. But there is consensus in the general conception. Indeed, if the organism were a camera and cognition a kind of photographic image of the outside world, it would be hard to understand why the cognitive process takes the circuitous route admirably described by Arieti (1965) via fantasmic, mythical and magical universes, only finally and lately to arrive at the supposedly "objective" world outlook of the average American and of Western science. Such a new "image of man," replacing the robot concept by that of system, emphasizing immanent activity instead of outerdirected reactivity, and recognizing the specificity of human culture compared to animal behavior, should lead to a basic reevaluation of problems of education, training, psychotherapy, and human attitudes in generaL Systems in the Social Sciences Finally, we should look for the application of the systems conception to the widest perspective, i.e., human groups, societies, and humanity as a whole. For purposes of discussion, let us understand "social science" in a broad sense, including sociology, economics, politica! science, social psychology, cultural anthropology, linguistics, a good part The System Concepts in the Sciences of Man 195 of history and the humanities, etc. Let us understand "science" as a nomothetic endeavor, i.e. not a description of singularities but an ordering of facts and elaboration of generalities. Presupposing these definitions, it may, in my opinion, be stated quite confidently: Social science is the science of social systems. For this · reason, it will have to use the approach of general systems science. This appears to be an almost trivia! statement, and it can hardly be denied that "contemporary sociological theories" (Sorokin, 1928, 1966) and even their development through history, foliowed this program. However, proper study of social systems contrasts with two widespread conceptions: first, with atomistic conceptions which neglect study of "relations"; secondly, with conceptions neglecting the specificity of the systems concerned, such as a "social physics" as was often attempted in a reductionist spirit. This requires some comment. Research into systems of organisms is extensive. It forms an important part of biology, in the study of communities and societies of animals and plants, their growth, competition, struggle for existence, etc., both in the ecological and genetic aspects. Certain aspects of human societies offer themselves for similar considerations; not only aspects so obvious as the growth of human populations but also armament races and warlike confticts which, according to Richardson and others, can be elaborated in diffetential equations similar to those used in ecology and, though oversimplified, provide an amount of explanation and even prediction. The spread of rumors can be described by generalized diffusion equations; the flow of automobile traffic can be analyzed in considerations formally conesponding to kinetics and thermodynamics. Such cases are rather typical and straightforward applications of general system theory. However, this is only part of the problem. Sociology with its allied fields is essentially the study of human groups or systems, from small groups like the family or working crew, over innumerable intermediates of informal and formal organizations to the largest units like nations, power blocks and international relations. The many attempts to provide theoretica! formulations are all elaborations of the concept of system or some synonym in this realm. Ultimately the problem of human history looms as the widest possible application of the systems idea. 196 GENERAL SYSTEM THEORY Concepts and theories provided by the modern systems approach are being increasing1y introduced into sociology, such as the concept of general system, of feedback, information, communication, etc. Present sociological theory largely consists in attempts to define the sociocultural "system," and in discussion of functionalism, i.e., consideration of social phenomena with respect to the "whole" they serve. In the first respect, Sarokin's characterization of sociocultural system as causal-logical-meaningful (as the present author would loosely transcribe it, the biological, the symbolic and value levels) seems best to express the various complexly interconnected aspects. Functionalist theory has found various expressions as represented by Parsons, Merton, and many others; the recent hook by Demerath and Petersou (1968) gives excellent insight into the various currents. The main critique of functionalism, particularly in Parsons' version, is that it overemphasizes maintenance, equilibrium, adjustment, homeostasis, stabie institutional structures, and so on, with the result that history, process, sociocultural change, inner-directed development, etc., are underplayed and, at most, appear as "deviants" with a negative value connotation. The theory therefore appears to be one of conservatism and conformism, defending the "system" (or the megamachine of present society, to use Mumfotd's term) as is, conceptually neglecting and hence obstructing social change. Obviously, general system theory in the form here presented is free of this objection as it incorporates equally maintenance and change, preservation of system and internal conflict; it may therefore be apt to serve as logica! skeleton for improved sociological theory (cf. Buckley, 1967). The practical application, in systems analysis and engineering, of systems theory to probierus arising in business, government, international polities, demonstrates that the approach "works" and leads to both understanding and predictions. It especially shows that the systems approach is not limited to material entities in physics, biology and other natura! sciences, but is applicable to entities which are partly immaterial and highly heterogeneous. Systems analysis, for example, of a business enterprise encompasses men, machines, buildings, inflow of raw material, outflow of products, monetary values, good will and other imponderables; it may give definite answers and practical advice. The System Concept in the Sciences of Man 197 The difficulties are not only in the complexity of phenomena but in the definition of entities under consideration. At least part of the difficulty is expressed by the fact that the social sciences are concerned with "socio-cultural" systems. Human groups, from the smallest of personal friendships and family to the largest of nations and civilizations, are not only an outcome of social "forces" found, at least in primitive form, in subhuman organisms; they are part of a man-created universe called culture. Natura! science has to do with physical entities in time and space, particles, atoms and molecules, living systems at various levels, as the case may be. Social science has to do with human beings in their self-created universe of culture. The cultural universe is essentially a symbolic universe. Animals are surrounded by a physical universe with which they have to cope: physical environment, prey to catch, predators to avoid, and so forth. Man, in contrast, is surrounded by a universe of symbols. Starting from language which is the prerequisite of culture, to symbolic relationships with his fellows, social status, laws, science, art, morals, religion and innumerable other things, human behavior, except for the basic aspects of the biologica! needs of hunger and sex, is governed by symbolic entities. We may also say that man has values which are more than biologica! and transeend the sphere of the physical world. These cultural values may be biologically irrelevant or even deleterious: It is hard to see that music, say, has any adaptive or survival value; the values of nation and state become biologically nefarious when they lead to war and to the killing of innumerable human beings. A System-Theoretical Concept of Ristory In contrast to biologica! species which have evolved by way of genetic transformation, only mankind shows the phenomenon of history, which is intimately linked with culture, language and tradition. The reign of nature is dominated by laws progressively revealed in science. Are there laws of history? In view of the fact that laws are relations in a conceptual model or theory, this question is identical with another one: apart from description of happenings, is a theoretica! history possible? If this is possible at all, it must be an investigation of systems as suitable units 198 GENERAL SYSTEM THEORY of research-of human groups, societies, cultures, civilizations, or whatever the appropriate objects of research may be. A widespread conviction among historians is that this is not so. Science is essentially a nomothetic endeavor-it establishes laws, based on the fact that events in nature are repeatable and recurrent. In contrast, history does not repeat itself. It has occurred only once, and therefore, history can only be idiographic-i.e., a description of events which have occurred in a near or distant past. Contrary to this opinion, which is the orthodox one of historians, heretics have appeared who held the opposite view and, in one way or another, tried to construct a theoretica! history with laws applying to the historica! process. This current started with the Italian philosopher Vico in the early 18th century, and continued in the philosophical systems and the investigations by Regel, Marx, Spengler, Toynbee, Sorokin, Kroeber and others. There are great and obvious differences between these systems. They all agree, however, that the historica! process is not completely accidental but follows regularities or laws which can be determined. As already said, the scientific approach is undisputedly applicable to eertaio aspects of human society. One such field is statistics. We can, and do, formulate many statistica! laws or at least regularities for social entities. Population statistics, mortality statistics-without which insurance companies would go bankrupt -Gallup polls, predictions of voting behavior or of the sa1e of a product show that statistica! methods are applicable to a wide range of social phenomena. Moreover, there are fields where the possibility of a hypotheticodeductive system is generally accepted. One such field is mathematica! economics or econometries. The correct system of economics may be disputed, but such systems exist and, as in every science, it is hoped that they will be improved. Mathematica! economics also is a case in point of general systems theory which does not concern physical entities. The many-variables problems, different models and mathematica! approaches in economics offer a good example of model building and the general systems approach. Even for those mysterious entities, human values, scientific theories are emerging. In fact, information theory, game theory, and decision theory provide models to deal with aspectsof human The System Concept in the Sciences of Man 199 and social behavior where the rnathematics of classica! science is not applicable. Works like Rapoport's Fights, Games, Debates (1960) and Boniding's Conflict and Defence (1962) present detailed analyses of phenomena such as armament races, war and war games, competition in the economie and other fields, treated by such comparatively navel methods. It is of partienlar interest that these approaches are concerned with aspects of human behavior which were believed to be outside of science: values, rational decisions, information, etc. They are not physicalistic or reductionist. They do not apply physical laws or use the traditional rnathematics of the natura! sciences. Rather, new developments of rnathematics are emerging, intended to deal with phenomena not encountered in the world of physics. Again there are uncontested laws with respect to eertaio immaterial aspects of culture. For example, language is not a physical object, but a product or rather aspect of that intangible entity we call human culture. Nevertheless, linguistics tells about laws allowing description, explanation and prediction of observed phenomena. Grimm's laws of the consonant mutations in the history of Germanic languages is one of the simpler examples. In somewhat vaguer form, a lawfulness of cultural events is generally accepted. For example, it appears to be a quite general phenomenon that art goes through a number of stages of archaism, maturity, baroque, and dissalution found in the evolution of art in far-away places and times. Thus statistica! regularities and laws can be found in socia1 phenomena; eertaio specific aspects can be approached by recent approaches, models and techniques which are outside and different from those of the natura! sciences; and we have some ideas about intrinsic, specific and organizational laws of social systems. This is no matter of dispute. The' bone of contention comes in with "theoretica! history," the great visions or constructs of history, as those of Vico, Regel, Marx, Spengler, Toynbee, to mention only some prominent examples. Regularities in "microhistory," i.e., happenings in limited spaces, time-spans, and fields of human activity, certainly are vague, needy of exploration, and far from being exact statements; but their existence is hardly disputable. The attempts at finding regularities in "macrohistory" are almast unequivocally rejected by official history. Taking away romanticism, metaphysics and moralizing, the 200 GENERAL SYSTEM THEORY "great systems" appear as models of the historica! process, as Toynbee, somewhat belatedly, recognized in the last volume of his Study. Conceptual models which, in simplified and therefore comprehensible form, try to represent certain aspects of reality, are basic in any attempt at theory; whether we apply the Newtonian model in mechanics, the model of corpusde or wave in atomie physics, use simplified models to describe the growth of a population, or the model of a game to describe politica! decisions. The advantages and dangers of models are well known. The advantage is in the fact that this is the way to create a theory -i.e., the model permits deductions from premises, explanation and prediction, with often unexpected results. The danger is oversimplification: to make it conceptually controllable, we have to reduce reality to a conceptual skeleton-the question remaining whether, in doing so, we have not cut out vital parts of the anatomy. The danger of oversimplification is the greater, the more multifarious and complex the phenomenon is. This applies not only to "grand theories" of culture and history but to models we find in any psychological or sociological journal. Obviously, the Great Theories are very imperfect models. Factual errors, misinterpretations, fallacies in condusion are shown in an enormous critica! literature and need not concern us here. But taking this criticism for granted, a number of observations still remain. One thing the various systems of "theoretica! history" appear to have demonstrated is the nature of the historica! process. History is notaprocessin an amorphous humanity, or in Homo sapiens as a zoological species. Rather it is borne by entities or great systems, called high cultures or civilizations. Their number is uncertain, their delimitations vague, and their interactions complex. But whether Spengler has counted eight great civilizations, Toynbee some 20, Sorokin applies still other categories, or recent research has unveiled so many lost cultures, it appears to he a fact that there was a limited number of cultural entities hearing the historica! process, each presenting a sort of life cyde as indeed smaller socio-cultural systems such as businesses, schools in art and even scientific theories certainly do. This course is not a predetermined life span of a thousand years as Spengler maintained (not even individual organisms have a fixed life span but may die earlier or later); nor does it run in splendid isolation. The System Concept in the Sciences of Man 201 The extent of cultural diffusion became impressive when archaeologists explored the prehistorie Amber Road or the Silk Road which dated from the beginning of the Christian era or even earlier, or when they found an Indian Lakshmi statuette in Pompeii and Roman trade stations at the Indian coasts. Expansion undreamed of by Spengler and yet by Toynbee, as well as new problems, became apparent in relatively recent years. Certainly the culture of the Khmer, the Etruscans or the preRoman Celts deserve their place in the scheme; what was the megalithic culture expanding over the edges of the Mediterranean, the Atlantic and the Baltic Sea, or the Iberian culture which producedas early as 500 B.c. such astonishing workas the Prado's Lady of Elche? Nevertheless, there is sarnething like an Egyptian, Greco-Roman, Faustian, Magie, Indian culture (or whatever nomendature we may prefer), each unique in its "style" (i.e., the unity and whole of its symbolic system), even when absorbing and assimilating culture traits from others and interacting with cultural systems contemporaneous and past. Furthermore, the ups and downs in history (not exactly cydes or recurrences, but fluctuations) are a matter of public record. As Kroeber (1957) and Sorokin (1950) emphasized, there remains, after subtracting the errors and idiosyncrasies of the philosophers of history, a large area of agreement; and this consists of wellknown facts of history. In other words, the disagreements among the theorists of history, and with official history, are not so much a question of data as of interpretation, that is of the models applied. This, after all, is what one would expect according to history of science; for a scientific "revolution," the introduetion of a new "paradigm" of scientific thinking (Kuhn, 1962), usually manifests itself in a gamut of competing theories or models. In such a dispute, the influence of semantics pure and simple should not he underrated. The meaning of the concept of culture itself is a matter of dispute. Kroeber and Kluckhohn (1952) collected and discussed some 160 definitions without coming out with a definitive one. In particular, the anthropologist's and the historian's notions are different. For example, Ruth Benediet's Patterns of Culture of New Mexico, British Columbia and Australia inhabitants is essentially timeless; these patterns existed since times unrecorded, and if they underwent minor changes in the past, these are outside the scope and methods of the cultural 202 GENERAL SYSTEM THEORY anthropologist. In contrast, the culture or more properly civilization (to follow idiomatic English) with which the historian is concerned, is a processin time: the evolution of the Greco-Roman culture from the Ionian city states to the Roman Empire, of its plastic art from archaic statuary to Hellenism, of German music from Bach to Strauss, of science from Copernicus to Einstein, and so forth. So far as we know, only a limited number of "high cultures" had and made history-i.e., showed major change in time, while the hundreds of cultures of the anthropologist remained stationary at their stone and bronze age levels, as the case may be, before the European impact. In this respect, Spengler is certainly right, with his concept of culture as a dynamic and self-evolving entity, against anthropologists to whom one "culture" -be it of Australian aborigines, of Greece or of the Western world-is as good as the other, all belonging to one stream of amorphous humanity with accidental and environment-caused eddies, rapids and standstills. Incidentally, such verbal distinctions are more than scholasticism and have politica! impact. In Canada, we presently have the fight about Biculturalism (or of Two Nations, English and French, in another version). What do we mean? Do we understand culture in the anthropological sense and wish to fight about tribal differences as they exist between savage peoples in Africa or Borneo and cause endless warfare and bloodshed? Or do we mean culture as the French culture and German Kultur-i.e., creative manifestations which still have to be proved, and to be proved as different between English- and French-Canadians? Clearly, politica! opinions and decisions will largely depend on the definition. The concept of nation in the U.N. has been based on the "anthropological" notion (if not on arbitrary frontiers left from the Colonial period); the result has been somewhat less than encouraging. Another semantic problem is implied in "organismic" theories of sociology and history. Spengler called the great civilizations organisms with a life cycle including birth, growth, maturity, senescence and death; an enormous host of critics proved the obvious, namely, that cultures are not organisms like animals or plants, individual entities well-bounded in time and space. In contrast, the organismic conception is rather well-treated in sociology because its metaphorical character is understood. A business firm or manufacturing plant is a "system" and therefore The System Concept in the Sciences of Man 203 shows "organismic" features; but the difference of a "plant" in the botanist's and industrialist's sense is too obvious to present a problem. The fight would hardly have been possible in. the French Ianguage where it is good usage to speak of the organzsme of an institution (say the postal service), of a commercial firm or a professional association; the metaphor is understood and, therefore, not a subject of dispute. Instead of emphasizing the shortcomings of the cyclic historians which are rather natura! in an embryonic stage of the science, it seems more profitable to emphasize their agreement in many respects. One point of agreement makes the issue into more than an academie question. This issue has, as it were, touched a raw nerve, and gained for Toynbee and Spengler both popular acclaim and an emotional reaction otherwise uncommon in academie debate. It is the thesis expressed in Spengler's title, The Decline of the West, the statement that in spite or perhaps because of our magnificent technological achievements, we live in a time of cultural decay and impending catastrophe. The Future in System-Theoretical Aspect The dominanee of mass man and the suppression of the individual by an ever extending social machinery; the breakdown of the traditional system of values and its replacement by pseudoreligions, ranging from nationalism to the cult of status symbols, to astrology, psychoanalysis and Californian sectarianism; the decay of creativity in art, music and poetry; the willing submission of the mass to authoritarianism, be it a dictator or an impersonal élite; the colossal fights between a decreasing number of super-states: these are some of the symptoms recurring in our days. "We note the psychological change in those classes of society which had been up till then the creators of culture. Their creative power and creative energy dry up; men grow weary and lose interest in creation and cease to value it; they are disenchanted; their effort is no longer an effort toward a creative ideal for the benefit of humanity, their minds are occupied either with material interests, or with ideals unconnected with life on earth and realized elsewhere." This is not an editorial of yesterday's newspaper, but a description of the decay of the Roman Empire by its well-known historian, Rostovtzeff. However, against these and other symptoms catalogued by the 204 GENERAL SYSTEM THEORY prophets of doom, there are two factors in which our civilization obviously is unique in comparison to those that have perished in the past. One is the technological development which permits a control of nature never before achieved and would open a way to alleviate the hunger, disease, overpopulation, etc. to which humanity was previously exposed. The other factor is the global nature of our civilization. Previous ones were limited by geographical boundaries, and comprised only limited groups of human beings. Our civilization comprises the whole planet and even reaches beyond in the conquest of space. Our technological civilization is not the privilege of comparatively small groups such as the citizens of Athens or of the Roman Empire, of Germans or French, or of white Europeans. Rather it is open to all human beings of whatever color, race or creed. These are indeed singularities which explode the cyclic scheme of history and seem to place our civilization at a different level from previous ones. Let us try an admittedly tentative synthesis. I believe the "decline of the west" is not a hypothesis or a prophesy-it is an accomplished fact. That splendid cultural development which started in the European countries around the year 1000 and produced Gothic cathedrals, Renaissance art, Shakespeare and Goethe, the precise architecture of Newtonian physics and all the glory of European culture-this enormous cycle of history is accomplished and cannot he reviyified by artificial means. We have to reekon with the stark reality of a mass civilization, technological, international, encompassing the earth and all of mankind, in which cultural values and creativity of old are replaced by novel devices. The present power struggles may, in their present explosive phase, lead to universa! atomie devastation. If not, the differences between West and East probably will, one way or the other, become insignificant because the similarity of material culture in the long run will prove stronger than ideological differences. 9 General System Theory in Psychology and Psychiatry The Quandary of Modern Psychology In recent years the concept of "system" bas gained increasing influence in psychology and psychopathology. Numerous ïnvestigations have referred to general system theory or to some part of it (for example, F. Allport, 1955; G. W. Allport, 1960; Anderson, 1957; Arieti, 1962; Brunswik, 1956; Bühler, 1959; Krech, 1950; Lennard & Bernstein, 1960; Menninger, 1957; Menninger et al., 1958; Miller, 1955; Pumpian-Mindlin, 1959; Syz, 1963). Gordon W. Allport ended the reedition of bis classic (1961) with "Personality as System"; Karl Menninger (1963) based bis system of psychiatry on general system theory and organismic biology; Rapaport (1960) even spoke of the "epidemiclike popularity in psychology of open systems" (p. 144). The question arises why such a trend has appeared. American psychology in the first half of the 20th century was dominated by the concept of the reactive organism, or, more dramatically, by the model of man as a robot. This conception was common to all major schools of American psychology, dassical and neobehaviorism, learning and motivation theories, psychoanalysis, cybernetics, the concept of the brain as a computer, and so forth. According to a leading personality theorist, 206 GENERAL SYSTEM THEORY Man is a computer, an anima!, or an infant. His destiny is completely determined by genes, instincts, accidents, early conditionings and reinforcements, cultmal and social forces. Love is a secondary drive based on hunger and oral sensations or a reaction formation to an innate underlying hate. In the majority of our personological formulations there are no provisions for creativity, no admitted margins of freedom for voluntary decisions, no fitting recognitions of the power of ideals, no bases for selfless actions, no ground at all for any hope that the human race can save itself from the fatality that now confronts it. If we psychologists were all the time, consciously or unconsciously, intending out of malice to reduce the concept of human nature to its lowest camman denominator, and were gloating over our success in so doing, then we might have to admit that to this extent the Satanic spirit was alive within us. (Murray, 1962, pp. 36-54) The tenets of robot psychology have been extensively criticized; for a survey of the argumept, the reader may consult Allport's well-balanced evaluations (1955, 1957, 1961) and the recent historica! outline by Matson (1964) which is both brilliantly written and well documented. The theory nevertheless remained dominant for obvious reasons. The concept of man as robot was bath an expression of and a powerful motive force in industrialized mass society. It was the basis for behaviaral engineering in commercial, economie, politica!, and other advertising and propaganda; the expanding economy of the "affiuent society" could not subsist without such manipulation. Only by manipulating humans ever more into Skinnerian rats, robots, buying automata, homeostatically adjusted conformers and opportunists (or, bluntly speaking, into morons and zombies) can this great society follow its progress toward ever increasing gross national product. As a matter of fact (Henry, 1963), the principles of academie psychology were identical with those of the "pecuniary conception of man" (p. 45ff.). Modern society provided a large-scale experiment in manipulative psychology. If its principles are correct, conditions of tension and stress should lead to increase of mental disorder. On the other hand, mental health should be improved when basic needs for food, shelter, personal security, and so forth, are satisfied; when General System Theory in Psychology and Psychiatry 207 repression of infantile instincts is avoided by permissive training in bodily functions; when schalastic demands are reduced so as not to overlaad a tender mind; when sexual gratification is provided at an early age, and so on. The behavioristic experiment led to results contrary to expectation. World War 11-a period of extreme physiological and psychological stress~did not produce an increase in neurotic (Opler, 1956) or psychotic (Llavero, 1957) disorders, apart from direct shock effects such as combat neuroses. In contrast, the affiuent society produced an unprecedented number of mentally ill. Precisely under conditions of reduction of tensions and gratification of biologica! needs, novel forms of mental disorder appeared as existential neurosis, malignant boredom, and retirement neurosis (Alexander, 1960), i.e., farms of mental dysfunction originating not from repressed drives, from unfulfillèd needs, or from stress but from the meaninglessness of life. There is the suspicion (Arieti, 1959, p. 474; von Bertalanffy, 1960a) (although not substantiated statistically) that the recent increase in schizophrenia may be caused by the "other-directedness" of man in modern society. And there is no doubt that in the field of ebaraeter disorders, a new type of juvenile delinquency has appeared: crime not for want or passion, but for the fun of it, for "getting a kick," and born from the emptiness of life (Anonymous, Crime and Criminologists, 1963; Hacker, 1955). Thus theoretica! as well as applied psychology was led into malaise regarding basic principles. This discomfort and the trend toward a new orientation were expressed in many different ways such as in the various neo-Freudian schools, ego psychology, personality theories (Murray, Allport), the belated reception of European developmental and child psychology (Piaget, W erner, Charlotte Bühler), the "new look" in perception, self-realization (Goldstein, Maslow), client-centered therapy (Rogers), phenomenological and existential approaches, sociological concepts of man (Sorokin, 1963), and others. In the variety of modern currents, there is one common principle: to take man not as reactive autornaton or robot but as an active personality system. The reason for the current interest in general system theory therefore appears to he that it is hoped that it may contribute toward a more adequate conceptual framework for normal and pathological psychology. 208 GENERAL SYSTEM THEORY System Concepts in Psychopathology General system theory has its roots in the organismic conception in biology. On the European continent, this was developed by the present author (1928a) in the 1920's, with parallel developments in the Anglo-Saxon countries (Whitehead, Woodger, Coghill and others) and in psychcilogical gestalt theory (W. Köhler). It is interesting to note that Eugen Bleuier (1931) foliowed with sympathetic interest this development in its early phase. A similar development in psychiatry was represented by Goldstein (1939). ÜRGANISM AND PERSONALITY In contrast to physical farces like gravity or electricity, the phenomena of life are found only in individual entities called organisms. Any organism is a system, that is, a dynamic order of parts and processes standing in mutual interaction (Bertalanffy, 1949a, p. 11). Similarly, psychological phenomena are found only in individualized entities which in man are called personalities. "Whatever else personality may be, it has the properties of a system" (G. Allport, 1961, p. 109). The "molar" concept of the psychophysical organism as system contrasts with its conception as a mere aggregate of "molecular" units such as reflexes, sensations, brain centers, drives, reinforeed responses, traits, factors, and the like. Psychopathology clearly shows mental dysfunction as a system disturbance rather than as a loss of single functions. Even in localized traumas (for example, cortical lesions), the ensuing effect is impairment of the total action system, particularly with respect to higher and, hence, more demanding functions. Conversely, the system has considerable regulative capacities (Bethe, 1931; Goldstein, 1959; Lashley, 1929). THE AcnvE ÜRGANISM "Even without external stimuli, the organism is not a passive but an intrinsically active system. Reflex theory has presupposed that the primary element of behavior is response to external stimuli. In contrast, recent research shows with increasing clarity that autonomous activity of the nervous system, resting in the system itself, is to be considered primary. In evolution and General System Theory in Psychology and Psychiatry 209 development, reactive mechanisms appear to be superimposed upon primitive, rhythmic-locomotor activities. The stimulus (i.e., a change in external conditions) does not cause a process in an otherwise inert system; it only modifies processes in an autonomously active system" (Bertalanffy, 1937, pp. 133 ff.; also 1960). The living organism maintains a disequilibrium called the steady state of an open system and thus is able to dispense existing potentials or "tensions" in spontaneous activity or in response to releasing stimuli; it even advances toward higher order and organization. The robot model considers response to stimuli, reduction of tensions, reestablishment of an equilibrium disturbed by outside factors, adjustment to environment, and the like, as the basic and universa! scheme of behavior. The robot model, however, only partly covers animal behavior and does not cover an essential portion of human behavior at all. The insight into the primary immanent activity of the psychophysical organism necessitates a basic reorientation which can be supported by any amount of biologica!, neurophysiological, behavioral, psychological, and psychiatrie evidence. Autonomous activity is the most primitive form of behavior (von Bertalanffy, 1949a; Carmichael, 1954; Herrick, 1956; von Holst, 1937; Schiller, 1957; H. Werner 1957a); it is found in brain function (Hebb, 1949) and in psychological processes. The discovery of activating systems in the brain stem (Berlyne, 1960; Hebb, 1955; Magoun, 1958) has emphasized this fact in recent years. N atural behavior encompasses innumerable activities beyond the S-R scheme, from exploring, play, and rituals in animals (Schiller, 1957) to economie, intellectual, esthetic, religious, and the like pursuits to self-realization and creativity in man. Even rats seem to "look" for problems (Hebb, 1955), and the healthy child and adult are going far beyond the reduction of tensions or gratification of needs in innumerable activities that cannot be reduced to primary or secondary drives (G. Allport, 1961, p. 90). All such behavior is performed for its own sake, deriving gratification ("function pleasure," after K. Bühler) from the performance itself. For similar reasons, complete relaxation of tensions as in sensory-deprivation experiments is not an ideal state but is apt to produce insufferable anxiety, hallucinations, and other psychosislike symptoms. Prisoner's psychosis, or exacerbation of symp- 210 GENERAL SYSTEM THEORY toms in the closed ward, and retirement and weekend neurosis are related clinical conditions attesting that the psychophysical organism needs an amount of tension and activity for healthy existence. It is a symptom of mental disease that spontaneity is impaired. The patient increasingly becomes an autornaton or S-R machine, is pushed by biologica! drives, obsessed by needs for food, elimination, sex gratification, and so on. The model of the passive organism is a quite adequate description of the stereotype behavior of compulsives, of patients with brain lesions, and of the waning of autonomous activity in catatonia and related psychopathology. But by the same token, this emphasizes that normal behavior is different. RoMEOSTASIS Many psychophysiological reguiadons follow the principles of homeostasis. However, there are apparent limitations (cf. pp. l60ff.). Generally, the homeostasis scheme is not applicable (I) to dynamic regulations-i.e., reguiadons not based upon fixed mechanisms but taking place within a system functioning as a whole (for example, regulative processes after brain lesions); (2) to spontaneous activities; (3) to processes whose goal is not reduction but is building up of tensions; and (4) to processes of growth, development, creation, and the like. We mayalso say that homcostasis is inappropriate as an explanatory principle for those human activities which are nonutilitarian-i.e., not serving the primary needs of self-preservation and survival and their secondary derivatives, as is the case with many cultmal manifestations. The evolution of Greek sculpture, Renaissance painting, or German music had nothing to do with adjustment or survival because they are of symbolic rather than biologica! value (Bertalanffy, 1959; also l964c) (compare below). But even living nature is by no means merely utilitarian (von Bertalanffy, 1949a, pp. I06ff). The principle of homeostasis has sometimes been inflated to a point where it becomes silly. The martyr's death at the stake is explained (Freeman, 1948) "by abnormal displacement" of his internal processes so that death is more "homeostadng" than continuing existence (pp. I42ff.); the mountain dimher is supposed to risk his life because "losing valued social status may be General System Theory in Psychology and Psychiatry 211 more upsetting" (Stagner, 1951). Such examples show to what extremes some writers are willing to go in order to save a scheme which is rooted in economie-commercial philosophy and sets a premium on conformity and opportunism as ultimate values. It should not be forgotten that Cannon (1932), eminent physiologist and thinker that he was, is free of such distordons; he explicitly emphasized the "priceless unessentials" beyond homcostasis (p. 323) (cf. also Frank!, 1959b; Toch and Hastorf, 1955). The homeostasis model is applicable in psychopathology bè-; cause nonhomeostatic functions, as a rule, decline in mental · patients. Thus Karl Menninger (1963) was able to describe the progress of mental disease as a series of defense mechanisms, setding down at ever lower homeostatic levels until mere preservadon of physiological life is left. Arieti's (1959) concept of progressive teleological regression in schizophrenia is similar. DIFFERENTlATION "Differentiation is transformation from a more general and homeogeneous to a more special and heterogeneous condition" (Conklin after Cowdry, 1955, p. 12). "Wherever development occurs it proceeds from a state of relative globality and lack of differentiation to a state of increasing differentiation, articuladon, and hierarchic order" (H. Werner, I957b). The principle of differentiation is ubiquitous in biology, the evolution and development of the nervous system, behavior, psychology, and culture. We owe to Werner (1957a) the insight that mental functions generally progress from a syncredc state where percepts, motivation, feeling, imagery, symbols, concepts, and so forth are an amorphous unity, toward an ever clearer distinction of these funcdons. In perception the primitive state seems to be one of synesthesia (traces of which are left in the human adult and which may reappear in schizophrenia, mescaline, and LSD experience) out of which visual, auditional, tactual, chemical, and other experiences are separated. * In animal and a good deal of human behavior, there is a perceptual"Cf. recently J. J. Gibson, The Senses Considered as Perceptual Systems, (Boston, Houghton Miffiin, 1966); the model of neural hologram in brain physiology (K. H. Pribram, "Four R's of Remembering" in The Neuro· physiological and Biochemica! Bases of Learning, Cambridge, Harvard University Press) , and so on. 212 GENERAL SYSTEM THEORY emotive-motivational unity; perceived objects without emotionalmotivational undertones are a late achievement of mature, civilized man. The origins of language are obscure; but insofar as we can form an idea, it seems that :'holophrastic" (W. Humboldt, cf. Werner, 1957a) language and thought-i.e., utterances a.nd thoughts.with a broad aura of associations-preceded sepa'ratwn of meanmgs and articulate speech. Similarly, the categories of developed mental life such as the distinction of "I" and objects, space, time, number, causality, and so forth, evolved from a perceptual-conceptual-motivational continuurn represented by the "paleologie" perception of infants, primitives, and schizophrenics .(Arieti, 1959; Piaget, 1959; Werner, 1957a). Myth was the proldie chaos from which language, magie, art, science, medicine, mores, morals, andreligion were differentiated (Cassirer, 1953-1957). Thus "I" and "the world," "mind" and "matter," or Descartes's "res cogitans" and "res extensa" are not a simple datum and primordial antithesis. They are the final outcome of a long process in biologica! evolution, mental development of the child, a.nd cultural and 1inguistic history, wherein the perceiver is not s1mply a receptor of stimuli but in a very real sense creates his world (for example Bruner, 1958; Cantril, 1962; Geertz, 1962; Matson, 1964, pp. 18lff.). The story can be told in different ways (for example, G. Allport, 1961, pp. 110-138; von Bertalanffy, 1964a and 1965; Cassirer, 1953-1957; Freud, 1920; Merloo, 1956, pp. 196-199; Piaget, 1959; Werner, 1957a), but there is general agreement that differentiation arose from an "undifferentiated absolute of self and environment" (Berlyne, 1957), and that the a~im~stic e~perie~ce of .the child and the primitive (persisting still m Anstotehan philosophy), the "physiognomic" outlook (Werner, 1957a), the experience of "we" and "thou" (still much stronger in Griental than in Western thinking-Koestler, 1960), empathy, etc., were steps on the way until Renaissance physics eventually "discovered inanimate nature." "Things" and "self" emerge by a slow build-up of innumerable factors of gestalt dynamics, of learning processes, and of social, cultural, and linguistic determinants; the full distinction between "public objects" and "private self" is certainly not achieved without naming and language, that is, processes at the symbolic level; and General System Theory in Psychology and Psychiatry 213 perhaps this distinction presupposes a language of the IndoGermanic type (Whorf, 1956). In psychopathology and schizophrenia, all these prim1t1ve states may reappear by way of regression and in bizarre manifestations; bizarre because there are arbitrary combinations of archaic elements among themselves and with more sophisticated thought processes. On the other hand, the experience of the child, savage, and non-Westerner, though primitive, nevertheless forms an organized universe. This leads to the next group of concepts to be considered. CENTRALIZATION AND RELATEn CoNCEPTs "Organisms are not machines; but they can to a certain extent become machines, congeal into machines. Never completely, however; for a thoroughly mechanized organism would be incapable of reacting to the incessantly changing conditions of the outside world" (von Bertalanffy, 1949a, pp. 17ff.). The principle of progressive mechanization expresses the transition from undifferentiated wholeness to higher function, made possible by specialization and "division of labor"; this principle implies also loss of potentialities in the components and of regulability in the whole. Mechanization frequently leads to establishment of leading parts, that is, components dominating the behavior of the system. Such centers may exert "trigger causality," i.e., in contradistinction to the principle, causa aequat effectum, a small change in a leading part may by way of amplification mechanisms cause large changes in the total system. In this way, a hierarchic order of parts or processes may be established (cf. Chapter 3). These concepts hardly need comment except for the one debated point. In the brain as well as in mental function, centralization and hierarcbic order are achieved by stratification (A. Gilbert, 1957; Lersch, 1960; Luthe, 1957; Rothacker, 1947), i.e., by superimposition of higher "layers" that take the role of leading parts. Particulars and disputed points are beyond the present survey. However, one will agree that-in gross oversimplification-three major layers, or evolutionary steps, can be distinguished. In the brain these are (1) the paleencephalon, in lower vertebrates, (2) the neeneephalon (cortex), evolving from reptiles to mammals, 214 GENERAL SYSTEM THEORY and (3) certain "highest" centers, especially the motoric speech (Broca's) region and the large association areas which are found only in man. Concurrently there is an anterior shift of controlling centers, for example, in the apparatus of vision from the colliculi opt~ci of the mesencephalon (lower vertebrates) to the corpora gemculata lateraHa of the dieneephalon (mammals) to the regio calcarina of the telencephalon (man).* I~ some way parallel is stratification in the mental system which can he roughly circumscribed as the domains of instincts, drives, emotions, the primeval "depth personality"; perception and voluntary action; and the symbolic activities characteristic ?f man. None of the available formulations (for example, Freud's ~d, ego, ~nd. superego, and those of German stratification theorists) IS unobJectwnable. The neurophysiological meaning of a small portion of brain processes being "conscious" is completely unknown. The Freudian unconscious, or id, comprises only limited aspects and already pre-Freudian authors have given a much more comprehensive survey of unconscious functions (Whyte, 1960). Although these problems need further clarification it is incorrect when Anglo-Saxon authors refuse stratification for,being "philosophical" (Eysenck, 1957) or insist that there is no fundamental difference between the behavior of rat and that of man (Skinn:r, 1963). Such an attitude simply ignores elementary zoological facts. Moreover, stratification is indispensable for understanding psychiatrie disturbances. REGRESSION The psychotic state is sometimes said to be a "regression to older and more infantile forms of behavior." This is incorrect; already E. Bleuier noted that the child is not a little schizophrenic but a normally functioning though primitive being. "The schizophrenic will regress to, but not integrate at, a lower l~vel; he will remain disorganized" (Arieti, 1959, p. 475). Regression is essentially disintegration of personality; that is, dedifferentiation and decentralization. Dedifferentiation means that there is not a loss of meristic functions, but a reappearance of primitive states (syncretism, synesthesia, paleologie thinking, and so forth). Decentralization is, in the extreme, functional dysencephalization *Cf. recently A. Koestler, The Ghost in the Machine, (London, Hutchinson, 1967). General System Theory in Psychology and Psychiatry 215 in the schizophrenic (Arieti, 1955). Splitting of personality, according to E. Bleuler, in milder form neurotic complexes (i.e., psychological entities that assume dominance), disturbed ego function, weak ego, and so forth, similarly indicate loosening of the hierarcbic mental organization. BouNDARIEs Any system as an entity which can be investigated in its own right must have boundaries, either spatial or dynamic. Strictly speaking, spatial boundaries exist only in naive observation, and all boundaries are ultimately dynamic. One cannot exactly draw the boundaries of an atom (with valences sticking out, as it were, to attract other atoms), of a stone (an aggregate of molecules and atoms which mostly consist of empty space, with particles in planetary distances), or of an organism (continually exchanging matter with environment). In psychology, the boundary of the ego is both fundamental and precarious. As already noted, it is slowly established in evolution and development and is never completely fixed. It originates in proprioceptive experience and in the body image, but selfidentity is not completely established before the "I," "Thou," and "it" are named. Psychopathology shows the paradox that the ego boundary is at once too ftuid and too rigid. Syncretic perception, animistic feeling, delusions and hallucinations, and so on, make for insecurity of the ego boundary; but within his self-created universe the schizophrenic lives "in a shell," much in the way animals live in the "soap bubbles" of their organizationbound worlds (Schiller, 1957). In contrast to the animal's limited "ambient," man is "open to the world" or has a "universe"; that is, his world widely transcends biologica! bondage and even the limitations of his senses. To him, "encapsulation" (Royce, 1964) -from the specialist to the neurotic, and in the extreme, to the schizophrenic-sometimes is a pathogenie limitation of potentialities. These are based in rnan's symbolic functions. SYMBOLIC AcnviTIEs "Except for the immediate satisfaction of biologica! needs, man Jives in a world not of things but of symbols" (von Bertalanffy, 216 GENERAL SYSTEM THEORY 1956a). We may also say that the various symbolic universes, material and non-material, which distinguish human cultures from animal societies, are part, and easily the most important part, of rnan's behavior system. It can be justly questioned whether man is a rational animal; but he certainly is a symbolcreating and symbol-dominated being throughout. Symbolism is recognized as the unique criterion of man by biologists (von Bertalanffy, 1956a; Herrick, 1956), physiologists of the Pavlovian school ("secondary signal system") (Luria, 1961), psychiatrists (Appleby, Scher & Cummings, 1960; Arieti, 1959; Goldstein, 1959), and philosophers (Cassirer, 1953-1957; Langer, 1942). It is not found even in leading textbooks of psychology in consequence of the predominant robot philosophy. But it is precisely for symbolic functions that "motives in animals will not be an adequate model for motives in man" (G. Allport, 1961, p. 221), and that human personality is not finished at the age of three or so, as Freud's instinct theory assumed. The definition of symbolic activities will not be discussed here; the author has attempted to do so elsewhere (von Bertalanffy, 1956a and 1965). It suffices to say that probably all notions used to characterize human behavior are consequences or different aspects of symbolic activity. Culture or civilization; creative proception in contrast to passive perception (Murray, G. W. Allport), objectivation of both things outside and the self (Thumb, 1943), ego-world unity (Nuttin, 1957), abstract against concrete stratum (Goldstein, 1959); having a past and future, "timebinding," anticipation of future; true (Aristotelian) purposiveness (cf. Chapter 3), intention as conscious planning (G. Allport, 1961, p. 224); dread of death, suïcide; will to meaning (Frank!, 1959b), interest as engaging in self-gratifying cultmal activity (G. Allport, 1961, p. 225), idealistic devotion to a (perhaps hopeless) cause, martyrdom; "forward trust of mature motivation" (G. Allport, 1961, p. 90); self-transcendence; ego autonomy, conflictfree ego functions; essen ti al aggression (von Bertalanffy, 1958); conscience, superego, ego ideal, values, morals, dissimulation, truth and lying-all these stem from the root of creative symbolic universes and can therefore not be reduced to biologica! drives, psychoanalytic instincts, reinforcement of gratifications, or other biologica} factors. The distinction of biologica! and specific human values is that the former concerns the maintenance of the in- General System Theory in Psychology and Psychiatry 217 dividual and the survival of the species; the latter always concern a symbolic universe (Bertalanffy, 1959 and 1964c). . In consequence, mental disturbances in man, as a rule, 1nvolve disturbances of symbolic functions. Kubie (1953), appears to be correct when, as a "new hypothesis" on neuroses, he distinguishes "psychopathological processes which arise through the distarting impact of highly charged experiences at an early age" from those "consisting in the distartion of symbolic functions." Disturbances in schizophrenia are essentially also at the symbolic le:el. and able to take many different forms: Loosening of assonatwnal structure, breakdown of the ego boundary, speech and thought disturbances, concretization of ideas, desymbolization, paleologie thinking, and others. We refer to Arieti's (1959) and Goldstein's (1959) discussions. . The condusion (which is by no means generally accepted) IS that mental illness is a specifically human phenomenon. Animals may behaviarally show (and for all we know by empathy experience) any number of perceptional, motoric and mood disturbances, hallucinations, dreams, faulty reactions, and the like. Animals cannot have the disturbances of symbolic functions that are essential ingredients of mental disease. In animals there cannot be disturbance of ideas, delusions of grandeur or of persecution, etc., for the simple reason that there ~re no ideas to start with. Hence, "animal neurosis" is only a partlal model of the clinical entity (von Bertalanffy, 1957a). This is the ultimate reason why human behavior and psychology cannot be reduced to biologistic notions like restoration of homeostasis, conflict of biologica! drives, unsatisfactory motherinfant relationships, and the like. Another consequence is the culture-dependenee of mental illness both in symptomatology and epidemiology. To say that psychiatry has a physio-psychosociological framework is but another expression of the same fact. For the same reason, human striving is more than self-realization; it is directed toward objective goals and realization of values (Frank!, 1959a, 1959b; 1960), which means nothing else tha_n symbolic entities which in a way become detached from the1r creators (von Bertalanffy, 1956a; also 1965). Perhaps we may venture a definition. There may be conflict between biologica! drives and a symbolic value system; this is the situation of psychoneurosis. Or there may be conflict between symbolic universes, 218 GENERAL SYSTEM THEORY or loss of value orientation and experience of meaninglessness in the individual; this is the situation when existential or "noogenic" neurosis arises. Similar considerations apply to "character disorders" like juvenile delinquency that, quite apart from their psychodynamics, stem from the breakdown or erosion of the value system. Among other things, culture is an important psycho-hygienic factor (von Bertalanffy, 1959 and 1964c). SYSTEM-A NEw CoNcEPTVAL FRAMEWORK Having gone through a primer of system-theoretical notions, we may summarize that these appear to provide a consistent framework for psychopathology. Mental disease is essentially a disturbance of system functions of the psychophysical organism. For this reason, isolated symptoms or syndromes do not define the disease entity (von Bertalanffy, 1960a). Look at some classica! symptoms of schizophrenia. "Loosening of associational structure" (E. Bleuler) and unbridled chains of associations; quite similar examples are found in "purple" poetry and rhetoric. Auditory hallucinations; "voices" told Joan of Are to liberate France. Piercing sensations; a great mystic like St. Teresa reported identical experience. Fantastic world constructions; those of science surpass any schizophrenic's. This is not to play on the theme "genius and madness," but it is apt to show that not single criteria but integration makes for the difference. Psychiatrie disturbances can be neatly defined in terms of system functions. In reference to cognition, the worlds of psychotics, as impressively described by writers of the phenomenological and existentialist schools (for example, May et al., 1958), are "products of their brains." But our normal world is shaped also by emotional, motivational, social, cultural, linguistic, and the like factors, amalgamated with perception proper. Illusions and delusions, and hallucinations at least in dreams, are present in the healthy individual; the mechanisms of illusion play even an important role in constancy phenomena, without which a consistent world image would be impossible. The contrast of normality to schizophrenia is not that normal perception is a plane mirror of reality "as is," but that schizophrenia has subjective elements that run wild and that are disintegrated. General System Theory in Psychology and Psychiatry 219 The same applies at the symbolic level. Scientific notions such as the earth running with unimaginable speed through the universe or a solid body consisting mostly of empty space interlaced with tiny energy specks at astronomical distances, contradiet all everyday experience and "common sense" and are more fantastic than the "world designs" of schizophrenics. N evertheless the scientific notions happen to be "true" -i.e., they fit into an integrated scheme. Similar considerations apply to motivation. The concept of spontaneity draws the borderline. Normal motivation implies autonomous activity, integration of behavior, plasticity in and adaptability to changing situations, free use of symbolic anticipation, decision, and so forth. This emphasizes the hierarchy of functions, especially the symbolic level superimposed upon the organismic. Hence beside the organismic principle of "spontaneous activity" the "humanistic" principle of "symbolic functions" must be basic in system-theoretical consideration. Hence the answer whether an individual is mentally sound or not is ultimately determined by whether he has an integrated universe consistent within the given cultural framework (von Bertalanffy, l960a). So far as we can see, this criterion camprises all phenomena of psychopathology as compared with normality and leaves room for culture-dependenee of mental norms. What may be consistent in one culture may be pathological in another, as cultmal anthropologists (Benedict, 1934) have shown. This concept has definite implications for psychotherapy. lf the psychophysical organism is an active system, occupational and adjunctive therapies are an obvious consequence; evacation of creative potentialities will be more important than passive adjustment. If these concepts are correct, more important than "digging the past" will be insight into present conflicts, attempts at reintegration, and orientation toward goals and the future, that is, symbolic anticipation. This, of course, is a paraphrase of recent trends in psychotherapy which thus may be grounded in "personality as system." If, finally, much of present neurosis is "existential," resulting from meaninglessness of life, then "logotherapy" (Frankl, 1959b), i.e., therapy at the symbolic level, will be in place. It therefore appears that-without falling into the trap of 220 GENERAL SYSTEM THEORY "nothing-but" philosophy and disparaging other conceptionsa system theory of personality provides a sound basis for psychology and psychopathology. Condusion System theory in psychology and psychiatry is not a dramàtic dénouement of new discovery, and if the reader has a déjà vu feeling, we shall not contradiet him. It was our intention to show that system concepts in this field are not speculation, are not an attempt to press facts into the straitjacket of a theory which happens to be in vogue, and have nothing to do with "mentalistic anthropomorphism," so feared by behaviorists. Nevertheless, the system concept is a radical reversal with respect to robotic theories, leading to a more realistic (and incidentally more dignified) image of man. Moreover, it entails far-reaching consequences for the scientific world view which can only be alluded to in the present outline: (l) The system concept provides a theoretica! framework which is psychophysically neutra!. Physical and physiological terms such action potentials, chemical transmission at synapses, neural network, and the like are not applicable to mental phenomena, and even less can psychological notions be applied to physical phenomena. System terms and principles like . those discussed can be applied to facts in either field. (2) The mind-body problem cannot be discussed here, and the author has to refer to another investigation (von Bertalanffy, l964a). We can only summarize that the Cartesian dualism between matter and mind, objects outside and ego inside, brain and consciousness, and so forth, is incorrect bath in the light of direct phenomenological experience and of modern research in various fields; it is a conceptualization stemming from l7thcentury physics which, even though still prevailing in modern debates (Hook, 1961; Scher, 1962), is obsolete. In the modern view, science does not make metaphysical statements, whether of the materialistic, idealistic, or positivistic sense-data variety. It is a conceptual construct to reproduce limited aspects of experience in their formal structure. Theories of behavior and of psychology should be similar in their formal structure or isomorphic. Possibly systems concepts are the first beginning of such "common General System Theory in Psychology and Psychiatry 221 language" (compare Piaget and Bertalanffy in Tanner and Inhelder, 1960). In the remote future this may lead to a "unified theory" (Whyte, 1960) from which eventually materialand mental, conscious and unconscious aspects could be derived. (3) Within the framework developed, the problem of free will or determinism also receives a new and definite meaning. It is a pseudo-problem, resulting from confusion of different levels of experience and of epistemology and metaphysics. We experience ourselves as free, for the simple reason that the category of causality is not applied in direct or immediate experience. Causality is a category applied to bring order into objectivated experience reproduced in symbols. Within the latter, we try to explain mental and behaviaral phenomena as causally determined and can do so with increasing approximation by taking into account ever more factors of motivation, by refining conceptual models, etc. Will is not determined, but is determinable, particularly in the machine-like and average aspects of behavior, as motivation researchers and statisticians know. However, causality is not metaphysical necessity, but is one instrumenttobring order into experience, and there are other "perspectives" (Chapter 10), of equal or superior standing. (4) Separate from the epistemological question is the moral and legal question of responsibility. Responsibility is always judged within a symbolic framework of values as accepted in a society under given circumstances. For example, the M'Naghten rules which excuse the offender if "he cannot tell right from wrong," actually mean that the criminal goes unpunished if his symbolic comprehension is obliterated; hence his behavior is determined only by "animal" drives. Killing is prohibited and is punished as murder within the symbolic framework of the ordinary state of society, but is commanded (and refusal of the command is punished) in the different value frame of war. The Relativity of Categories 10 The Relativity of Categories The Whorfian Hypothesis Among recent developments in the anthropological sciences, hardly any have found so much attention and led to so much controversy as have the views advanced by the late Benjamin Whorf. The hypothesis offered by Whorf is, that the commonly held belief that the cognitive processes of all human beings possess a common logical structure which operates prior to and independently of communication through language, is erroneous. It is Whorf's view that the linguistic patterns themselves determine what the individual perceives in this world and how he thinks about it. Since these patterns vary widely, the modes of thinking and perceiving in groups utilizing different linguistic systems will result in basically different world views (Fearing, 1954). We are thus introduced to a new principle of relativity which holds that all observers are not led by the same physical evidence to the same picture of the universe, unless their linguistic backgrounds are similar .... We cut up and organize the spread and flow of events as we do largely because, through 223 our mother tongue, we are parties of an agreement to do so, not because nature itself is segmented in exactly that way for all to see (Whorf, 1952, p. 21). For example, in the Indo-European languages substantives, adjectives and verbs appear as basic gramrnatic units, a sentence being essentially a combination of these parts. This scheme of a persisting entity separable from its properties and active or passive behavior is fundamental for the categories of occidental thinking, from Aristotle's categories of "substance," "attributes" and "action" to the antithesis of matter and force, mass and energy in physics. Indian languages, such at Nootka (Vancouver Island) or Hopi, do not have parts of speech or separable subject and predicate. Rather they signify an event as a whole. When we say, "a light flashed" or "it (a dubious hypostatized entity) flashed," Hopi uses a single term, "flash (occurred) ."1 It would be important to apply the methods of mathematica! logic to such languages. Can statements in languages like Nootka or Hopi be rendered by the usuallogistic notation, or is the latter itself a formalization of the structure of Indo-European language? It appears that this important subject has not been investigated. Indo-European languages emphasize time. The "give-and-take" between language and culture· leads, according to Whorf, to keeping of records, diaries, mathernaties stimulated by accounting; to calendars, clocks, chronology, time as used in physics; to the bistorical attitude, interest in the past, archeology, etc. It is interesting to compare this with Spengler's conception of the central role of time in the occidental world picture (cf. p. 234f.), which, from a different viewpoint, comes to the identical conclusion. However, the-for us-self-evident distinction between past, present, and future does not exist in the Hopi language. It makes no distinction between tenses, but indicates the validity a statement has: fact, memory, expectation, or custom. There is no difference in Hopi between "he runs," "he is running," "he ran," all being rendered by wari, "running occur." An expectation is rendered by warinki ("running occur [IJ daresay"), which covers "he will, shall, should, would run." If, however, it is a statement of a generallaw, warikngwe ("running occur, characteristically") 224 GENERAL SYSTEM THEORY is applied (La Barre, 1954, pp. 197 ff.). The Hopi "has no general notion or intuition of time as a smooth ftowing continuurn in which everything in the universe proceeds at an equal rate, out of a future, through a present, into a past." (Whorf, 1952, p. 67) . Instead of our categories of space and time, Hopi rather distinguishes the "manifest," all that which is accessible to the senses, with no distinction between present and past, and the "unmanifest" comprising the future as well as what we call mentaL Navaho (cf. Kluckhohn and Leighton, 1951) has little development of tenses; the emphasis is upon types of activity, and thus it distinguishes durative, perfective, usitative, repetitive, iterative, optative, semifactive, momentaneous, progressive, transitional, conative, etc., aspects of action. The difference can be defined ~hat the first. co~cern of English (and Indo-European Ianguage m _?~neral) IS time, of Hopi-validity, and of Navaho-type of actiVIty (personal communication of Professor Kluckhohn). Whorf asks: How would a physics constructed along these Iines work, with no t (time) in its equations? Perfectly, as far as I can see, though of course it would require different ideology and perhaps different mathematics. Of course, v (velocity) would have to go, too (1952, p. 7). ~gai~, it can be mentioned that a timeless physics actually exists, m the form of Greek statics (cf. p. 234). For us, it is part of a wider system, dynamics, for the particular case that t ~ ro , i.e., time approaches the infinite and drops out of the equations. i.e., time approaches the infinite and drops out of the equations. As regards space, the Indo-European tongues widely express nonspatial relations by spatial metaphors: long, short for duration; heavy, light, high, low for intensity; approach, rise, fall for tendency; Latin expressions like educo, religio, comprehendo as metaphorical spatial (probably more correct: corporeal, L.v.B.) references: lead out, tying back, grasp, etc.2 This is untrue of Hopi where rather physical things are named by psychological metaphors. Thus the Hopi word for "heart" can be shown to be a late formation from a root meaning "think" or "remember." Hopi language is, as Whorf states, capable of ac- The Relativity of Categories 225 counting for and descrihing correctly, in a pragmatical or observational sense, all observable phenomena of the universe. However, the implicit metaphysics is entirely different, being rather a way of animistic or vitalistic thinking, near to the mystica! experience of oneness. Thus, Whorf maintains, "Newtonian space, time and matter are no intuitions. They are recepts from culture and language." (1952, p. 40). Just as it is possible to have any number of geometries other than the Euclidean which give an equally perfect account of space configurations, so it is possible to have descriptions of the universe, all equally valid, that do not contain our familiar contrast of time and space. The relativity viewpoint of modern physics is one such view, conceived in mathematica! terms, and the Hopi Weltanschauung is another and quite different one, non-mathematica! and linguistic (Whorf, 1952, p. 67). The ingrained mechanistic way of thinking which comes into difficulties with modern scientific developments is a consequence of our specific linguistic categories and habits, and Whorf hopes that insight into the diversity of linguistic systems may contribute to the reevaluation of scientific concepts. La Barre (1954, p. 301) has vividly summarized this viewpoint: Aristotelian Substance and Attribute look remarkable like Indo-European nouns and predicate adjectives . . . . More modern science may well raise the question whether Kant's Forms, ortwin "spectacles" of Time and Space (without which we can perceive nothing) are not on the one hand mere IndoEuropeau verbal tense, and on the other hand human stereoscopy and kinaesthesis and life-process-which might be more economically expressed in terms of the c, or light-constant, of Einstein's formula. But we must remember all the time that E = mc 2 is also only a grammatica! conception of reality in terms of Indo-European morphological categories of speech. A Hopi, Chinese, or Eskimo Einstein might discover via his grammatica! habits wholly different mathematica! conceptualizations with which to apperceive reality. This paper is not intended to discuss the linguistic problems posed by Whorf as was exhaustively done in a recent symposium 226 GENERAL SYSTEM THEORY (Hoijer et al., 1954). However, it has occured to the present author that what is known as the Whorfian hypothesis is not an isolated statement of a somewhat extravagant individual. Rather the Whorfian hypothesis of the linguistic determination of the categories of cognition is part of a general revision of the cognitive process. It is embedded in a powerful current of modern thought, the sourees of which can be found in philosophy as well as in biology. It seems that these connections are not realized to the extent they deserve. The general problem posed may be expressed as follows: In how far are the categories of our thinking modeled by and dependent on biologica! and cultmal factors? It is obvious that, stated in this way, the problem far exceeds the borders of linguistics and touches the question of the foundations of human knowledge. Such analysis will have to start with the classica!, absolutistic world view which found its foremost expression in the Kantian system. According to the Kantian thesis, there are the so-called forms of intuition, space and time, and the categories of the intellect, such as substance, causality and others which are universally committal for any rational being. Accordingly science, based upon these categories, is equally universa!. Physical science using these a priori categories, namely, Euclidean space, Newtonian time and strict deterministic causality, is essentially dassical mechanics which, therefore, is the absolute system of knowledge, applying to any phenomenon as well as to any mind as observer. It is a well-known fact that modern science has long recognized that this is not so. There is no need to helahor this point. Euclidean space is but one form of geometry beside which other, non-Eueliclean geometries exist which have exactly the same logica! structure and right to exist. Modern science applies whatever sort of space and time is most convenient and appropriate for descrihing the events in nature. In the world of medium dimensions, Euclidean space and Newtonian time apply in the way of satisfactory approximations. However, coming to astronomical dimensions and, on the other hand, to atomie events, nonEueliclean spaces or the many-dimensional configuration spaces of quanturn theory are introduced. In the theory of relativity, space and time fuse in the Minkowski union, where time is The Relativity of Categories 227 another coordinate of a four-dimensional continuum, although of a somewhat peculiar character. Solid matter, this most obtrusive part of experience and most trivia! of the categories of naïve physics, consists almost completely of holes, being a void for the greatest part, only interwoven by centers of energy which, consiclering their magnitude, are separated by astronomical distances. Mass and energy, somewhat sophisticated quantifications of the categorical antithesis of stuff and force, appear as expressions of one unknown reality, interchangeable according to Einstein's law. Similarly, the strict determinism of classica! physics is replaced in quanturn physics by indeterminism or rather by the insight that the laws of nature are essentially of a statistica! character. Little is left of Kant's supposedly a priori and absolute categories. Incidentally, it is symptomatic of the relativity of world views that Kant who, in his epoch, appeared to be the great destroyer of all "dogmatism," to us appears a paradigm of unwarranted absolutism and dogmatism. So the question arises-what is it which determines the categories of human cognition? While, in the Kantian system, the categories appeared to be absolute for any rational observer, they now appear as changing with the advancement of scientific knowledge. In this sense, the absolutistic conception of earlier times and of classica! physics is replaced by a scientific relativism. The argument of the present discussion may be defined as follows. The categories of knowledge, of everyday knowledge as well as of scientific knowledge, which in the last resort is only a refinement of the former, depend, first, on biologica! factors; second, on cultmal factors. Third, notwithstanding this all-toahuman entanglement, absolute knowledge, emancipated from human limitations, is possible in a certain sense. The Biologica! Relativity of Categories Cognition is dependent, firstly, on the psycho-physical organization of man. We may refer here in particular to that approach in modern biology which was inaugurated by Jacob von Uexküll under the name of Umwelt-Lehre. It essentially amounts to the statement that, from the great cake of reality, every living organism cuts a slice, which it can perceive and to which it can react owing to its psycho-physical organization, i.e., the structure 228 GENERAL SYSTEM THEORY of receptor and effector organs. Von Uexküll and ~riszat (1934) have presented fascinating pictures how the same sectwn of nature looks as seen by various animals; they should be compared to Whorf's equally amusing drawings whièh show how the world is modeled according to linguistic schemes. Here only a few examples, chosen from Uexküll's extensive behaviaral studies, can be mentioned. Take, e.g., a unicellular organism like the paramecium. lts almost only way of response is the flight reaction (phobotaxis) by which it reacts to the most diverse, chemical, tactile, thermal, photic, etc., stimuli. This simple reaction, howe:er, suffices safely to guide that animal which possesses no speCific sense organs, into the region of optima! conditions. The many things in the environment of the paramecium, algae, other infusoria, little crustaceans, mechanica! obstacles and the like, are nonexistent for it. Only one stimulus is received which leads to the flight reaction. As this example shows, the organizational and functional plan of a living being determines what can become "stimulus" and "characteristic" to which the organism responds with a certain reaction. According to von Uexküll's expression, any organism, so to speak, cuts out from the multiplicity of surrounding objects a small number of characteristics to which it reacts and whose ensemble forms its "ambient" (Umwelt). All the rest is nonexistent for that particular organism. Every animal is surrounded, as by a soapbubble, by its specific ambient, replenished by those characteristics which are amenable to it. If, reconstructing an animal's ambient, we enter this soapbubble, the world is profoundly changed: Many characteristics disappear, others arise, and a completely new world is found. Von Uexküll has given innumerable examples delineating the ambients of various animals. Take, for instance, a tick lurking in the bushes for a passing mammal in whose skin it setties and drinks itself full of blood. The signal is the odor of butyric acid, flowing from the dermal glands of all mammals. Followin~ this stimulus, it plunges down; if it feil on a warm body-as momtored by its sensitive thermal sense-it has reached its prey, a warmblooded anima!, and only needs to find, aided by tactile sense, a hair-free place to pierce in. Thus the rich environment of the tick shrinks to metamorphize into a scanty contiguration out of The Relativity of Categories 229 which only three signals, beaconlike, are gleaming which, however, suffice to lead the animal surely to its goal. Or again, some sea urchins respond to any darkening by striking together their spines. This reaction invariably is applied against a passing cloud or boat, or the real enemy, an approaching fish. Thus, while the environment of the sea urchin contains many different objects, its ambient only contains one characteristic, namely, dimming of light. This organizational constraint of the ambient goes even much farther than the examples just mentioned indicate (von Bertalanffy, 1937). It also concerns the forms of intuition, considered by Kant as a priori and immutable. The biologist finds that there is no absolute space or time but that they depend on the organization of the perceiving organism. Three-dimensional Euclidean space, where the three rectangular coordinates are equivalent, was always identified with the a priori space of experience and perception. But even simple contemplation sho':s, and experiments in this line (von Allesch, 1931; von Skramhk, 1934, and others) prove that the space of visual and tactual perception is in no way Euclidean. In the space of perception, the coordinates are in no way equivalent, but there is a fundamental difference between top and bottom, right and left, and fore and aft. Already the organization of our body and, in the last resort, the fact that the organism is subjected to gravity, makes for an inequality of the horizontal and vertical dimensions. This is readily shown by a simplefact known to every photographer. We experience it as quite correct that, according to the laws of perspective, parallels, such as railraad tracks, converge in the distance. Exactly the same perspective foreshortening is, however, experienced as being wrong if it appears in the vertical dimension. If a picture was taken with the camera tilted, we obtain "falling lines," the edges of a house, e.g., running together. This is, perspectively, just as correct as are the converging railroad tracks; nevertheless, the latter perspective is experienced as being correct, while the converging edges of a house are experienced as wrong; the explanation being that the human organism is such as to have an ambient with considerable horizontal, but negligible vertical extension.s A similar relativity is found in experienced time. Von Uexküll has introduced the notion of the "instant" as the smallest unit 230 GENERAL SYSTEM THEORY of perceived time. For man, the instant is about .lfl8 sec., i.e., impressions shorter than this duration are not perce1ved separately but fuse. It appears that the duration of the instant depends not on conditions in the sense organs but rather in the central nervous system, for it is the same for different sense or~ans .. This flicker fusion is, of course, the raison d' être of mov1e p1ctures when frames presented in a sequence faster than 18 per secoud fuse into continuous motion. The duration of the instant varies in different species. There are "slow motion-pictu re animals" (von Uexküll) which perceive a greater number of impressions per secoud than man. Thus, the fighting fish (Betta) does not recognize its image in a mirror if, by a mechanica! device, it is presented 18 times per second. lt has to be presented at least 30 times per second; then the fish attacks his imaginary opponent. Hence, these small and very active animals consume a larger number of impressions than man does, per unit of astronomica l time; time is decelerated. Conversely, a snail is a "rapid motionpicture animal." It erawis on a vibrating stick if it approaches four times per second, i.e., a stick vibrating four times per secoud appears at rest to the snail. . . Experienced time is not Newtonian. Far f~om flowmg umfor~ly (aequilabilit er fluit, as Newton has it), 1t depends on physwlogical conditions. The so-called time memory of animals and man seems to be determined by a "physiologic al doek." Thus hees, conditioned to appear at a certain time at the feeding place, will show up earlier or later if drugs which increase o~ decr~ase the rate of metabolism are administered (e.g., von Stem-Belmg , 1935; Kalmus, 1934; Wahl, 1932; and others). Experienced time seems to fty if it is filled with impressions, and creeps if we are in a state of tedium. In fever, when body temperature and metabolic rate are increased, ti~e seem.s ~o linger since the number of "instants" per astronom1ca l umt m Uexküll's senseis increased. This time experience is paralleled by a correspondi ng increase of the frequency of the et-waves in the brain (Hoagland, 1951). With increasing age, time appears to run faster, i.e., a smaller number of instauts is experienced per astronomica l unit of time. Correspondi ngly, the rate of cicatrization of wounds is decreased proportiona l to age, the psychologica l as well as physiologica l phenomena obviously being connected ! ! ! The Relativity of Categories 231 with the slowing-dow n of metabolic processes in senescence (du Noüy, 1937). Several attempts (Brody, 1937; Backman, 1940; von Bertalanffy, 1951, p. 346) have been made to establish a biologica! as compared to astronomica l time. One means is the homologizat ion of growth curves: If the course of growth in different animals is expressed by the same formula and curve, the units of the time scale (plotted in astronomica l time) will be different, and important physiologica l changes presumably will appear at corresponding points of the curve. From the standpoint of physics, a thermadyna mie time, based upon the secoud principle and irreversible processes, can be introduced as opposed to astronomical time (Prigogine, 1947). Thermadyna mie time is nonlinear but logarithmic since it depends on probabilities ; it is, for the same reason, statistica!; and it is local because determined by the events at a certain point. Probably biologica! time bears an intimate although by no means simple relation to thermadyna mie time. How the categories of experience depend on physiologica l states, is also shown by the action of drugs. U nder the inftuence of mescaline, e.g., visual impressions are intensified, and the perception of space and time undergoes profound changes (cf. Anschütz, 1953; A. Huxley, 1954). It would make a most interesting study to investigate the categories of schizophreni cs, and it would probably be found that they differ considerably from those of "normal" experience, as do iudeed the categoties in the experience of dreams. Even the most fundamenta l category of experience, namely, the distinction of ego and nonego, is not absolutely fixed. It seems gradually to evolve in the developmen t of the child. It is essentially different in the animistic thinking of the primitives (still in force even in the Aristotelian theory where everything "seeks" its natura! place), and in Western thinking since the Renaissance which "has discovered the inanimate" (Schaxel, 1923). The object-subje ct separation again disappears in the empathie world view of the poet, in mystica! ecstasy and in states of intoxication . There is no intrinsic justification to consider as "true" representation of the world what we take to be "normal" experience 232 GENERAL SYSTEM THEORY (i.e., the experience of the average adult European of .the twentieth century) , and to consider all other sorts of expenence that are equally vivid, as merely abnormal, , fantastic or, at best, a primitive precursor to our "scientific" world pic~ure. The discussion of these problems could easily be enlarged, but the point important for the present topic will have become clear. The categories of experience or forms of intuition, to use Kant's term, are not a universa! a priori, but rather they depend on the psychophysical organization and physio~ogical _c~nditions of the experiencing animal, man included. Th1s relat1v1sm from the biologica! standpoint is an interesting parallel to the relativism of categories as viewed from the standpoint of culture and language. The Cultural Relativity of Categories We now come to the secoud point, the dependenee of categories on cultural factors. As already mentioned, the Whorfian thesis of the dependenee of categories on linguistic factors is part of a general conception of cultural relativism which has develo_red in the past 50 years; although even this is not quite correct, smce Wilhelm von Humboldt has already emphasized the dependenee of our world perspective on linguistic factors and the structure of language. It appears that this development started !n the histor~ of _art. At the beginning of this century, the V1ennese art-h1stonan, Riegl, published a very learned and tedious treatise on lateRoman artcraft. He introduced the concept of Kunstwollen, a term which may be translated as "artistic intention." The uilnaturalistic character of primitive art was conceived to be a consequence not of a lack of skill or know-how, but rather as exp:ession of an artistic intention which is different from ours, bemg not interested in a realistic reproduetion of nature. The same applies to the so-called degeneration of classic art in the late Hellenistic period. This conception later was expanded by Worringer who demonstrated in the example of Gothic art that artistic modes diametrically opposed to the classica! canon are an outcome not of teehuical impotence, but rather of a different world view. It was not that Gothic sculptors and painters did not know how to represent nature correctly, but their intention was The Relativity of Categories 233 different and not directed towards representative art. The conneetion of these theories with the primitivism and expressionism in modern art needs no discussion. I wish to offer another example of the same phenomenon which is instructive since it has nothing to do with the antithesis of representative and expressionistic, objective and abstract art. It is found in the history of the J apanese woodcut. J apanese pictures of the later period apply a certain kind of perspective, known as parallel perspective, which is different from central perspective as used in European art since the Renaissance. It is well known that Dutch treatises on perspectives were introduced into Japan in the late eighteenth century, and were eagerly studied by the Ukiyoye (woodcut) masters. They adopted perspective as a powerful means to represent nature, but only to a rather subtie limit. While European painting uses central perspective where the picture is conceived from a focal point and consequently parallels converge in the distance, the Japanese only accepted parallel perspective; i.e., a way of projection where the focal point is in the infinite, and hence parallels do not converge. We may be sure that this was not lack of skill in those eminent J apanese artists who, like Hokusai and Hiroshige, later exerted a profound influence on modern European art. They certainly would have found no difficulty to adopt an artistic means which even was handed to them ready-made. Rather we may conjecture that they felt central perspective, dependent on the standpoint of the observer, to be contingent and accidental and not representing reality since it changes as the observer moves from one place to another. In a similar way, the Japanese artists never painted shadows. This, of course, does not mean that they did not see shadow or go into the shade when the sun was burning. However, they did not wish to paint it; for the shadow does not belong to the reality of things but is only changing appearance. So the categories of artistic creation seem to be dependent on the culture in question. It is well known that Spengler has expanded this thesis to include cognitive categories. According to him, the so-called a priori contains, besides a small number of universally human and logically necessary forms of thinking, also forms of thinking that are universa! and necessary not for humanity as a whole but only for the particular civilization in 234 GENERAL SYSTEM THEORY question. So there are various and different "styles of cognition," characteristic of certain groups of human beings. Spengler does not deny the universa! validity of the formal laws of logic or of the empirica! verités de fait. He contends, however, the relativity of the contentual a prioris in science and philosophy. It is in this sense that Spengler states the relativity of rnathematics and mathematica! science. The mathematica! formulae as such carry logical necessity; but their visualizable interpretation which gives them meaning is an expression of the "soul" of the civilization which has created them. In this way, our scientific world picture is only of relative validity. lts fundamental concepts, such as the infinite space, force, energy, motion, etc., are an expression of our occidental type of mind, and do not hold for the world picture of other civilizations. The analysis upon which Spengler's cultmal relativism of the categories is mainly based is his famous antithesis of Apollonian and Faustian man. According to him, the primeval symbol of the Apollonian mindof antiquity is the material and bodily existence of individuals; that of the Faustian mind of the occident is infinite space. Thus "space," for the Greeks, is the mè ón, that which is not. Consequently, Apollonian rnathematics is a theory of visualizable magnitudes, culminating in stereometry and geometrie construction which, in occidental mathematics, is a rather inconsequential elementary topic. Occidental mathematics, governed by the primeval symbol of the infinite space, in contrast, is a theory of pure relations, culminating in differential calculus, the geometry of many-dimensional spaces, etc., which, in their unvisualizability, would have been completely inconceivable to the Greeks. A secoud antithesis is that of the static character of Greek, and the dynamic character of occidental thought. Thus, for the Greek physicist, an atom was a miniature plastic body; for occidental physics, it is a center of energy, radiating actions into an infinite space. Connected with this is the meaning of time. Greek physics did not contain a time dimension, and this is at the basis of its being a staties. Occidental physics is deeply concerned with the time course of events, the notion of entropy being probably the deepest conception in the system. From the concern with time further follows the bistorical orientation of the occidental mind expressed in the dominating influence of the The Relativity of Categories 235 doek, in the biography of the individual, in the enormous perspective of "world history" from historiography to cultmal history to anthropology, biologica! evolution, geological history, and finally astronomical history of the universe. Again, the same contrast is manifest in the conception of the mind. Static Greek psychology imagines a harmonie soul-body whose "parts," according to Plato, are reasou (logistikón), emotion (thymoeidés), and cathexis (epithymetikón). Dynamic occidental psychology imagines a soul-space where pyschological forces are interacting. Taking exception from Spengler's metaphysics and intuitive method, and disregarding questionable details, it will be difficult to deny that his conception of the cultmal relativity of categories is essentially correct. It suffices to remember the first lines of the Iliad, telling of the heroes of the Trojan war autoiJS te helória teîiche kynessin, that their selves were given a prey to the hounds and birds, the "self" being essentially the body or soma. Compare this with Descartes' cogito ergo sum-and the contrast between Apollonian and Faustian mind is obvious. While the German philosophers of history were concerned with the small number of high cultures (Hochkulturen), it is the hallmark and merit of modern and, in particular, American anthropology to take into account the entire field of human "cultures" including the multiplicity exhibited by primitive peoples. So the theory of cultmal relativism wins a broader basis but it is remarkable that the conclusions reached are very similar to those of the German philosophers. In particular, the Whorfian thesis is essentially identical with the Spenglerian-the one based upon the linguistics of primitive tribes, the other on a general view of the few high cultures of history. 4 So it appears well established that the categories of cognition depend, first, on biologica! factors, and secondly, on cultmal factors. A suitable formulation perhaps can he given in the following way. Our perception is essentially determined by our specifically human, psychophysical organization. This is essentially von Uexküll's thesis. Linguistic, and cultmal categories in genera!, will not change the potentialities of sensory experience. They will, however, change apperception, i.e., which features of experienced reality are focused and emphasized, and which are underplayed. 236 GENERAL SYSTEM THEORY There is nothing mysterious or particularly paradoxical in this statement which, on the contrary, is rather trivial; nothing w~ich would justify the heat and passion which, has aften _ch_aractenzed the dispute on the Whorfian, Spen_gleria~, and simllar th:ses. Suppose a histological preparadon Is _studie~ under_ the microscope. Any observer, if he is not color-blmd,_ will perceive th~ sa_me picture, various shapes and colors, etc., as given by the ~pphcatw~ of histological stains. However, what he actually s:es, I.e., what lS his apperception (and what he is able to con:mumcate) , depends widely on whether he is an untrained or a tramed observer. Where for the layman there is only a chaos of shapes and col~rs, the bistalogist sees cells with their various components: different tissues, and signs of malignant growth. And even th:s depe_nds on his line of interest and training. A cytochemist will possibly notice fine granulations in the cytoplasm of cells which represe~t to him certain chemically defined inclusions; the patholagist may, instead, entirely ignore these niceties, and rather "see" how a tumor has infiltrated the organ. Thus what is seen depends on our apperception, on our line of attention and interest which, in turn, is determined by training, i.e., by linguistic symbols by which we represent and summarize reality. . . It is equally trivial that the same object is somethmg qmte different if envisaged from different viewpoints. The same table is to the physicist an aggregate of electrons, protons, and neutrons, to the chemist a composition of certain organic compounds, to the biologist a complex of wood cells, to the art historian a baroque object, to the economist a utility of certain money val~e, etc. All these perspectives are of equal status, and none can claim more absolute value than the other (cf. von Bertalanffy, 1953b). Or, take a slightly Iess trivia! example. Organic for~s can he considered from different viewpoints. Typology considers them as the expression of different plans of organization; the th_eory of evolution as a product of a historica! process; a dynamic m?rphology as expression of a play of processes and forces for which mathematica! laws are sought (von Bertalanffy, 1941). Each of these viewpoints is perfectly Iegitimate, and there is little point to play one against the other. What is obvious in these special examples equally holds for what traits of reality are noticed in our general world picture. It is an important trend of the development of science that new I ,I The Relativity of Categories 237 aspects, previously unnoticed, are "seen," i.e., come under the focus of attention and apperception; and conversely, an important obstacle that the goggles of a certain theoretica! conception do nat allow to realize phenomena which, in themselves, are perfectly obvious. Ristory of science is rich in examples of such kind. For instance, the theoretica! speetades of a one-sided "cellular pathology" simply did not allow one to see that there are regulative relations in the organism as a whole which is more than a sum or aggregate of cells; relations which were known to Hippocrates and have found a happy resurrection in the modern doctrine of hormones, of sarnatotypes and the like. The modern evolutionist, guided by the theory of random mutation and selection, does not see that an organism is obviously more than a heap of hereditary characteristics or genes shuffied tagether by accident. The mechanistic physicist did not see the so-called secondary qualities like color, sound, taste, etc., because they do not fit into his scheme of abstractions; although they are just as "real" as are the supposedly basic "primary qualities" of mass, impenetrability, motion and the like, the metaphysical status of which is equally dubious, according to the testimony of modern physics. Another possible formulation of the same situation, but emphasizing another aspect, is this. Perception is universally human, determined by rnan's psychophysical equipment. Conceptualization is culture-bound because it depends on the symbolic systems we apply. These symbolic systems are largely determined by Iinguistic factors, the structure of the language applied. Technica! language, including the symbolism of mathematics, is, in the last resort, an effiorescence of everyday language, and so will not be independent of the structure of the latter. This, of course, does not mean that the content of rnathematics is "true" only within a certain culture. It is a tautological system of hypotheticodeductive nature, and hence any rational being accepting the premises must agree to all its deductions. But which aspects or perspectives are mathematized depends on the cultmal context. It is perfectly possible that different individuals and cultures have different predilections for choosing certain aspects and neglecting others. 5 Hence, for example, the Greek's concern with geometrical problems and the concern of occidental rnathematics with calculus, as emphasized by Spengler; hence the appearance of unorthodox fields of mathematics, such as topology, group 238 GENERAL SYSTEM THEORY theory, game theory and the like, which do not. ~t i'~to the popu~ar notion of rnathematics as a "science of quant1t1es ; hence the mdividual physicist' s predilection for, say, "macr~sc~pic" classic~! thermodyna mics or "microscopie " molecular statistics, for matnx mechanics or wave mechanics to approach the same phenomena. Or, speaking more generally, the analytic type of U:ind concerned with what is called "molecular" interpretatio ns, 1.e., the resolution and reduction of phenomena to elementarist ic components ; and the holistic type of mind concerned with "molar" interpretations, i.e., interested in the laws that govern the phenomeno n as a whole. Much harm has been done in science by playing one aspect against the other and so, in the elementarist ic appr_oa_ch, to neglect and deny obvious and most important cha~actensucs; or, in the holistic approach, to deny the fundamenta l 1mportance and necessity of analysis. . It may he mentioned, in passing, that the relauon_ between Ianguage and world view is not unidirection al but renprocal, a fact which perhaps was not made sufficiently clea~ by ~horf. The structure of Ianguage seems to determine wh1ch tra~ts of reality are abstracted and hence what form the categones of thinking take on. On the other hand, the world outlook determines and forms the language. A good example is the evolution from classica! to medieval Latin. The Gothic world view has recreated an ancient language, this being true for the lexica! as well as the grammatica! as~e~t. Thus the schalastics invented hosts of words which are atront1es from the standpoint of Cicero's language (as the humanists of the Renaissance so deeply feit in their revivalistic struggle) ; words introduced to cope with abstract aspects foreign to the corporeally- thinking Roman mind, like leonit~s, quidditas and the rest of them. Equally, although the superfinal rules of grammar were observed, the line of thinking and construction was profoundly altered. This also applies to the rhetorica! asp:ct, as in the introduetion of the end-rhyme in contrast to the class1cal meters. Comparison , say, of the colossal lines of the Dies irae with some Virgilian or Horatian stanza makes obvious not only the tremenclous gap between different "world-feelin gs" but the determinati on of language by the latter as well. [, I i: I The Relativity of Categories 239 The Perspectivistic View Having indicated the biologica! and cultural relativity of the categories of experience and cognition, we can, on the other hand, also indicate the limits of this relativity, and thus come to the third topic stated in the beginning. Relativism has often been formulated to express the purely conventiona l and utilitarian character of knowledge, and with the emotional background of its ultimate futility. We can, however, easily see that such consequence is not implied. A suitable starting point for such discussion are the views on human knowledge expressed by von Uexküll in conneetion with his Umweltlehre which we have discussed earlier. According to him, the world of human experience and knowledge is one of the innumerable ambients of the organisms, in no way singular as compared to that of the sea urchin, the fly or the dog. Even the world of physics, from the electrans and atoms up to galaxies, is a merely human product, dependent upon the psychophysi cal organization of the human species. Such conception, however, appears to he incorrect. This may be shown in view of the levels both of experience and of abstract thinking, of everyday life and of science. As far as direct experience is concerned, the categories of perception as determined by the biophysiolog ical organization of the species concerned cannot be completely "wrong," fortuitous and arbitrary. Rather they must, in a certain way and to a certain extent, correspond to "reality"-wh atever this means in a metaphysical sense. Any organism, man included, is not a mere spectator, looking at the world scene and hence free to adopt spectacles, however distorting, such as the whims of God, of biologica! evolution, of the "soul" of culture, or of language have put on his metaphorica l nose. Rather he is a reactor and actor in the drama. The organism has to react to stimuli coming from outside, according to its innate psychophysi cal equipment. There is a latitude in what is picked up as a stimulus, signa! and characteristi c in Uexküll's sense. However, its perception must allow the animal to find its way in the world. This would be impossible if the categories of experience, such as space, time, substance, causality, were entirely deceptive. The categories of The Relativity of Categories 240 GENERAL SYSTEM THEORY experience have arisen in biologica! evolution, ~nd have continually to justify themselves in the struggle for existence. If they would not, in some way, correspond to r~ality, appropriate reaction would he impossible, and such organism would quickly he eliminated by selection. . . Speaking in anthropomorph ic terms: A group of schiZophremcs who share their illusions may get along with each other pretty well; they are, however, utterly unfit to react and adapt themselves to real outside situations, and this is precisely the reason why they are put into the asylum. Or, in term~ of Plato's simil:: the prisoners in the cave do not see the real thmgs but only the1r shadows; but if they are not only looking at the spectacle, but have to take part in the performance, the shadows must, in some way, he representative of the real things. It seems to he the most serious shortcoming of classic occidental philosophy, from Plato to Descartes and Kant, to consider man primarily as a spectator, as ens cogitans, while, for biologica! reasons, ~e has ess_entially to be a performer, an ens agens in the world he IS thro';~ m. . ." Lorenz (1943) has convincingly shown that the a pnon forms of experience are of essentially the sa~e na~ure a~ the innate schemata of instinctive behavior, followmg which ammals respond to companions, sexual partners, offspring or parents, prey or predators, and other outside situations. They are _based upon psychophysiolo gical mechanisms, such as the percept~on of space is based on binocular vision, parallax, the c?ntr_actiOn of the ciliary muscle, apparent increase or decrease m siZe of an approaching or receding object, etc. The "a priori" forms of intuition and categories are organic functions, based upon corporeal and even machine-like structures of the sense _orga~s and the nervous system, which have evolved as adaptat10ns m the millions of years of evolution. Hence they are fitted to the "real" world in exactly the same way and for the same reason, as the equ1ne hoof is fitted to the steppe terrain, the fin of the fish to the water. It is a preposterous ;mthropomorph ism to assume that the human forms of experience are the only possible ones, valid for any rational being. On the other hand, the concep~ion ?f. the forms of experience as an adaptive apparatus, proved m_ milbons of years of struggle for existence, guarantees that there Is a sufficient correspondence between "appearance" and "reality." Any stimulus is experienced not as it is but as the organism reacts 241 to it, and thus the world-picture is determined by psychophysical organization. However, where a paramecium reacts with its phobotactic reaction, the human observer, though his world outlook is quite different, also actually finds an obstacle when he uses his microscope. Similarly, it is well possible to indicate which traces of experience correspond to reality, and which, comparable to the colored fringes in the field of a microscope which is not achromatically corrected, do not. So Pilate's question, "What is Truth," is to he answered thus: Already the fact that animals and human beings are still in existence, proves that their forms of experience correspond, to some degree, with reality. In view of this, it is possible to define what is meant by the intentionally loose expression used above, that experience must correspond "in a certain way" to "reality whatever. this means." It is not required that the categories of experience fully correspond to the real universe, and even less that they represent it completely. It suffices-and that is Uexküll's thesis-that a rather small selection of stimuli is used as guiding signals. As for the connections of these stimuli, i.e., the categories of experience, they need not mirror the nexus of real events but must, with a certain toleranee allowed, he isomorphic to it. For the biologica! reasons mentiomid above, experience cannot he completely "wrong" and arbitrary; but, on the other hand, it is sufficient that a certain degree of isomorphism exists between the experienced world and the "real" world, so that the experience can guide the organism in such way as to preserve its existence. Again, to use a simile: The "red" sign is not identical with the various hazards it indicates, oncoming cars, trains, crossing pedestrians, etc. It suffices, however, to indicate them, and thus "red" is isomorphic to "stop," "green" isomorphic to "go." Similarly, perception and experience categories need not mirror the "real" world; they must, however, he isomorphic to it to such degree as to allow orientation and thus survival. But these deductive requirements are precisely what we actually find. The popular forms of intuition and categories, such as space, time, matter and causality, work well enough in the world of "medium dimensions" to which the human animal is biologically adapted. Here, Newtonian mechanics and classica! physics, as based upon these visualizable categories, are perfectly satisfactory. They break down, however, if we enter universes to which the 242 GENERAL SYSTEM THEORY human organism is not adapted. This is the case, on the one hand, in atomie dimensions, and in cosmie dimensions on the other. Coming now to the world of science, 'Uexküll's conception of the physical universe as but one of the innumerable biologica! ambients, is incorrect or at least incomplete. Here a most remarkable trend comes in which may be called the progressive de-anthropomo rphization of science (von Bertalanffy, 1937, 1953b). It appears that this process of de-anthropomo rphization takes place in three major lines. It is an essential characteristic of science that it progressively de-anthropomo rphizes, that is, progressively eliminates those traits which are due to specifically human experience. Physics necessarily starts with the sensory experience of the eye, the ear, the thermal sense, etc., and thus builds up fields like opties, acoustics, theory of heat, which correspond to the realms of sensory experience. Soon, however, these fields fuse into such that do not have any more relation to the "visualizable" or "intuitable": Opties and electricity fuse into electromagnetic theory, mechanics and theory of heat into statistica! thermodynamic s, etc. This evolution is connected with the invention of artificial sense-organs and the replacement of the human observer by the recording instrument. Physics, though starting with everyday experience, soon transgresses it by expanding the universe of experience through artificial sense organs. Thus, for example, instead of seeing only visible light with a wave length between 380 and 760 millimicra, the whole range of electromagnetic radiation, from shortest cosmie rays up to radio waves of some kilometers wave length, is disclosed. Thus it is one function of science to expand the observable. It is to be emphasized that, in contrast to a mechanistic view, we do not enter another metaphysical realm with this expansion. Rather the things surrounding us in everyday experience, the cells seen in a microscope, the large molecules observed by the electron microscope, and the elementary particles "seen," in a still more indirect and intricate way, by their traces in a Wilson chamber, are not of a different degree of reality. It is a meebanistic superstition to believe that atoms and molecules (speaking with Alice in the Wonderland of Physics) are "realer" than iJ The Relativity of Categories 243 apples, stones and tables. The ultimate particles of physics are not a metaphysical reality bebind observation; they are an expansion of what we observe with our natmal senses, by way of introducing suitable artificial sense organs. In any way, however, this leads to an elimination of the limitations of experience as imposed by the specifically human psychophysical organization, and, in this sense, to the deanthropomorph ization of the world picture. A second aspect of this development is what is called the convergence of research (cf. Bavink, 1949). The constants of physics have often been considered as only conventional means for the most economie description of nature. The progress of research, however, shows a different picture. First, natmal constants such as the mechanica! equivalent of heat or the charge of electrans vary widely in the observation of individual observers. Then, with the refinement of techniques, a "true" value is approached asymptotically so that consecutive determinations alter the estahlisbed value only in progressively smaller digits of decimals. Not only this: Physical constants such as Loschmidt's number and its like are established not by one metbod but perhaps by 20 methods which are completely independent of each other. In this way, they cannot be conceived as being simply conventions for descrihing phenomena economically; they represent certain aspects of reality, independent of biological, theoretica! or cultural biases. It is indeed one of the most important occupations of natural science thus to verify its findings in mutually independent ways. However, perhaps the most impressive aspect of progressive de-anthropomo rphization is the third. First, the so-called secondary qualities go, that is, color, sound, smell, taste disappear from the physical world picture since they are determined by the so-called specific energy of the diverse and specifically human senses. So, in the world picture of classica! physics, only the primary qualities such as mass, impenetrability , extension, etc., are left which, psychophysically, are characterized as being the common ground of visual, tactual, acoustical experience. Then, however, these forms of intuition and categories also are eliminated as being all-too-human. Even Euclidean space and Newtonian time of classica! physics, as was noted previously, are I I 244 GENERA L SYSTEM THEORY not identical with the space and time of direct experien ce; they already are construct s of physics. This, of course, is true even more of the theoretic a! structure s of modern physics. Thus, what is specific of our human experien ce is progressi vely eliminate d. What eventual ly remains is only a system of mathematica! relations . Some time ago it was considere d a grave objection against the theory of relativity and quanturn theory that it became increasingly "unvisua lizable," that its construct s cannot be represen ted by imaginab le models. In truth, however, this is a proof that the system of physics detaches itself from the bondage of our specifically human sensory experien ce; a pledge that the system of physics in its consumm ate form-lea ving it undecide d whether this is attained or even is attainabl e at all-does not belong to the human ambient (umwelt in Uexküll' s sense) any more but is universal ly committa l. In a way, progressi ve de-anthr opomorp hization is like Muenchh ausen pulling himself out of the quagmire on his own pigtail. It is, however, possible because of a unique property of symbolis m. A symbolic system, an algorithm , such as that of mathema tica! physics, wins a life of its own as it were. It becomes a thinking machine, and once the proper instrucdo ns are fed in, the machine runs by itself, yielding unexpect ed results that surpass the initia! amount of facts and given rules, and are thus unforese eable by the limited intellect who originall y has created the machine. In this sense, the mechanic a! chess player can outplay its maker (Ashby, 1952a), i.e., the results of the ~utoma~ized symbolis m transeend the original input of facts and mstructw ns. This is the case in any algorithm ic predictio n, be it a forma! deductio n on any level of mathema tica! difficulty or a physical predictio n like that of still unknown chemica! elements or ~la~ets (cf. von Bertalanf fy, 1956a). Progressi ve de-anthropomorph1~auon, that is, replacem ent of direct experien ce by a self-runm ng algorithmi c system, is one aspect of this state of affairs. Thus, the developm ent of physics naturally depends on the psychoph ysical constitut ion of its creators. If man would not perceive light but radium or x-rays which are invisible to ~s, not only the human ambient but also the developm ent of phys1cs would have been different. But in a similar way, as we have discovere d, by means of suitable apparatu s and supplem enting The Relativit y of Categories 245 our sensory experienc e, x-rays and all the range of electrom agnetic radiation s, the same would be true of beings with an entirely different psychoph ysical constitut ion. Suppose there are intelligen t beings or "angels" on a planet of the Sirius who perceive only x-rays; they would have detected, in a conespon ding way, those wave lengths that mean visible light to us. But not only this: The Sirius angels would possibly calculate in quite different systems of symbols and theories. However , since the system of physics, in its consumm ate state, does not contain anything human any more, and the conespon ding thing would be true of any system of physics, we must conclude that those physics, although different in their symbolic systems, have the same content, that is, the mathema tica! relations of one physics could be translate d by means of a suitable "vocabul ary" and "gramma r" into those of the other. This speculati on is not quite utopian, but, to a certain extent, seen in the actual developm ent of physics. Thus, classica! thermodynamics and molecula r statistics are different "languag es" using different abstracti ons and mathema tica! symbolisms, but the statements of one theory can readily be translate d into the other. This even has quite timely implicati ons; thermody namics and the modern theory of informat ion obviously are similarly isomorphic systems, and the elaborati on of a complete "vocabul ary" for translatio n is in progress. If, in the sense just indicated , the system of physics in its ideal state, which can be approach ed only asymptot ically, is absolute, we must, however, not forget another and in some way antithetic al aspect. What traits of reality we grasp in our theoretic a! system is arbitrary in the epistemo logical sense, and determin ed by biologica!, cultural and probably linguistic factors. This, again, has first a trivia! meaning. The Eskimos are said to have some 30 different narnes for "snow," doubtless because it is vitally importan t for them to make fine distinctio ns while, for us, ditierenc es are negligibl e. Conversely, we call machines which are only superfici ally different, by the narnes of Fords, Cadillacs , Pontiacs and so forth, while for the Eskimos they would be pretty much the same. The same, however, is true in a non-trivi a! sense, applying to general categorie s of thinking. It would be perfectly possible that rational beings of another structure choose quite different traits and aspects of reality for II, 246 GENERA L SYSTEM THEORY building theoretic a! systems, systems of rnathema tics and physics. Our main concern, probably determin ed by the grammar of Indo-Eur opean language , is with measurab le qualities , isolable units, and the like. Our physics negleet's the so-called primary qualities ; they come in only rudimen tarily in the system of physics or in certain abstracti ons of physiolog ical opties like the color cycle or triangle.s Similarly , our way of thinking is conspicuous ly unfit for dealing with problems of wholenes s and form. Therefor e, it is only with the greatest effort that holistic as contraste d to elementa listic traits can he included -althoug h they are not less "real." The way of thinking of occident al physics leaves us on the spot if we are confront ed with problems of form -hence this aspect, predomi nant in things biologica !, is but a tremenclo us embarras sment to physics. It may well he that quite different farms of science, of mathematics in the sense of hypothet ico-dedu ctive systems, are possible for beings who don't carry our biologica ! and linguistic constraints; mathema tica! "physics" that are much more fit than ours to deal with such aspects of reality. The same seems even to he true of mathema tica! logic. So far, it seems to cover only a relatively small segment of what can easily he expressed in vernacul ar or mathema tica! language . The Aristotel ian logic, for millenia considere d as giving the general and supreme laws of reasoning , actually covers only the extremel y small field of subject-p redicate relations . The all-or-no ne concepts of tradition al logic fall short of continuit y concepts basic for mathema tica! analysis (cf. von Neuman n, 1951, p. 16). Probably it is only a very small field of possible deductiv e reasonin g which Is axiomati zed even by the efforts of modern logicians . It may he that the structure of our logic is essentiall y determined by the structure of our central nervous system. The latter is essentiall y a digital compute r, since the neurons work according to the all-ar-no thing law of physiolog y in terms of yes-or-no decisions. To this correspon ds the Heraclite an principle of our thinking in opposites , our bivalent yes-or-no logic, Boolean al7 gebra, and the binary system of numbers to which also the can he reduced (and system decadie nt practical ly more convenie ). Supposin g machines ng calculati is actually reduced in modern digital type the after not ted construc that a nervous system were it may rule), slide a e.g., as, (such r but as an analog compute The Relativit y of Categories 247 contrast in y, he imagined that a quite different logic of continuit to our yes-or-no logic, would arise. Thus we come to a view which may he called perspecti vism (cf. von Bertalanf fy, l953b). In contrast to the "reductio nist" thesis that physical theory is the only one to which all possible science and all aspects of reality eventual ly should he reduced, we take a ~ore mo~est .view. The system of physics is committa l for any ratwnal hemg m the sense explaine d; that is, by a process of deanth:opo morphiz ation it approach es a represen tation of certain re~atwnal aspects of reality. It is essentiall y a symbolic algorithm smtable for the purpose. However , the choice of the symbolis ms we apply and conseque ntly the aspects of reality we represen t ~epend on biologica ! and cultural factors. There is nothin~ smgular or ~articularly sacred about the system of physics. Within our own SCience, other symbolic systems, such as those of taxonomy, of genetics or the history of art, are equally legitimat e altho~gh they are far from having the same degree of precision . ~nd ~n other cultures of human beings and among non-hum an I?telhge~ces, basically different kinds of "science" may he possibie which would represen t other aspects of reality as well or even bett~r than does our so-called scientific world picture. Th~re Is, perhaps: a deep-lyin g reason why our mental representatw~ of the un.Iverse always mirrors only certain aspects or perspecti ves of reahty. Our thinking, at least in occident al but pos~ibly in any h~man la1_1guage, is essentiall y in terms of opposltes. As Heraclitu s has It, we are thinking in terms of warm and cold, ~lack and white, day and night, life and death, being and becommg . These are naive formulat ions. But it appears that al~o the construct s of physics are such opposites , and that for t~Is very re.ason prove inadequa te in view of reality, certain relatiOns of which ar~ exp:essed in the formulas of theoretic a! physics. The popular antithesi s between motion and rest becomes meaningless in the theory of relativity . The antithesis of mass and energy is superserl ed by Einstein' s cornerva tion Iaw which accounts for their mutual transform ation. :~orpuscle and wave are bot? le?itimat~ and complem entary a~ects of physical reality wh1ch, m eertam phenome na and respécts, is to be described in one way, in others in the second. The contrast between structure and ~rocess breaks down .in the a torn as well as in the living orgamsm whose structure Is at the same time the expressio n and GENERAL SYSTEM THEORY 248 the bearer of a continuous flow of matter and energy. Perhaps the age-old problem of body and mind is of ~ similar nature, these being different aspects, wrongly hypostatiZed, of one and the same reality. . . All our knowledge, even if de-anthropo morphtzed, only mtrrors certain aspects of reality. If what has been said is true, reality is what Nicholas of Cusa (cf. von Bertalanffy, 1928b) called the coincidentia oppositorum. Discoursive thinking al~ays repr~sents only one aspect of ultimate reality, called God m Cusa s terminology; it can never exhaust its infinite manifoldnes s. Hence ultimate reality is a unity of opposites; any statement holds from a certain viewpoint only, has only relative validity, .and ~ust be supplemente d by antithetic statements from opposlte pomts of view. Thus, the categories of our experience and thinking appear to be determined by biologica! as well as cultural factors. Se~ondly, this human bondage is stripped by a process of progresstve deanthropomo rphization of our world picture. Thirdly, even though de-anthropo morphized, knowledge only mirrors certain aspects or facets of reality. However, fourthly, ex omnibus partibus relucet totum, again to use Cusa's expression: Each such aspect has, though only relative, truth. This, it seems, indicates the limitation as wellas the dignity of human knowledge. Notes I. This and other examples in Whorf's argument are criticized by Whatmough (1955). "As Brugmann showed (Syntax des einfachen Satzes, 1925, pp. 17-24), fulget, pluit, tonat are simple old tt-sterns (nouns 'lightning there, rain there, thunder there') and Whorf w~s quite wrong when he said that tonat (h~ used ~~~t ~er.y word). IS structurally and logically unparalleled m Hopt. S~mllarly, the Hopi for 'prepare,' we are told, is 'to try-for, to pracuse-up.on .' B_ut this is exactly prae-paro.'' "lt will not do to say that Hopt phystcs could not have had concepts such as space, velocity, and _mass, or that they would have been very different from ours. Hopt.has no physics because the Hopi are hindered by taboo or magtc from experimental investigation. " Although one has to surrender to the Iinguist's authority, it seems amply. d.e~o~strated that the style ~f thinking is different in the several ctvthzatwns even .tho~g~ Whorf s supposition that this is more or less solely due to lmgmstlc factors, is open to criticism. The Relativity of Categories 249 2. It is interesting to note that exactly the same viewpoint was stated by Lorenz (1943) in terros of the bio1ogica1 determinatio n of categ~ries: "The terros which language has formed for the highest funcu~ns o~ ~:mr rational thi.nking still bear so clearly the stamp of thetr ongm that they mtght be taken from the 'professional language' of a cliimpanzee. We 'win insight' into intricate connections, just as the ape into a maze of branches, we found no better expression for our most abstract ways to acliieve goals than 'method,' meaning detour. Our tactile space still has, as it were from time to non-jumping lemurs, a particular preponderanc e over the visual. Herre~ we have 'grasped' (erfasst) a 'connection' (Zusammenha ng) only 1f we can 'comprehend' (begreifen, i.e., seize) it. Also the notion. of object . (Gegenst~nd, that which stands against us) originated m the haptic perceptwn of space .... Even time is represented, for good or wrong, in terros of the visualizable model of space (p. 344) .... Time is absolutely unvisualizab1e and is, in our cat~go~ical thinking, made visualizable always [?; perhaps a Western preJudtce, L. v. B.] on1y by way of spatio-tempor al processes .... The 'course of time' is symbolized, linguistically and certainly a1so conceptually, by motion in space (the stream of time). Even our pr~~ositions 'before' and 'after,' our nouns 'past, present and future' o.ngmally ha:e conn?tations representing spatio-tempor al contiguratlons of motwn. It IS hardly possible to e1iminate from them the element of motion in space" (pp. 351 ff.). 3. As far as can be seen, this simple demonstratio n of the nonEuclidean structure of the visual space was first indicated by von Bertalanffy (1937, p. 155), while "curious enough, no reference whatever is found in the literature on the physiology of perception" (Lorenz, 1943, p. 335). 4. ~n excellent analys~s on the culture-depen denee of perception, cogniuon, affect, evaluatwn, unconscious processes, normal and abnormal behavior, etc., is given in Kluckhohn (1954). The reader is referred to this paper for ample anthropologic al evidence. 5. I ~nd that Toynbee (1954, pp. 699 ff.), in his otherwise not overly fnendly comment on Spengler's theory of types of mathematica1 thinking, arrives at an identical formu1ation. He speaks of a different "penchant" of civilizations for certain types of mathematica! reasoning, which is the same as the above-used notion of "predilection ." ~he p~esent writer's interpretation of Spengler was, in the essentials, gtv~n m 1924, and he has seen no reason to change it. 6. Thts perhaps can lead to a fairer interpretation of Goethe's "Theory of Co1ors." Goethe's revolt against Newtonian opties which is a scan~al and complete1y devious within the history of occidenta1 p~yst~s, can. be. _under_stood in this way: Goethe, an eminently etdettc and mtmuve mmd, had the feeling (which is quite correct) that Newt~~ian o~tics purpose1y neg1ects, and abstracts from, exactly those quaht!es whtcli are most prominent in sensory experience. His 250 GENERAL SYSTEM THEORY Farbenlehre, then, is an attempt to deal with those aspects. of reality which are not covered by conventional physics; a theoretica! enter. . prise which remained abortive. 7. Notice the theological motive in Leibniz:s inventwn of the bmary system. It represented Creatio.n s.~nce any n~mber. ca,~ be produced by a combination of "somethmg. (1) a~d. nothmg (0) · B_ut has this antithesis metaphysical reahty, or IS 1t but an express10n of linguistic habits and of the mode of action of our nervous system? :I 11 I,. 'I: Appendix: The Meaning and Unity of Science* At a time of universa! crises such as we are experiencing today, the question of the meaning and purpose of natmal sciences arises. That science is to be blamed for the miseries of our time is a reproach frequently heard; it is believed that men have been enslaved by machines, by technology at large, and eventually have been driven into the carnage of the world wars. We do not have the power to substantially influence the course of history; our only choice is to recognize it or to be overrun by it. A renowned scholar, Professor Dr. Ludwig von Bertalanffy, addressed a crowded audience in the Department of Forensic Medicine within the framework of a scientific lecture series spousored by FöST (Freie österreichische Studentenschaft). He spoke on vital present-day questions in conneetion with the problem of the special position of man in nature. In contrast to the animal which has an "ambient" (Umwelt) determined by its organization, man himself creates his world, which we call human culture. Among the presuppositions for its evolution are two factors, language and formation of concepts, which are closely related to each other. "Language" as appeal or cammand can already be observed in the animal world; examples for this are the singing- of birds, the warning whistle of mountain chamois, etc. Language as representation and commumca*Review of a lecture at the University of Vienna, 1947. 252 GENERAL SYSTEM THEORY tion of facts, however, is rnan's monopoly. Language, in the wider sense of the word, comprises not only oral speech but also script and the symbolic system of mathematics. These are systems not of inherited but of freely created an'd traditional symbols. First of all, this explains the specificity of human history in contrast to biologica! evolution: Tradition in contrast to hereditary mutations which occur only over a long period of time. Secondly, physical trial-and-error, largely characteristic of animal behavior, is replaced by mental experimentation-i.e., one with conceptual symbols. For this reason, true goal-directedness becomes possible. Goal-directedness and teleology in a metaphorical sense-i.e., regulation of happenings in the sense of maintenance, production and reproduetion of organic wholeness, is a general criterion of life. True purposiveness, however, implies that actions are carried out with knowledge of their goal, of their future final results; the conception of the future goal does already exist and influences present actions. This applies to primitive actions of everyday life as well as to the highest achievements of the human intellect in science and technology. Furthermore, the symbolic world created by men gains a life of its own, as it were; it becomes more intelligent than its creator. The symbol system of mathematics, for example, is embodied in an enormous thinking machine which, fed with a statement, produces in return a solution on the basis of a fixed process of concatenation of symbols, which could hardly be anticipated. On the other hand, however, this symbolic world becomes a power which can lead to grave disturbances. If it comes to a conflict between the symbolic worldwhich in human society has emerged in moral values and social conventions-and biologica! drives, which are out of place in cultural surroundings, the individual is confronted with a situation prone to psychoneurosis. As a social power the symbolic world, which makes man human, at the same time produces the sanguinary course of history. In contrast to the naive struggle for existence of organisms, human history is largely dominated by the struggle of ideologies-i.e., of symbolisms, which are the more dangerous, the more they disguise primitive instincts. We cannot revoke the course of events, which has produced what we call "man"; it is up to him, however, whether he applies his power of foresight for his enhancement or for his own annihilation. In this sense the question of what course the scientific world- Appendix: The Meaning and Unity of Science 253 conception will take is at the same time a question of the destiny of mankind. A survey of scientific developments reveals a strange phenomenon. Independently of each other, similar general principles start to take shape in the various fields of science. As such, the lecturer emphasized especially the aspects of organization, wholeness, and dynamics, and sketched their influence in the various sciences. In physics, these conceptions are characteristic of modern in contrast to classica! physics. In biology, they are emphasized by the "organismic conception" represented by the lecturer. Similar conceptions are found in medicine, psychology (gestalt psychology, theory of stratification) and in modern philosophy. This results in a tremendous perspective, the prospect of a unity of the world-view hitherto unknown. How does this unity of general principles come about? Dr. von Bertalanffy answers this question by demanding a new field in science which he calls "General System Theory" and which he attempted to found. This is a logico-mathematical field, whose task is the formulation· and derivation of those general principles that are applicable to "systems" in generaL In this way, exact formulations of terms such as wholeness and sum, differentiation, progressive mechanization, centralization, hierarchical order, finality and equifinality, etc., become possible, terms which occur in all sciences dealing with "systems" and imply their logical homology. Last century's mechanistic world picture was closely related to the domination of the machine, the theoretica! view of living beings as machines and the mechanization of man himself. Concepts, however, which are coined by modern scientific developments, have their most obvious exemplification in life itself. Thus, there is a hope that the new world concept of science is an expression of the development toward a new stage in human culture. References REFERENCES ACKOFF, R. 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SUGGESTIONS FOR FURTHER READING The following list is intended for further study in general system theory as defined in this book, and its major fields of application. For this reason, only a few representative examples are cited from the large literature in fields such as cybernetics, information, game and decision theories, irreversible thermodynamics, systems analysis and engineering, etc. Genera[, Mathernaties of General System Theory "Biologische Modelle," Symposium, Nova Acta Leopoldina (Halle, Germany), 1969. (Articles L. von Bertalanffy, H. Drischel, Benno Hess, etc.) . BOGUSLAW, W., The New Utopians, Englewood Cliffs (N.J.), Prentice-Hall, 1965. BUCKLEY, W. (ed.), Modern Systems Research for the Behaviaral ScienJist. A Sourcebook, Chicago, Aldine Publishing Co., 1968. General Systems, L. von Bertalanffy and A. Rapoport (eds.), Bedford (Mass.), P.O. Box 228, Society for General Systems Research, 12 vols. since 1956. GORDON, Jr., Charles K., Introduetion to Mathematica[ Structures, Belmont (Cal.), Dickenson, 1967. JONES, R. D. (ed.), Unity and Diversity, Essays in Honor of Ludwig von Bertalanffy, New York, Braziller, 1969. (~rticles A. Auersperg, W. Beier and R. Laue, R. Brunner, A. Koestler, A. Rapoport, R. B. Zufiiga, etc.) . KLIR, G. J., An Approach to General Systems Theory, Princeton (N.J.), Nostrand, 1968. MACCIA, Elizabeth Steiner, and George S. MACCIA, Development of Educational Theory Derived from Three Educational Theory Models, ,Columbus (Ohio), The Ohio State University, 1966. MESAROVIC, M. D., Systems Research and Design; View on General Systems Theory, Nèw York, Wiley, 1961 and 1964; Systems Theory and Biology, New York, Springer-Verlag, 1968. System Theory, Proceedings of the Symposium on, Brooklyn (N.Y.), Polytechnic Institute, 1965. Texty ke studiu teorie rizeni. Rada: Teorie systému a jeji aplikace, Prague, Vysoka Skola Politická ÜV Rsë, 1966. 276 GENERAL SYSTEM THEORY Biophysics BEIER, Walter, Einführung in die theoretische Biophysik, Stuttgart G Fischer, 1965. ' · BERTALANFFY, L. von, Biophysik des Fliessgleichgewichts, translated by W. H. Westphal, Braunschweig, Vieweg, 1953. Revised ed. with W. Beier and R. Laue, in preparation. BRAY, H. G. and K. WHITE, "Organisms as Physico-Chemical Machines," New Biology, 16 (1954) 70-85. FRA~KS, Roger G. E., Mathematica[ ModeZing in Chemica[ Engineermg, New York, Wiley, 1967. Quantitative Biology of Metabolism, International Symposia, A. Locker and 0. Kinne (eds.), Helgoländer Wissenschaftliche Meeresuntersuchungen, 9, 14 (1964), (1966). RESCIGNO, Aldo and Giorgio SEGRE, Drug and Tracer Kinetics Waltham (Mass.), Blaisdell, 1966. ' YOURGRAU, Wolfgang, A. VAN DER MERWE and G. RAW Treatise on Irreversible and Statistica[ Thermophysics, New York: Macmillan, 1966. Biocybernetics B~YLISS, L. E., Living Control Systems, San Francisco, Freeman, 1966. D1STEFANO, lil, Joseph J., A. R. STUBBERUD, and I. J. WILLIAMS Schaum's Outline of Theory and Problems of Feedback and Control Systems, New York, Schaum, 1967. FRANK, L. K. et al., Teleological Mechanisms, N. Y. Acad. Sc., 50 (1948) . GRODINS, Fred Sherman, Control Theory and Biologica[ Systems, New York, Columbia University Press, 1963. HASSENSTEIN, Bernhard, "Die bisherige Rolle der Kybernetik in der biologischen Forschung," Naturwissenschaftliche Rundschau, 13 (1960) 349-355, 373-382, 419-424. - - - , "Kybernetik und biologische Forschung," Handbuch der Biologie, L. von Bertalanffy and F. Gessner (eds.), Bd. I, Frankfurt a.M., Athenaion, 1966, pp. 629-730. KALMUS, H. (ed.), Regulation and Control in Living Systems, New York, Wiley, 1966. MILSUM, John H., Biologica[ Control Systems Analysis, New York, McGraw-Hill, 1966. WIENER, N., Cybernetics, New York, Wiley, 1948. Ecology and Related Fields BEVERTON, R. J. H., and S. J. HOLT, "On the Dynamics of Exploited Fish Populations," Fishery Investigation, Ser. Il, vol. XIX. London, Her Majesty's Stationery Office, 1957. WATT, Kenneth E. F., Systems Analysis in Ecology, New York, Academie Press, 1966. Suggestions for Further Reading 277 Psychology and Psychiatry BERTALANFFY, L. von, Robots, Men and Minds, New York, Braziller, 1967. GRAY, W., N. D. RIZZO and F. D. DUHL (eds.), General Systems Theory and Psychiatry, Boston, Little, Brown, 1968. GRINKER, Roy R. (ed.), Toward a Unified Theory of Human Behavior, 2nd ed., New York, Basic Books, 1967. KOESTLER, A., The Ghost in the Machine, New York, Macmillan, 1968. MENNINGER, K., with M. MAYMAN, and P. PRUYSER, The Vital Balance, New York, Viking Press, 1963. Social Sciences BUCKLEY, W., Sociology and Modern Systems Theory, Englewood Cliffs (N.J.), Prentice-Hall, 1967. DEMERATH lil, N. J., and R. A. PETERSON (eds.), System, Change, and Conflict. A Reader on Contemporary Sociological Theory and the Debate over Functionalism, New York, Free Press, 1967. HALL, Arthur D., A Methodology for Systems Engineering, Princeton (N.J.), Nostrand, 1962. PARSONS, Talcott, The Social System, New York, Free Press, 1957. SIMON, Herhert A., Models of Man, New York, Wiley, 1957. SOROKIN, P.A., Sociological Theories of Today, New York, London, Harper & Row, 1966. Index Ackoff, R. L., 9, 91, 100, 101 Actions of animal and human body, feedback mechanisms in regulation of, 43-44 Active personality system, model of man as, 192-93 Actuality principle, 116 Adams, ,H., 159 Adaptiveness, model for, 46 Adolph, E. F., 171 Afanasjew, W. G., 12 Alexander, Franz, 207 Allesch, G. J. von, 229 Allometric equation: definition, 63-65; in biology, 163-71 (tables, figs.); in social phenomena, 103 Allport, Floyd, 205 Allport, Gordon W., 193, 205, 206, 207, 208, 209, 212, 216 American Association for the Advancement of Science, 15 American Psychiatrie Association, 7 Analogies in science: definition, 84, 85; value 35-36 Analytica! procedure in science, 18-19 Anderson, Harold, 205 Anschütz, G., 231 Appleby, Lawrence, 216 Archaeology, process-school of, 9 Arieti, Silvano, 194, 205, 207, 211, 212, 214-15, 216, 217 Aristotle, 70, 79, 212, 216, 223, 225, 231, 246 Arrow, K. J., 113, 115 Ashby, W. R., 25, 46, 94, 96-99, 244 Atomie energy development, 118, 187 Attneave, F., 100 Ausubel, David P., 194 Automata, theory of, 22, 25, 141 Automation Revolution, 187 Backman, G., 231 Bavink, B., 76, 243 Bayliss, L. E., 22 Beadle, G. W., 152 Beckner, M., 12 Beer, S., 96 Behavior: adaptiveness, purposiveness, and goal-seeking in, 45-46, 79, 92, 131; unitary and elementalistic conceptions of, 70-71; stimulusresponse (S-R) scheme, 107, 188-89, 191, 193, 209; and principle of rationality, 115-16; and environmentalism, 189--90; equilibrium principle in, 190; principle of economy in, 190; see also Human behavior Behavioristic psychology, 7, 107, 187 Beier, W., 145, 149 Bell, E., 100 Bendmann, A., 12 Benedict, Ruth, 201, 219 280 Bentley, A. F., 41 Berg, K., 181 Berlin, Sir Isaiah, 9, 113, 114 Berlyne, D. E., 209, 212 Bemal, J. D., 5, 12 Bemard, Claude, 12 Bernstein, A., 205 Bertalanffy, Felix D., 147 Bertalanffy, Ludwig von, 6, 7, 9, 11, 12, 13, 14, 38, 46, 67, 70, 72, 73, 76, 77, 79, 89, 94, 95, 98, 99, 102, 103, 104, 106, 116, 118, 121, 135, 136, 141, 142, 145, 148, 151, 153, 158, 159, 171, 174, 181, 183, 207, 208, 209, 210, 212, 213, 215, 216, 217, 218, 219, 220, 221, 226, 229, 231, 236, 242, 244, 247, 248, 249, 251, 253 Bethe, Albert, 208 Beverton, R. J. H., 104, 148 Biculturalism in Canada, 202 Biocoenoses, 68, 138, 149 Biologica! equilibria, theory of, 32, 47 Biologica! relativity of categories, 227-32 Biologism, 88, 118 Biology: molecular, 6; higher levels of organization, 6, 28, 31; organismic conception in, 6, 12, 31, 89, 102-3, 205, 208, 253; mechanism-vitalism con troversy in, 89; aspects of system theory in, 155-85 Blandino, G., 12 Blasius, W., 158 Bleuler, Eugen, 208, 214-15, 218 Blood, as open system, 148 Bode, H., 49-50 Boffey, Philip M., 4 Boguslaw, W., 3, 10 Bohr, Niels Henrik David, 182 Boltzmann, Ludwig, 30, 151, 152 Borelli, Giovanni Alfonso, 140 Boulding, K. E., 14, 27, 47, 103, 104, 199 Bradley, D. F., 96, 147 Brainwashing, 191 Brave New World (A. Huxley), 10, 52, 108, 118 Bray, H. G., 102 Bray, J. R., 102 British Ministry of Agriculture and Fisheries, I 04 Brody, S., 165, 231 Bronowski, J., 23 Bruner, Jerome, 212 GENERAL SYSTEM THEORY Brunner, R., 149 Brunswik, Egon, 205 Buckley, W., 8, 17, 196 Bühler, CharlQtte, 107, 205, 207 Bühler, K., 209 Burton, A. C., 141, 144, 147 Butenandt, A., 158 Calvin, M., 96, 147 Cannon, W. B., 12, 16, 23, 78, 161, 211 Cantril, Hadley, 194, 212 Carlyle, Thomas, 111 Carmichael, Leonard, 209 Carnap, R., 86, 87 Carter, L. J., 4 Cartesian dualism between matter and mind, 220 Casey, E. J., 161 Cassirer, Ernst, 194, 212, 216 Categories: Kant's table of, 45; theory of (N. Hartmann), 85-86; introduetion of new, in scientific thought and research, 10, 18, 92, 94; relativity of, and Whorfian hypothesis, 222-27; biologica! relativity of, 227-32; cultural relativity of, 232-38; relativity of, and the perspectivistic view, 239-48 Causa! laws, 44-45 Center for Actvaneed Studyin the Behavioral Sciences (Palo Alto) , 14 Centralization: definition, 71-74; in psychopathology, 213-14 Chance, B., 147, 163 Chemica! equilibria, 121-125 Chemodynamic machine, 140 Chomsky, N., 189 Chorley, R. J., 102 "Classica!" system theory, 19-20 Clausius, Rudolf J. E., 151 Closed and open systems, 39-41, 121-25, 141 Coghill, G. E., 208 Commoner, B., 12 Communication, theory of, 41; and flow of information, 41-42; and concept of feedback, 42-44 (fig.) Communication engineering, 22 Compartment theory, 21, 144 Competition between parts: equations defining, 63-66, 149; "wholes" based upon, 66, 91; and allometry, 163-164 Index Complexesof "elements," 54-55 (fig.) Computer technology and cybernetics, 15 Computerization and simulation, as approach in systems research, 20-21 (table), 144 Conceptual experimentation at random, 101 Conditioning, 52, 189 Conflict and Defence (Boulding), 199 Conklin, E. W., 211 Constitutive and summative characteristics, 54-55 Control engineering and power engineering, 3 Convergence of research, 243 Copernican Revolution, 99 Cowdry, Edmund, 211 Crime and Criminologists (Anon.), 207 Critique of Practical Reason (Kant) , 186 Cultmal relativity of categories, 232-38 Culture: Iaws in development of, 199; concept of, 201-2; as psycho· hygienic factor, 218; multiplicity of, 235 Cummings, J., 216 Cusa, Nicholas of, 11, 248 Cybernetic machines, 140 Cybernetics: development of, in technology and science, 16-17, 23, I 0 I; as part of general theory of systems, 17, 21-22; feedback mechanisms in, 44, 78, 90, 150, 161; and open systems, 149-50 Cybernetics (Wiener) , 15 Damude, E., 7 D'Ancona, V., 56, 57, 76, 80, 133, 134, 138 Darwinism, 24, 152, 154 De-anthropomorphization irt science, 242-44, 247, 248 Decision theory approach to systems problems, 22, 90, 100, 114, 115, 198-199 Decline of the West, The (Spengler), 118, 203 Decline of the West, as accomplished fact, 204 De ludo globi (Nicho1as of Cusa) , 11 Demerath, N. J., 196 281 Denbigh, K. G., 144, 151 Descartes, René, 19, 140, 212, 235, 240 De-Shalit, A., 5 Determinism, 114, 221 Differentiation, principle of, in psychopathology, 211-13; see also Segregation Diffusion, 126-27; cultural, 201 Directed graph (digraph) theory, 21 Directiveness of processes, 16-17, 45-46, 78, 92 Dobzhansky, T., 12 Donnan, F. G., 57, 134 Dost, F. H., 148, 158, 175 Driesch, Hans, 26, 27, 40, 72, 133, 144 Drischel, H., 19 Druckery, H., 148 Drug kinetics, 56, 138, 148 Dubos, R., 12 Dunn, M. S., 180 Dynamic ecology, 102 "Dynamic State of Body Constituents" (Schönheimer) , 160 Dynamic equilibrium, 131; see also Steady state Dynamic teleology, 78-79 Dynamics of biologica! populations, theory of, 32 Ecology, theory of, 32, 47, 102 Economics and econometrics, 32 Economy, principle of, in human behavior, 190 Eddington, Sir Arthur Stanley, 151 Education, general system theoty in, 49-51, 193 "Education of Scientific Generalists, The" (Bode, et al.) , 49-50 Ego boundary, in psychopathology, 215 Einstein, Albert, 154, 225, 247 Elsasser, W. M., 25, 161 Emergence, 55 Entropy, 39, 41, 143, 144, 145, 151, 152, 159; see also Thermodynamics Environmentalism, principle of, 189-90, 191 Equifinality, 46, 102, 136, 144; definition, 40, 132-134; of growth, 142 (fig.)' 148-49 Equilibrium principle in human behavior, 190 Euler, Leonhard, 75 282 Evolution: and contrast between wholeness and sum in, 70; synthetic theory of, 152, 153, 187 Excitation, phenomena of, and open systems concept, 137, 138 Existentialism, 109, 193 Explanation in principle, 36, 47, 106, 113 Exponentiallaw, 61-62 (fig.), 82 Eysenck, Hans, 214 Factor analysis, 90 Fagen, R. E., 95 Fearing, F., 222 Fechner, Gustav Theodor, 107 Feedback: concept of, 42-44 (fig.) , 46, 150; and homeostasis, 43, 78, 101, 150, 160-63, 184; and cybernetics, 44, 78, 79, 150, 161; criteria of control systems, 161--63 Fights, Games and Debates (Rapoport), 199 Finality systems, 75-77, 91, 131; types of, 77-80 Fitness, and teleology, 77, 79 Flannery, Kent V., 9 Foerster, H. von, 163 Food and Agricultural Organization of U.N., 104 Foster, C. A., 151 Foundation for lntegrated Education, 50 "Four R's of Remembering" (Pribram), 211n. Frank, L.K., 16, 17, 78 Frankl, Victor, 211, 216, 217, 219 Franks, R. G. E., 144 Free will, 114, 115, 116, 221 Freeman, Graydon, 210 Freud, Sigmund, 105, 107, 115, 189, 190, 194, 212, 214, 216 Friedell, Egon, 192 Fuhrmann, F. A., 168 Functionalism, and sociological theory, 196 Future, system-theoretical view of, 203-4 Galileo, 19, 182, 186 Gallup polls, 116, 198 Game theory, 15, 22, 23, 90, 100, 110, 114, 115, 198, 238 Garavaglia, C., 147 Ganse, G. F., 47, 56, 103 GENERALSYSTEM THEORY Gauss, Karl Friedrich, 90 Gazis, Denos C., 20 Geertz, Clifford, 212 General syste~ theory: history of, 10-17, 89-90; trends in, 17-29; approaches to methodological problems of, 19-23; axiomatization, 21; quest for, 30-36; trends toward generalized theories in multiple fields, 32; postulation of new discipline of, 32, 37, 90; meaning of, 32-33; and isomorphisms in different fields, 33-34; as a general science of organization and wholeness, 34, 36-37; objections to, 35-36; aim defined, 15, 38; examples, 38-49; and unity of science, 48-49, 86-88, 253; integrative function of, 48-49; in education, 49-51, 193; motives leading to postulate of, 91-94; advances in, 99-119; see also System, etc. General systems research, methods in, 94-99; empirico-intuitive method, 95-96; deductive approach, '96-99 General Systems, Yearbooks of Society for General Systems Research, 15 Geomorphology, 102 Gerard, Ralph W., 15, 34 Gessner, F., 103 Gestalt psychology, 6, 31, 208 Geyl, Peter, 110 Ghost in the Machine, The (Koestler) , 214n. Gibson, J. J., 211n. Gilbert, Albin, 213 Gilbert, E. N., 22 Glansdorff, P ., 151 Glasperlenspiel (Hesse), 11 Global nature of our civilization, 204 Goal-seeking behavior, 16, 43-44, 45, 79, 92, 131, 150 Goethe, Johann Wolfgang von, 145, 249 Goldstein, Kurt, 105, 207, 208, 216, 217 Graph theory approach to systems problems, 90, 211 Gray, William, 7 Grinker, Roy R., 7 Grodin, F. S., 161 Gross, J., 77 Group theory, 237-38 Index Growth: general systems equations, 60-63 (fig.); exponential, 61-62; logistic, 62--63; gr. equations (model) after Bertalanffy, 103, 135-36, 148, 171-84; relative, 103, 149, see also Allometric equation; equifinality of, 142 (fig.) , 148-49 Guerra, E., 171 Günther, B., 171 Hacker, Frederick, 207 Hahn, Erich, 6, 10 Haire, M., 96, 103, 114, 118 Hall, A. D., 91, 95, 105 Hall, C. S., 105 Hart, H., 26 Hartmann, E. von, 77 Hartmann, M., 124 Hartmann, Nicolai, 72, 86 Harvey, William, 140 Hastorf, Albert, 211 Hayek, F. A., 36, 113 Hearn, G., 95 Hearon, J. F., 144 Hebb, Donald 0., 106, 209 Hecht, S., 137, 148 Regel, Georg Wilhelm Friedrich, 11, 110, 198, 199 Heisenberg, Werner, 31 Hemmingsen, A. M., 183 Hempel, C. G., 12 Henry, Jules, 206 Heraclitus, 160, 246, 247 Hering, Ewald, 137 Herrick, Charles, 209, 216 Hersh, A. H., 62, 103 Herzberg, A., 13 Hess, B., 20, 144, 147, 163 Hess, W. R., 16 Hesse, Hermann, 11 Heterostasis, 23 Hierarcbic order in general systems theory, 27-29 (table) , 74, 213 Hili, A. V., 137 Hippocrates, 237 Ristorical inevitability, 8-9, 113-114, 118 History: cyclic model of, 118, 203, 204; impact of systems thinking on conception of, 8-9; theoretica!, 109-19, 197-203; nature of historica! process, 200-201; organismic theory of, 202-203 Hoagland, H., 230 283 Höber, R., 135 Höfler, Otto, 8ln. Hoijer, H., 226 Holst, Erich von, 16, 106, 209 Holst, S.J., 104, 148 Homeostasis: Cannon's concept of, 12, 16, 23, 78, 161; and feedback, 43, 78, lOl, 150, 160-63, 184; in psychology and psychopathology, 210-11 Homology, logica!, 84-85 Hook, Sidney, 220 Horvath, W. J., 117 Human behavior: theory of, 105; robot model of, 188, 190-91, 206; aspects of, outside of physical laws, 199; see also Behavior Human element, as component in systems engineering, 10 Human engineering, 91 Human society: application of general system theory to, 47-48; laws and science of, 51-52; evaluation of man as an individual in, 52-53; and statistica! laws, 116, 198 Humanistic psychology, 193 Humboldt, Wilhelm von, 194, 212, 232 Huxley, Aldous, 49, 52, 231 Huxley, Sir Julian, 149 Hypothetic-deductive approach, 198 lbn-Kaldun, 11 ldiographic method in history, 8, 110, 111, 114, 198 lnanimate and animate nature, apparent contrast between 40-41, 139 "Immense" numbers, problem of, in systems theory, 25-27 lndividualization within system, 71-74 lndustria1 chemistry, 122, 142 lndustrial Revolution, 118, 186-87 lnformation theory, 15, 22, 90, 93, 94, 100, 151, 152, 163, 198, 245 lnhelder, Bärbel, 221 Instinct, theory of, 106 lnstitute for Advanced Study in Princeton, 5 lntegrative function of general system theory, 48-49 284 "Integrative Studies for General Education" (Mather) , 50 Interdisciplinary theory: implications of, 48-49; basic principles of, 51; and new conceptual models, 93-94 Isomorphisms: in different fields, 33-34, 48-49, 88, 103; in science, 80-86 J effries, L. A., 27 Jones, R. W., 161 Jung, Carl, 105 Jung, F., 102 Kafka, Franz, 77 Kalmus, H., 22, 230 Kamaryt, J., 12 Kanaev, I. 1., 12 Kant, Immanuel, 45, 101, 186-87, 225, 227, 229, 232, 240 Keiter, F., 95, 103 Kelvin, William Thomson, 40 Kinetics, 13, 56, 120, 141, 150, 156, 159 Kleiber, M., 165 Kluckhohn, C., 201, 224, 249 Kment, H., 101, 161 Koestler, Arthur, 29, 212, 214n. Köhler, W., 11, 131, 208 Kottje, F., 124 Krech, David, 41, 105, 205 Kremyanskiy, V. 1., 96 Kriszat, G., 228 Kroeber, A. L., 156, 198, 201 Kubie, Lawrence, 217 Kuepfmüller, K., 148 Kuhn, T. S., 18, 24, 201 La Barre, W., 224, 225 Landois-Rosemann textbook, 158 Langer, S., 216 Lapicque, L., 137 Laplace, Pierre Simon, 21, 26, 30, 87, 113 Lashley, K., 26, 208 Lau, C., 147 Laue, R., 145 Laws of nature, modern concept of, 113 Le Chatelier's principle in physical chemistry, 75, 80, 131 Lecomte du Noüy, P., 231 Lehmann, G., 165 GENERAL SYSTEM THEORY Leibniz, Gottfried Wilhelm, 11, 250 Leighton, D., 224 Lennard H., 205 Lenz's rule of electricity, 75, 80 Lersch, P., 213 Lewada, J., 10 Lindzey, G., 105 Linguistic determination of categodes of cognition, Whorfian hypothesis of, 194, 222-27 Linguistic systems, diversity of, and reevaluation of scientific concepts, 225 Living organism: as open system, 32, 39, 44, 121-23, 141, 156-60 (fig.)' 191; and dynamic interplay of processes, 44; and machine conception, 139-41; biophysics of, 142, 158 Llavero, F., 207 Locker, A., 25, 144, 145, 166, 168, 169 Loewe, S., 138, 148 Logistic curve, 62-63 (fig.) Lorenz, K., 106, 240, 249 Lotka, A. J., 11, 32, 47, 56, 103 Lumer, H., 64 Luria, Aleksandr, 216 Luthe, Wolfgang, 213 Maccia, E. S. and G. S., 21 "Macrohistory," 199 Magoun, Horace, 209 Malek, E., 149 Malthusian law of population, 48, 62, 104 Man: image of, in contemporary thought, 6, 188-92, 194; role of, in the Big System, 10; as the individual, ultimate precept of theory of organization, 52-53; system concept in sciences of, 186-204; model of, as robot, 188, 190-91, 194, 205, 206; pecuniary conception of man, 206; as active personality system, 207; special position of, in nature, 251-52 Man-machine systems, 91 Manipulative psychology, 206-207 Manning, Hon. E. C., 4 Martin, A. W., 168 Marx, Karl, 11, 110, 198, 199 Maslow, A. H., 105, 109, 193, 207 Mass action, law of, 120, 122, 125 Mass behavior, 114 Index Mass civilization, 204 Mass suggestion, methods of, 52 Materialism, 94 Mathematica! approaches in general systems theory, 19-23, 38, 90-91 Mathematica! models, advantages of, 24 Mathematica[ Systems Theory journal, 15 Mather, K. F., 50 Matson, Floyd, 206, 212 Maupertuis, Pierre Louis Moreau de, 75 May, Rollo, 218 Mayer, J., 180 McClelland, C. A., 118 McCulloch, W. S., 25 McNeill, W., 9 Mechanica! machines, 140 Mechanistic world view, 27, 45, 47, 49, 55, 87-88, 92, 253 Mechanization within system, 44, 69-70, 72, 73, 91, 213; and loss of reguiability, 70, 213 Meixner, J. R., 142 Mendel's laws, 182 Menninger, Karl, 7, 105, 205, 211 Merloo, Joost, 212 Merton, Robert K., 196 Mesarovic, M. D., 21 Metabolism, 39, 65, 121, 122, 135, 137, 141, 147, 148; self-regulation of, 124, 131; surface law of (Rubner's law), 164-65, 174 Meteorology, 102-103 Metzger, W., 73 Meunier, K., 171 Michelangelo, 192 "Microhistory," 199 Miller, James, 205 Milsum, J. H., 22 Minimum action, principle of, 75, 76, 80 Minsky, Marvin L., 22 Mittasch, A., 71 Mittelstaedt, H., 161 M'Naughten rules, and the crimina!, 221 Model and reality, incongruence between, 23-24, 94, 200 Molecular machines, 140 Morchio, R., 102 Morgenstern, 0., 15, 22 Morphogenesis, 148-49 285 Morris, Charles, 90 Moser-Egg, 0., 121 Moser, H., 121 Mosteller, F., 49 Motivation research, 116, 189, 191 M üller, 1., 181 Mumford, L., 196 Murphy, Gardner, 109 Murray, Henry, 206, 207, 216 Nagel, E., 12 Napoleon, 110-11 Naroll, R. S., 103 Nation, concept of, in U.N., 202 Natura! selection, theory of, 47 Neopositivism, 12 Nervous system, new conception of, 106 Net theory approach to systems problems, 21, 90 Netter, H., 102, 158 Neumann, J. von, 15, 22, 25, 27, 246 Newton, Sir Isaac, 186 Nicholas of Cusa, 11, 248 Nietzsche, Friedrich Wilhelm, 187 Nihilism, 187 1984 (Orwell), 10, 52, 118 Nomothetic method in science, 110, 111, 114, 198 "Nothing-but" fallacy in evaluating models, 118-19 Nuttin, Joseph, 216 Oligopoly, law of, and organizations, 48, 104 Onsager, L., 142 Open systems, 11, 13, 21, 23, 32, 39-41, 90, 102-103, 120-124, 141; general characteristics of, 124-32, 141-45; biologica! applications of concept of, 134-38, 145-49; kinetic theory of, 142, 148, 150; thermodynamic theory of, 142, 144, 148, 150; steady state, false start, and oversboot in, 143 (fig.), 160; theory of, as part of general system theory, 149, 154; and cybernetics, 149-50; unsolved problems, 150-53; and steady states, 156-60; in technological chemistry, 122, 142 Operations research, 9, 91, 104 Opinion research, 116 Opler, Marvin, 207 286 Organic mechanism, philosophy of, 12 Organism: concept of, 67-6S; and personality, 105, 20S; as open system, 120-24, 134, 153-54; machine model of, and its limitations, 139---41; as active system, 20S-10; see also Living organism Organismic analogy in sociology and history, li6-1S Organismic biology, 6, 12, 31, SS, S9, 102-103, 205, 20S, 253 Organismic psychology, 193 Organismic revolution, 1S6-SS Organismic theory: of personality, 105, 20S; of sociology and history, 202-03 Organization: concept of, 46-4S, 92, 94, 253; general theory of, 34; characteristics of, 47; aspects of, not subject to quantitative interpretation, 21, 47; Theory of (formal) organizations, 9, 10; Iron Laws of, 47--4S, 53, 104; law of optimum size, 4S, 104; law of oligopoly, 4S, 104; ultimate precept of theory of, 52-53 Organizational Revolution, The (Boulding), 47 Organized complexity, problems of, 34, 93 Ortega y Gasset, José, liS Orwell, George, 52 Osterhout, W. J. V., 134 Oxenstierna, Count Axel Gustaffson, li6 Paracelsus, li Parallelism of cognitive principles in different fields, 31 Pareto's law in sociology, 65, S2 Parseval, August von, 13 Parsons, Talcott, 196 Patten, B. C., 102 Patterns of Culture (Benedict) , 201 Pavlov, Ivan Petrovich, 1S9, 216 Permeability (cell), and open system, 134-35 Personality: theory of, 105-109, 1S7, 193; and organism, 105, 20S; and environmentalism, 1S9-90; splitting of, 215; as system, 219 Perspectivism, 49, 247 Peterson, R. E., 196 GENERAL SYSTEM THEORY Pharmacodynamics, basic laws of, 56, 13S, 14S Phenomenological principles of life, 152 Physical cheniistry: trend toward generalized theories in, 32; kinetics and equilibria in chemica! systems, 12ü-22; of enzyme reactions, 143, 147; see also Open systems Physicalism, SS Physics: impact of systems thinking on, 5-6; modern developments in 5-6, 3ü-31; generalized theories in, 32; and theory of unorganized complexity, 34, 93 Physiological doek, 230 Piaget, Jean, 6, 193, 194, 207, 212, 221 Picard, E., 133 Pirozynski, W. J. P., 171 Pitts, W. H., 25 Plato, 52, 235, 240 Politicians, and application of systems approach, 4 Population: periadie cycles in, 4S; Malthusian law of, 4S, 62, 104; Verhulst law of growth of, 62 Population dynamics, 32, 102, 103-104, 13S Population explosion, liS Positivism, 94 Pötzl, Otto, 13 Pribram, K. H., 2lln. Prigogine, I., 103, 142, 144, 151, 231 Prigogine's Theorem, 151 Psychiatry: systems concepts in, 20S-220; increasing interest in general system theory, 7, 193, 205; modem trends in, 193-94; physico-psycho-sociologi cal framework of, 217 Psychoanalysis, 7, 24, 107, 1S7, 190 Psychological technology, 52 Psychology: application of G. S. T., 6, 105-107, 220; trends in, 31, 193-94; developmental, 194; quandary of modem psychology, 190, 205-207; holistic orientation in, 193; re-orientation of, 193; see also Psychiatry Pumpian-Mindlin, Eugene, 205 Purposiveness, 216, 252; see also Behavior Püter, A., 137, 171 Index Quanturn physics, 31 Quastler, H., 22 Queuing theory approach to systems problems, 23 Rameaux, 164 Rapaport, D., 107, 205 Rapoport, A., 15, 19, 21, 25, 100, 101, 104, 113, ll4, ll7, 199 Rashevsky, N., 21, 113, 133, 134, 137, 144 Rationality, principle of, 115; and human behavior, 115-16 Reafferenzprinzip (Holst), 16 Reductionism, 4S, 49, S6-S7, 247 Regression, in psychopathology, 214-15 Reichenbach, Hans, 13 Riegl, A., 232 Reik, H. G., 142, 151 Reiner, J. H., 144 Relativity, theory of, 99, 225, 226, 247 Rensch, B., 153 Repge, R., 26 Rescigno, A., 21, 144, 147 Research, see General systems research; Motivation research; Operations research; Opinion research Responsibility, moral and legal question of, 221 Revolt of the Masses (Ortega y Gasset) , liS Richardson, Lewis F., 104, ll4, 195 Rise of the West (McNeill), 9 Rittenberg, D., 175 Robot model of human behavior, lSS, l9ü-9l, 194, 205, 206 Rogers, Carl R., 207 Roman Empire, decay of, 203 Rosen, R., 21 Rostovtzeff, Michael Ivanovich, 203 Rothacker, Erich, 213 Roux, Wilhelm, 66 Royce, Joseph R., 215 Rubner's law (surface law of metabolism), 164-65, 174 Ruesch, J., 10 Russell, Bertrand, 67, 6S Sarrus, P. F., 164 Schachtel, E. G., 194 Schaffner, Kenneth F., 12 Schaxel, J., 13, 231 Scher, Jordan, 216, 220 287 Schiller, Claire, 209, 215 Schlick, Moritz, 12, 77 Schönheimer, R., 160 Schrödinger, Erwin, 9S, 144 Schulz, G. V., 14S, 151 Science: and evolving of similar problems and conceptions in widely different fields, 3ü-31; and basic problem of general theory of organization, 34; unity of, 4S--49, S6-SS, 251-53; and society, 51-:-52; isomorphism in, Sü-S6; classical, limitations of, 92-93; generalization of basic concepts in, 94 Sciences of man, system concept in, 1S6-204 Scientific generalists, production of, 49-51 Scientific revolutions, 17-1S, 201 Scott, W. G., 9 Secoud Industrial Revolution, 4, 16 Segre, G., 21, 144 Segregation within system, 6S-69, 70, 71 Self-controlling machines, development of, 3, 15, 140 Self-realization as human goal, 109 Self-restoring tendendes of organismic systems, 27 Selye, H., 192 Senses Considered as Perceptual Systems, The (Gibson), 211n. Sensory physiology, 14S Servomechanism theory in technology, 22, 7S, 140 Set theory approach to systems problems, 21 Shannon, Claude, 15, 22, 100 Shannon's Tenth Theorem, 9S Shaw, Leonard, 17 Simon, H. A., 19, 29 Skinner, B. F., 1S9, 214 Skrabal, A., 56 Skramlik, E. von, 229 Smith, Vincent E., 12 Social phenomena, statistica! regularities and laws in, 199 Social sciences: systems perspective in, 7-S; and socio-cultural systems, 7-9, 196, 197, 20û-202; development of new concepts in, 31; broad application of term, 194-195; systems in, 194-197 288 Society for Empirica! Philosophy, Berlin; group of, 12-13 Society for General Systems Research, 15 Society, human, see Human society Socio-cultural systems, and social sciences, 7-9, 194-197, 200-202 Sociological technology, 51-52 Sociology, organismic theory of, 202-203 Sorokin, P. A., 7, 10, 195, 196, 198, 200, 201, 207 Space, conquest of, 187 Specialization in modern science, 30 Spemann, Hans, 72 Spengler, Oswald, 8, 12, 110, 112, 116, 117, 118, 198, 199, 200, 201, 202, 203, 223, 233-34, 237, 249 Spiegelman, S., 56, 65 Sprinson, D. B., 175 Stagner, Ross, 211 Static teleology, 77 Statistica! laws, and human society, 116, 198 Steady state in organism, 41, 125, 126, 127, 134, 143, 148, 156-60, 209; definition of, 129-31 Stein-Beling, J. von, 230 Stimulus-response (S-R) scheme, 107, 188-89, 191, 193, 209 Stoward, P. J., 151 Stress, 192 Study of History, A (Toynbee), 200 Summative characteristics in complex, 54-55, 91 Summativity, 67; in mathematica! sense, 68 Surface law of metabolism, 164-65, 174 Symbolic activities, 215-18, 252 System: as key concept in scientific research, 9; defined as complex of interacting elements, 19, 38, 55-56, 83-84; mathematica! definition, 56-60 (fig.) ; active, 150; definition as machine with input, 97 System-theoretical re-orientation in sciences of man, 192-94 Systems engineering, 3-4, 91, 104-105 Systems science, approaches and aims in, 3-10, 89-94; history of, 10-17; trends in, 17-29; mathematica! approaches to, 19-23; see also General system theory GENERAL SYSTEM THEORY Syz, Hans, 205 Szent-Györgyi, A., 5 Tales of Hof/man (Offenbach), 140 Tanner, James, 221 Technology: developments in contemporary, 3-5, 9-10, 12, 187, 204; sociological, 51-52; psychological, 52 Teleology, 45-46, 92; statie, 77; dynamic, 78-79; see also Purposiveness, Directiveness Theoretica! Biochemistry (Netter), 158 Theoretische Biologie (Bertalanffy), 13 "Theory of Colors" (Goethe), 249 Thermodynamics, 13, 39, 140, 141, 143, 150, 151, 156, 159, 245; irreversible, 13, 94, 131, 142, 148, 151, 152, 153, 159, 163; secoud principle of, 30, 34, 39, 40, 47, 93, 102, 125, 143-44, 159 Thompson, J. W., 102 Thumb, Norbert, 216 Toch, Hans, 211 Tolstoy, Leo, lll Topology, 90, 237 Totalitarianism, systems of modern, 52 Toynbee, Arnold, 8, llO, ll2, ll7, 118, 198, 199, 200, 201, 203, 249 Transport, active, 148 "Tree and the Candle, The" (Koestler) , 29 Tribifio, S. E. M. G. de, 12 Trincher, K. S., 152 Tschermak, A., 124 Tukey, F., 49 Turing machine, 22, 25, 141 Turnover rates, 145-147 (tables) Uexküll, Jacob von, 194, 227, 228, 229, 230, 235, 239, 241, 242, 244 Umrath; K., 137 Unconscious drives, 116 Underdeveloped nations, emergence of, 118 Ungerer, E., 12 Unilied Theory of Human Behavior, 7 Unity of science, and general system theory,48-49, 86-88,253 Unorganized complexity, 34 289 Index Verbal roodels in systems theory, 24 Verhulst law of populatioB growth, 62 Vickers, Sir Geoffrey, 117 Vico, Giovanni Battista, 11, 110, 117, 198, 199 Vienna Circle, 12 Vitalism, 40, 66, 77, 79, 124, 133, 141, 144, 145 Volterra, V., 32, 47, 48, 56, 57, 65, 66, 76, 80, lOl, 103, 104, 113, 133, 134, 138 Wagner, Richard, 16, lOl, 161 Wahl, 0., 230 Watson, John B., 189 Watt, K. E. F., 104 Weaver, Warren, 15, 22, 34, 93, 100 Weiss, P., 27, 100 Werner, G., 56, 148 Werner, Heinz, 193, 194, 207, 209, 211, 212 Western civilization, worldwide expansion of, 118 Whatmough, J., 248 White, K., 102 Whitehead, A. N., 12, 47, 208 Whittacker, R. H., 41, 102 Wholeness, 31, 55; general science of, 37, 45, 253; and sum, contrast between, and evolution, 70, 94; see also Organization Whorf, B. L., 194, 213, 222, 223, 224, 225, 238; hypothesis of linguistic determination of categories of cognition, 222-27 Whyte, Lancelot, 214, 221 Wiener, Norbert, 15, 44, 78, lOl, 161 Winsor, C., 49 Wolfe, Harry B., 4 Woodger, J. H., 29, 208 World, conception of: as chaos, 187; as organization, 188 Worringer, W., 232 Zacharias, ]. R., 93 Zeiger, K., 158 Zerbst, E., 144, 147 Zopf, G. W., Jr., 163 Zucker, L., 180 Zucker, T. F., 180 Zwaardemaker, H., 121