what if?
Serious Scientific Answers to
Absurd Hypothetical
Questions
RANDALL
MUNROE
HOUGHTON MIFFLIN
HARCOURT
2014 • BOSTON • NEW YORK
Copyright © 2014 by xkcd Inc.
ALL RIGHTS RESERVED
For information about permission
to reproduce selections from this
book, write to Permissions,
Houghton
Mifflin
Harcourt
Publishing Company, 215 Park
Avenue South, New York, New
York 10003.
www.hmhco.com
The Library of Congress has
cataloged the print edition as
follows:
Munroe, Randall, author.
What if? : serious scientific answers
to absurd hypothetical questions /
Randall Munroe.
pages cm
ISBN
978-0-544-27299-6
(hardback)
ISBN
978-0-544-45686-0
(international pbk.)
1. Science—Miscellanea. I. Title.
Q173.M965 2014
500—dc23
2014016311
Book design by Christina Gleason
Lyrics from “If I Didn’t Have You”
© 2011 by Tim Minchin.
Reprinted by permission of Tim
Minchin.
eISBN 978-0-544-27264-4
V1.0914
QUESTIONS
Disclaimer [>]
Introduction [>]
Global Windstorm [>]
Relativistic Baseball [>]
Spent Fuel Pool [>]
Weird (and Worrying)
Questions from the What If?
Inbox, #1 [>]
New York–Style Time Machine
[>]
Soul Mates [>]
Laser Pointer [>]
Periodic Wall of the Elements
[>]
Everybody Jump [>]
A Mole of Moles [>]
Hair Dryer [>]
Weird (and Worrying)
Questions from the What If?
Inbox, #2 [>]
The Last Human Light [>]
Machine-Gun Jetpack [>]
Rising Steadily [>]
Weird (and Worrying)
Questions from the What If?
Inbox, #3 [>]
Orbital Submarine [>]
Short-Answer Section [>]
Lightning [>]
Weird (and Worrying)
Questions from the What If?
Inbox, #4 [>]
Human Computer [>]
Little Planet [>]
Steak Drop [>]
Hockey Puck [>]
Common Cold [>]
Glass Half Empty [>]
Weird (and Worrying)
Questions from the What If?
Inbox, #5 [>]
Alien Astronomers [>]
No More DNA [>]
Interplanetary Cessna [>]
Weird (and Worrying)
Questions from the What If?
Inbox, #6 [>]
Yoda [>]
Flyover States [>]
Falling with Helium [>]
Everybody Out [>]
Weird (and Worrying)
Questions from the What If?
Inbox, #7 [>]
Self-Fertilization [>]
High Throw [>]
Lethal Neutrinos [>]
Weird (and Worrying)
Questions from the What If?
Inbox, #8 [>]
Speed Bump [>]
Lost Immortals [>]
Orbital Speed [>]
FedEx Bandwidth [>]
Free Fall [>]
Weird (and Worrying)
Questions from the What If?
Inbox, #9 [>]
Sparta [>]
Drain the Oceans [>]
Drain the Oceans: Part II [>]
Twitter [>]
Lego Bridge [>]
Longest Sunset [>]
Random Sneeze Call [>]
Weird (and Worrying)
Questions from the What If?
Inbox, #10 [>]
Expanding Earth [>]
Weightless Arrow [>]
Sunless Earth [>]
Updating a Printed Wikipedia
[>]
Facebook of the Dead [>]
Sunset on the British Empire [>]
Stirring Tea [>]
All the Lightning [>]
Loneliest Human [>]
Weird (and Worrying)
Questions from the What If?
Inbox, #11 [>]
Raindrop [>]
SAT Guessing [>]
Neutron Bullet [>]
Weird (and Worrying)
Questions from the What If?
Inbox, #12 [>]
Richter 15 [>]
Acknowledgments [>]
References [>]
DISCLAIMER
Do not try any of this at
home. The author of this
book is an Internet
cartoonist, not a health
or safety expert. He likes
it when things catch fire
or explode, which means
he does not have your
best interests in mind.
The publisher and the
author disclaim
responsibility for any
adverse effects resulting,
directly or indirectly, from
information contained in
this book.
INTRODUCTIO
THIS BOOK IS A collection
of answers to hypothetical
questions.
These
questions
were
submitted to me through my
website, where—in addition
to serving as a sort of Dear
Abby for mad scientists—I
draw xkcd, a stick-figure
webcomic.
I didn’t start out making
comics. I went to school for
physics, and after graduating,
I worked on robotics at
NASA. I eventually left
NASA to draw comics fulltime, but my interest in
science and math didn’t fade.
Eventually, it found a new
outlet:
answering
the
Internet’s
weird—and
sometimes
worrying
—questions.
This
book
contains a selection of my
favorite answers from my
website, plus a bunch of new
questions answered here for
the first time.
I’ve been using math to try
to answer weird questions for
as long as I can remember.
When I was five years old, my
mother had a conversation
with me that she wrote down
and saved in a photo album.
When she heard I was
writing this book, she found
the transcript and sent it to
me. Here it is, reproduced
verbatim from her 25-yearold sheet of paper:
Randall:
Are
there more soft
things or hard
things in our
house?
Julie: I don’t
know.
Randall:
How
about in the
world?
Julie: I don’t
know.
Randall:
Well,
each house has
three or four
pillows, right?
Julie: Right.
Randall:
And
each house has
about
15
magnets, right?
Julie: I guess.
Randall: So 15
plus 3 or 4, let’s
say 4, is 19,
right?
Julie: Right.
Randall: So there
are
probably
about 3 billion
soft
things,
and . . . 5 billion
hard
things.
Well, which one
wins?
Julie: I guess
hard things.
To this day I have no idea
where I got “3 billion” and “5
billion” from. Clearly, I didn’t
really get how numbers
worked.
My math has gotten a little
better over the years, but my
reason for doing math is the
same as it was when I was
five: I want to answer
questions.
They say there are no stupid
questions. That’s obviously
wrong; I think my question
about hard and soft things,
for example, is pretty stupid.
But it turns out that trying to
thoroughly answer a stupid
question can take you to some
pretty interesting places.
I still don’t know whether
there are more hard or soft
things in the world, but I’ve
learned a lot of other stuff
along the way. What follows
are my favorite parts of that
journey.
RANDALL MUNROE
what if?
GLOBAL
WINDSTORM
Q. What
would
happen if the
Earth and all
terrestrial
objects
suddenly
stopped
spinning, but
the
atmosphere
retained its
velocity?
—Andrew Brown
A. NEARLY
EVERYONE
WOULD DIE. Then things
would get interesting.
At the equator, the Earth’s
surface is moving at about
470 meters per second—a
little over a thousand miles
per hour—relative to its axis.
If the Earth stopped and the
air didn’t, the result would be
a sudden thousand-mile-perhour wind.
The wind would be highest
at the equator, but everyone
and everything living between
42 degrees north and 42
degrees
south—which
includes about 85 percent of
the
world’s
population
—would suddenly experience
supersonic winds.
The highest winds would
last for only a few minutes
near the surface; friction with
the ground would slow them
down. However, those few
minutes would be long
enough to reduce virtually all
human structures to ruins.
My home in Boston is far
enough north to be just barely
outside the supersonic wind
zone, but the winds there
would still be twice as strong
as those in the most powerful
tornadoes. Buildings, from
sheds to skyscrapers, would
be smashed flat, torn from
their foundations, and sent
tumbling
across
the
landscape.
Winds would be lower near
the poles, but no human cities
are far enough from the
equator to escape devastation.
Longyearbyen, on the island
of Svalbard in Norway—the
highest-latitude city on the
planet—would be devastated
by winds equal to those in the
planet’s strongest tropical
cyclones.
If you’re going to wait it
out, one of the best places to
do it might be Helsinki,
Finland. While its high
latitude—above
60°N—
wouldn’t be enough to keep it
from being scoured clean by
the winds, the bedrock below
Helsinki
contains
a
sophisticated network of
tunnels, along with a
subterranean shopping mall,
hockey
rink,
swimming
complex, and more.
No buildings would be safe;
even structures strong enough
to survive the winds would be
in trouble. As comedian Ron
White said about hurricanes,
“It’s not that the wind is
blowing, it’s what the wind is
blowing.”
Say you’re in a massive
bunker made out of some
material that can withstand
thousand-mile-per-hour
winds.
That’s good,
fine . . . if you
one
with
Unfortunately,
and you’d be
were the only
a
bunker.
you probably
have neighbors, and if the
neighbor upwind of you has a
less-well-anchored
bunker,
your bunker will have to
withstand a thousand-mileper-hour impact by their
bunker.
The human race wouldn’t
go extinct.1 In general, very
few people above the surface
would survive; the flying
debris
would
pulverize
anything that wasn’t nuclearhardened. However, a lot of
people below the surface of
the ground would survive just
fine. If you were in a deep
basement (or, better yet, a
subway tunnel) when it
happened, you would stand a
good chance of surviving.
There would be other lucky
survivors. The dozens of
scientists and staff at the
Amundsen–Scott
research
station at the South Pole
would be safe from the winds.
For them, the first sign of
trouble would be that the
outside world had suddenly
gone silent.
The mysterious silence
would probably distract them
for a while, but eventually
someone
would
notice
something even stranger:
The air
As the surface winds died
down, things would get
weirder.
The wind blast would
translate to a heat blast.
Normally, the kinetic energy
of rushing wind is small
enough to be negligible, but
this would not be normal
wind. As it tumbled to a
turbulent stop, the air would
heat up.
Over land, this would lead
to scorching temperature
increases and—in areas where
the air is moist—global
thunderstorms.
At the same time, wind
sweeping over the oceans
would churn up and atomize
the surface layer of the water.
For a while, the ocean would
cease to have a surface at all;
it would be impossible to tell
where the spray ended and
the sea began.
Oceans are cold. Below the
thin surface layer, they’re a
fairly uniform 4°C. The
tempest would churn up cold
water from the depths. The
influx of cold spray into
superheated air would create a
type of weather never before
seen on Earth—a roiling mix
of wind, spray, fog, and rapid
temperature changes.
This upwelling would lead
to blooms of life, as fresh
nutrients flooded the upper
layers. At the same time, it
would lead to huge die-offs of
fish, crabs, sea turtles, and
animals unable to cope with
the influx of low-oxygen
water from the depths. Any
animal that needs to breathe
—such as whales and
dolphins—would be hardpressed to survive in the
turbulent sea-air interface.
The waves would sweep
around the globe, east to
west, and every east-facing
shore would encounter the
largest storm surge in world
history. A blinding cloud of
sea spray would sweep inland,
and behind it, a turbulent,
roiling wall of water would
advance like a tsunami. In
some places, the waves would
reach many miles inland.
The windstorms would
inject huge amounts of dust
and
debris
into
the
atmosphere. At the same
time, a dense blanket of fog
would form over the cold
ocean surfaces. Normally, this
would
cause
global
temperatures to plummet.
And they would.
At least, on one side of the
Earth.
If the Earth stopped
spinning, the normal cycle of
day and night would end.
The Sun wouldn’t completely
stop moving across the sky,
but instead of rising and
setting once a day, it would
rise and set once a year.
Day and night would each
be six months long, even at
the equator. On the day side,
the surface would bake under
the constant sunlight, while
on the night side the
temperature would plummet.
Convection on the day side
would lead to massive storms
in the area directly beneath
the Sun.2
In some ways, this Earth
would resemble one of the
tidally locked exoplanets
commonly found in a red
dwarf star’s habitable zone,
but a better comparison
might be a very early Venus.
Due to its rotation, Venus
—like our stopped Earth
—keeps the same face
pointed toward the Sun for
months at a time. However,
its thick atmosphere circulates
quite quickly, which results in
the day and the night side
having about the same
temperature.
Although the length of the
day would change, the length
of the month would not! The
Moon hasn’t stopped rotating
around the Earth. However,
without the Earth’s rotation
feeding it tidal energy, the
Moon would stop drifting
away from the Earth (as it is
doing currently) and would
start to slowly drift back
toward us.
In fact, the Moon—our
faithful companion—would
act to undo the damage
Andrew’s scenario caused.
Right now, the Earth spins
faster than the Moon, and
our tides slow down the
Earth’s
rotation
while
pushing the Moon away from
us.3 If we stopped rotating,
the Moon would stop drifting
away from us. Instead of
slowing us down, its tides
would accelerate our spin.
Quietly, gently, the Moon’s
gravity would tug on our
planet . . .
. . . and Earth would start
turning again.
1 I mean, not right away.
2 Although without the
Coriolis force, it’s anyone’s
guess which way they would
spin.
3 See “Leap Seconds,”
http://what-if.xkcd.com/26, for
an explanation of why this
happens.
RELATIVISTIC
BASEBALL
Q. What
would
happen if you
tried to hit a
baseball
pitched at 90
percent the
speed of
light?
—Ellen McManis
Let’s set aside the question of how
we got the baseball moving that fast.
We’ll suppose it’s a normal pitch,
except in the instant the pitcher
releases the ball, it magically
accelerates to 0.9c. From that point
onward, everything proceeds
according to normal physics.
A. THE ANSWER TURNS
OUT to be “a lot of things,”
and they all happen very
quickly, and it doesn’t end
well for the batter (or the
pitcher). I sat down with
some physics books, a Nolan
Ryan action figure, and a
bunch of videotapes of
nuclear tests and tried to sort
it all out. What follows is my
best guess at a nanosecondby-nanosecond portrait.
The ball would be going so
fast that everything else
would
be
practically
stationary.
Even
the
molecules in the air would
stand still. Air molecules
would vibrate back and forth
at a few hundred miles per
hour, but the ball would be
moving through them at 600
million miles per hour. This
means that as far as the ball is
concerned, they would just be
hanging there, frozen.
The ideas of aerodynamics
wouldn’t
apply
here.
Normally, air would flow
around anything moving
through it. But the air
molecules in front of this ball
wouldn’t have time to be
jostled out of the way. The
ball would smack into them
so hard that the atoms in the
air molecules would actually
fuse with the atoms in the
ball’s surface. Each collision
would release a burst of
gamma rays and scattered
particles.1
These gamma rays and
debris would expand outward
in a bubble centered on the
pitcher’s mound. They would
start to tear apart the
molecules in the air, ripping
the electrons from the nuclei
and turning the air in the
stadium into an expanding
bubble
of
incandescent
plasma. The wall of this
bubble would approach the
batter at about the speed of
light—only slightly ahead of
the ball itself.
The constant fusion at the
front of the ball would push
back on it, slowing it down,
as if the ball were a rocket
flying tail-first while firing its
engines. Unfortunately, the
ball would be going so fast
that even the tremendous
force from this ongoing
thermonuclear
explosion
would barely slow it down at
all. It would, however, start to
eat away at the surface,
blasting tiny fragments of the
ball in all directions. These
fragments would be going so
fast that when they hit air
molecules, they would trigger
two or three more rounds of
fusion.
After about 70 nanoseconds
the ball would arrive at home
plate. The batter wouldn’t
even have seen the pitcher let
go of the ball, since the light
carrying that information
would arrive at about the
same time the ball would.
Collisions with the air would
have eaten the ball away
almost completely, and it
would now be a bullet-shaped
cloud of expanding plasma
(mainly
carbon,
oxygen,
hydrogen, and nitrogen)
ramming into the air and
triggering more fusion as it
went. The shell of x-rays
would hit the batter first, and
a handful of nanoseconds
later the debris cloud would
hit.
When it would reach home
plate, the center of the cloud
would still be moving at an
appreciable fraction of the
speed of light. It would hit
the bat first, but then the
batter, plate, and catcher
would all be scooped up and
carried backward through the
backstop
as
they
disintegrated. The shell of xrays and superheated plasma
would expand outward and
upward,
swallowing
the
backstop, both teams, the
stands, and the surrounding
neighborhood—all in the first
microsecond.
Suppose you’re watching
from a hilltop outside the
city. The first thing you
would see would be a
blinding light, far outshining
the sun. This would gradually
fade over the course of a few
seconds, and a growing
fireball would rise into a
mushroom cloud. Then, with
a great roar, the blast wave
would arrive, tearing up trees
and shredding houses.
Everything within roughly a
mile of the park would be
leveled, and a firestorm would
engulf the surrounding city.
The baseball diamond, now a
sizable crater, would be
centered a few hundred feet
behind the former location of
the backstop.
Major League Baseball
Rule 6.08(b) suggests that in
this situation, the batter
would be considered “hit by
pitch,” and would be eligible
to advance to first base.
1 After I initially published this
article, MIT physicist Hans
Rinderknecht contacted me to
say that he’d simulated this
scenario on their lab’s
computers. He found that early
in the ball’s flight, most of the
air molecules were actually
moving too quickly to cause
fusion, and would pass right
through the ball, heating it
more slowly and uniformly than
my original article described.
SPENT FUEL
POOL
Q. What if I
took a swim
in a typical
spent nuclear
fuel pool?
Would I need
to dive to
actually
experience a
fatal amount
of radiation?
How long
could I stay
safely at the
surface?
—Jonathan Bastien-
Filiatrault
A. ASSUMING YOU’RE A
REASONABLY
good
swimmer, you could probably
survive
treading
water
anywhere from 10 to 40
hours. At that point, you
would black out from fatigue
and drown. This is also true
for a pool without nuclear
fuel in the bottom.
Spent fuel from nuclear
reactors is highly radioactive.
Water is good for both
radiation
shielding
and
cooling, so fuel is stored at
the bottom of pools for a
couple of decades until it’s
inert enough to be moved
into dry casks. We haven’t
really agreed on where to put
those dry casks yet. One of
these days we should probably
figure that out.
Here’s the geometry of a
typical fuel storage pool:
The heat wouldn’t be a big
problem.
The
water
temperature in a fuel pool can
in theory go as high as 50°C,
but in practice it’s generally
between 25°C and 35°C
—warmer than most pools
but cooler than a hot tub.
The most highly radioactive
fuel rods are those recently
removed from a reactor. For
the kinds of radiation coming
off spent nuclear fuel, every 7
centimeters of water cuts the
amount of radiation in half.
Based on the activity levels
provided by Ontario Hydro
in this report, this would be
the region of danger for fresh
fuel rods:
Swimming to the bottom,
touching your elbows to a
fresh fuel canister, and
immediately swimming back
up would probably be enough
to kill you.
Yet outside the outer
boundary, you could swim
around as long as you wanted
—the dose from the core
would be less than the normal
background dose you get
walking around. In fact, as
long as you were underwater,
you would be shielded from
most
of
that
normal
background dose. You may
actually receive a lower dose
of radiation treading water in
a spent fuel pool than walking
around on the street.
Remember: I am a cartoonist. If you
follow my advice on safety around
nuclear materials, you probably
deserve whatever happens to you.
That’s if everything goes as
planned. If there’s corrosion
in the spent fuel rod casings,
there may be some fission
products in the water. They
do a pretty good job of
keeping the water clean, and
it wouldn’t hurt you to swim
in it, but it’s radioactive
enough that it wouldn’t be
legal to sell it as bottled
water.1
We know spent fuel pools
can be safe to swim in
because they’re routinely
serviced by human divers.
However, these divers have
to be careful.
On August 31, 2010, a
diver was servicing the spent
fuel pool at the Leibstadt
nuclear
reactor
in
Switzerland. He spotted an
unidentified length of tubing
on the bottom of the pool
and radioed his supervisor to
ask what to do. He was told
to put it in his tool basket,
which he did. Due to bubble
noise in the pool, he didn’t
hear his radiation alarm.
When the tool basket was
lifted from the water, the
room’s radiation alarms went
off. The basket was dropped
back in the water and the
diver left the pool. The diver’s
dosimeter badges showed that
he’d received a higher-thannormal whole-body dose, and
the dose in his right hand was
extremely high.
The object turned out to be
protective tubing from a
radiation monitor in the
reactor core, made highly
radioactive by neutron flux. It
had been accidentally sheared
off while a capsule was being
closed in 2006. It sank to a
remote corner of the pool,
where it sat unnoticed for
four years.
The
tubing
was
so
radioactive that if he’d tucked
it into a tool belt or shoulder
bag, where it sat close to his
body, he could’ve been killed.
As it was, the water protected
him, and only his hand—a
body part more resistant to
radiation than the delicate
internal organs—received a
heavy dose.
So, as far as swimming
safety goes, the bottom line is
that you’d probably be OK, as
long as you didn’t dive to the
bottom or pick up anything
strange.
But just to be sure, I got in
touch with a friend of mine
who works at a research
reactor, and asked him what
he thought would happen to
someone who tried to swim
in
their
radiation
containment pool.
“In our reactor?” He
thought about it for a
moment. “You’d die pretty
quickly, before reaching the
water,
from
gunshot
wounds.”
1 Which is too bad — it’d
make a hell of an energy drink.
WEIRD
(AND
WORRYING)
QUESTIONS
FROM
THE
WHAT IF?
INBOX, #1
Q. Would it be
possible to get
your teeth to
such a cold
temperature
that they
would shatter
upon drinking
a hot cup of
coffee?
—Shelby Hebert
Q.
How many
houses are
burned down
in the United
States every
year? What
would be the
easiest way to
increase that
number by a
significant
amount (say, at
least 15%)?
—Anonymous
NEW YORK–
STYLE TIME
MACHINE
Q. I assume
when you
travel back in
time you end
up at the
same spot on
the Earth’s
surface. At
least, that’s
how it
worked in the
Back to the
Future
movies. If so,
what would it
be like if you
traveled back
in time,
starting in
Times
Square, New
York, 1000
years? 10,000
years?
100,000
years?
1,000,000
years?
1,000,000,000
years? What
about forward
in time
1,000,000
years?
—Mark Dettling
1000 years back
Manhattan
has
been
continuously inhabited for
the past 3000 years, and was
first settled by humans
perhaps 9000 years ago.
In the 1600s, when
Europeans arrived, the area
was inhabited by the Lenape
people.1 The Lenape were a
loose confederation of tribes
who lived in what is now
Connecticut, New York, New
Jersey, and Delaware.
A thousand years ago, the
area was probably inhabited
by a similar collection of
tribes, but those inhabitants
lived half a millennium before
European contact. They were
as far removed from the
Lenape of the 1600s as the
Lenape of the 1600s are from
the modern day.
To see what Times Square
looked like before a city was
there, we turn to a remarkable
project called Welikia, which
grew out of a smaller project
called Mannahatta. The
Welikia project has produced
a detailed ecological map of
the landscape in New York
City at the time of the arrival
of Europeans.
The
interactive
map,
available online at welikia.org,
is a fantastic snapshot of a
different New York. In 1609,
the island of Manhattan was
part of a landscape of rolling
hills, marshes, woodlands,
lakes, and rivers.
The Times Square of 1000
years ago may have looked
ecologically similar to the
Times Square described by
Welikia. Superficially, it
probably resembled the oldgrowth forests that are still
found in a few locations in
the
northeastern
US.
However, there would be
some notable differences.
There would be more large
animals 1000 years ago.
Today’s
disconnected
patchwork of northeastern
old-growth forests is nearly
free of large predators; we
have some bears, few wolves
and coyotes, and virtually no
mountain lions. (Our deer
populations, on the other
hand, have exploded, thanks
in part to the removal of large
predators.)
The forests of New York
1000 years ago would be full
of chestnut trees. Before a
blight passed through in the
early twentieth century, the
hardwood forests of eastern
North America were about 25
percent chestnut. Now, only
their stumps survive.
You can still come across
these stumps in New England
forests
today.
They
periodically
sprout
new
shoots, only to see them
wither as the blight takes
hold. Someday, before too
long, the last of the stumps
will die.
Wolves would be common
in the forests, especially as
you moved inland. You might
also encounter
lions2,3,4,5,6 and
pigeons.7
mountain
passenger
There’s one thing you
would not see: earthworms.
There were no earthworms in
New England when the
European colonists arrived.
To see the reason for the
worms’ absence, let’s take our
next step into the past.
10,000 years back
The Earth of 10,000 years
ago was just emerging from a
deep cold period.
The great ice sheets that
covered New England had
departed. As of 22,000 years
ago, the southern edge of the
ice was near Staten Island,
but by 18,000 years ago it had
retreated
north
past
Yonkers.8 By the time of our
arrival, 10,000 years ago, the
ice had largely withdrawn
across
the
present-day
Canadian border.
The ice sheets scoured the
landscape down to bedrock.
Over the next 10,000 years,
life crept slowly back
northward. Some species
moved north faster than
others; when Europeans
arrived in New England,
earthworms had not yet
returned.
As the ice sheets withdrew,
large chunks of ice broke off
and were left behind.
When these chunks melted,
they left behind water-filled
depressions in the ground
called kettlehole ponds.
Oakland Lake, near the north
end of Springfield Boulevard
in Queens, is one of these
kettlehole ponds. The ice
sheets also dropped boulders
they’d picked up on their
journey; some of these rocks,
called glacial erratics, can be
found in Central Park today.
Below the ice, rivers of
meltwater flowed at high
pressure, depositing sand and
gravel as they went. These
deposits, which remain as
ridges called eskers, crisscross
the landscape in the woods
outside my home in Boston.
They are responsible for a
variety of odd landforms,
including the world’s only
vertical U-shaped riverbeds.
100,000 years back
The world of 100,000 years
ago might have looked a lot
like our own.9 We live in an
era of rapid, pulsating
glaciations, but for 10,000
years our climate has been
stable10 and warm.
A hundred thousand years
ago, Earth was near the end
of a similar period of climate
stability. It was called the
Sangamon interglacial, and
it probably supported a
developed ecology that would
look familiar to us.
The coastal geography
would be totally different;
Staten Island, Long Island,
Nantucket, and Martha’s
Vineyard were all berms
pushed up by the most recent
bulldozer-like advance of the
ice. A hundred millennia ago,
different islands dotted the
coast.
Many of today’s animals
would be found in those
woods—birds, squirrels, deer,
wolves, black bears—but
there would be a few dramatic
additions. To learn about
those, we turn to the mystery
of the pronghorn.
The modern pronghorn
(American antelope) presents
a puzzle. It’s a fast runner—in
fact, it’s much faster than it
needs to be. It can run at 55
mph, and sustain that speed
over long distances. Yet its
fastest predators, wolves and
coyotes, barely break 35 mph
in a sprint. Why did the
pronghorn evolve such speed?
The answer is that the
world
in
which
the
pronghorn evolved was a
much more dangerous place
than ours. A hundred
thousand years ago, North
American woods were home
to Canis dirus (the dire wolf),
Arctodus (the short-faced
bear), and Smilodon fatalis
(sabre-toothed cat), each of
which may have been faster
and deadlier than modern
predators. All died out in the
Quaternary extinction event,
which occured shortly after
the first humans colonized
the continent.11
If we go back a little
further, we will meet another
frightening predator.
1,000,000 years back
A million years ago, before
the most recent great episode
of glaciations, the world was
fairly warm. It was the middle
of the Quaternary period; the
great modern ice ages had
begun several million years
earlier, but there had been a
lull in the advance and retreat
of the glaciers, and the
climate was relatively stable.
The predators we met
earlier,
the
fleet-footed
creatures who may have
preyed on the pronghorn,
were joined by another
terrifying carnivore, a longlimbed hyena that resembled
a modern wolf. Hyenas were
mainly found in Africa and
Asia, but when the sea level
fell, one species crossed the
Bering Strait into North
America. Because it was the
only hyena to do so, it was
given
the
name
Chasmaporthetes,
which
means “the one who saw the
canyon.”
Next, Mark’s question takes
us on a great leap backward in
time.
1,000,000,000 years
back
A billion years ago,
continental
plates
pushed together into
great supercontinent.
the
were
one
This
was not the well-known
supercontinent Pangea—it
was Pangea’s predecessor,
Rodinia. The geologic record
is spotty, but our best guess is
that it looked something like
this:
In the time of Rodinia, the
bedrock that now lies under
Manhattan had yet to form,
but the deep rocks of North
America were already old.
The part of the continent that
is now Manhattan was
probably an inland region
connected to what is now
Angola and South Africa.
In this ancient world, there
were no plants and no
animals. The oceans were full
of life, but it was simple
single-cellular life. On the
surface of the water were
mats of blue-green algae.
These unassuming critters
are the deadliest killers in the
history of life.
Blue-green
algae,
or
cyanobacteria, were the first
photosynthesizers.
They
breathed in carbon dioxide
and breathed out oxygen.
Oxygen is a volatile gas; it
causes iron to rust (oxidation)
and wood to burn (vigorous
oxidation).
When
cyanobacteria first appeared,
the oxygen they breathed out
was toxic to nearly all other
forms of life. The resulting
extinction is called the
oxygen catastrophe.
After the cyanobacteria
pumped Earth’s atmosphere
and water full of toxic oxygen,
creatures evolved that took
advantage of the gas’s volatile
nature
to
enable
new
biological processes. We are
the descendants of those first
oxygen-breathers.
Many details of this history
remain uncertain; the world
of a billion years ago is
difficult to reconstruct. But
Mark’s question now takes us
into an even more uncertain
domain: the future.
1,000,000 years forward
Eventually, humans will die
out. Nobody knows when,12
but nothing lives forever.
Maybe we’ll spread to the
stars and last for billions or
trillions of years. Maybe
civilization will collapse, we’ll
all succumb to disease and
famine, and the last of us will
be eaten by cats. Maybe we’ll
all be killed by nanobots
hours after you read this
sentence. There’s no way to
know.
A million years is a long
time. It’s several times longer
than Homo sapiens has
existed, and a hundred times
longer than we’ve had written
language. It seems reasonable
to assume that however the
human story plays out, in a
million years it will have
exited its current stage.
Without us, Earth’s geology
will grind on. Winds and rain
and blowing sand will
dissolve and bury the artifacts
of our civilization. Humancaused climate change will
probably delay the start of the
next glaciation, but we
haven’t ended the cycle of ice
ages. Eventually, the glaciers
will advance again. A million
years from now, few human
artifacts will remain.
Our most lasting relic will
probably be the layer of
plastic we’ve deposited across
the planet. By digging up oil,
processing it into durable and
long-lasting polymers, and
spreading it across the Earth’s
surface,
we’ve
left
a
fingerprint that could outlast
everything else we do.
Our plastic will become
shredded and buried, and
perhaps some microbes will
learn to digest it, but in all
likelihood, a million years
from now, an out-of-place
layer
of
processed
hydrocarbons—transformed
fragments of our shampoo
bottles and shopping bags
—will serve as a chemical
monument to civilization.
The far future
The
Sun
is
gradually
brightening. For three billion
years, a complex system of
feedback loops has kept the
Earth’s temperature relatively
stable as the Sun has grown
steadily warmer.
In a billion years, these
feedback loops will have given
out. Our oceans, which
nourished life and kept it
cool, will have turned into its
worst enemy. They will have
boiled away in the hot Sun,
surrounding the planet with a
thick blanket of water vapor
and causing a runaway
greenhouse effect. In a billion
years, Earth will become a
second Venus.
As the planet heats up, we
may lose our water entirely
and acquire a rock vapor
atmosphere, as the crust itself
begins to boil. Eventually,
after several billion more
years, we will be consumed by
the expanding Sun.
The
Earth
will
be
incinerated, and many of the
molecules that made up
Times Square will be blasted
outward by the dying Sun.
These dust clouds will drift
through
space,
perhaps
collapsing to form new stars
and planets.
If humans escape the solar
system and outlive the Sun,
our descendants may someday
live on one of these planets.
Atoms from Times Square,
cycled through the heart of
the Sun, will form our new
bodies.
One day, either we will all
be dead, or we will all be New
Yorkers.
1 Also known as the Delaware.
2 Also known as cougars.
3 Also known as pumas.
4 Also known as catamounts.
5 Also known as panthers.
6 Also known as painted cats.
7 Although you might not see
the clouds of trillions of
pigeons encountered by
European settlers. In his book
1491, Charles C. Mann argues
that the huge flocks seen by
European settlers may have
been a symptom of a chaotic
ecosystem perturbed by the
arrival of smallpox, bluegrass,
and honeybees.
8 That is, the current site of
Yonkers. It probably wasn’t
called “Yonkers” then, since
“Yonkers” is a Dutch-derived
name for a settlement dating to
the late 1600s. However, some
argue that a site called
“Yonkers” has always existed,
and in fact predates humans
and the Earth itself. I mean, I
guess it’s just me who argues
that, but I’m very vocal.
9 Though with fewer
billboards.
10 Well, had been. We’re
putting a stop to that.
11 If anyone asks, total
coincidence.
12 If you do, email me.
SOUL MATES
Q. What if
everyone
actually had
only one soul
mate, a
random
person
somewhere in
the world?
—Benjamin Staffin
A. WHAT
A NIGHTMARE
THAT would be.
There are a lot of problems
with the concept of a single
random soul mate. As Tim
Minchin put it in his song “If
I Didn’t Have You”:
Your love is one in a
million;
You couldn’t buy it at any
price.
But of the 9.999 hundred
thousand other loves,
Statistically, some of them
would be equally nice.
But what if we did have one
randomly assigned perfect
soul mate, and we couldn’t be
happy with anyone else?
Would we find each other?
We’ll assume your soul
mate is chosen at birth. You
don’t know anything about
who or where they are, but
—as in the romantic cliché
—you recognize each other
the moment your eyes meet.
Right away, this would raise
a few questions. For starters,
would your soul mate even
still be alive? A hundred
billion or so humans have
ever lived, but only seven
billion are alive now (which
gives the human condition a
93 percent mortality rate). If
we were all paired up at
random, 90 percent of our
soul mates would be long
dead.
That sounds horrible. But
wait, it gets worse: A simple
argument shows we can’t
limit ourselves just to past
humans; we have to include
an unknown number of future
humans as well. See, if your
soul mate is in the distant
past, then it also has to be
possible for soul mates to be
in the distant future. After all,
your soul mate’s soul mate is.
So let’s assume your soul
mate lives at the same time as
you. Furthermore, to keep
things from getting creepy,
we’ll assume they’re within a
few years of your age. (This is
stricter than the standard agegap creepiness formula,1 but
if we assume a 30-year-old
and a 40-year-old can be soul
mates, then the creepiness
rule is violated if they
accidentally meet 15 years
earlier.) With the same-age
restriction, most of us would
have a pool of around half a
billion potential matches.
But what about gender and
sexual
orientation?
And
culture? And language? We
could
keep
using
demographics to try to
narrow things down further,
but we’d be drifting away
from the idea of a random
soul mate. In our scenario,
you wouldn’t know anything
about who your soul mate was
until you looked into their
eyes. Everybody would have
only one orientation: toward
their soul mate.
The odds of running into
your soul mate would be
incredibly small. The number
of strangers we make eye
contact with each day can
vary from almost none (shutins or people in small towns)
to many thousands (a police
officer in Times Square), but
let’s suppose you lock eyes
with an average of a few
dozen new strangers each day.
(I’m pretty introverted, so for
me
that’s
definitely
a
generous estimate.) If 10
percent of them are close to
your age, that would be
around 50,000 people in a
lifetime. Given that you have
500,000,000 potential soul
mates, it means you would
find true love only in one
lifetime out of 10,000.
With the threat of dying
alone
looming
so
prominently, society could
restructure to try to enable as
much eye contact as possible.
We could put together
massive conveyer belts to
move lines of people past
each other . . .
. . . but if the eye contact
effect works over webcams,
we could just use a modified
version of ChatRoulette.
If everyone used the system
for eight hours a day, seven
days a week, and if it takes
you a couple of seconds to
decide if someone’s your soul
mate, this system could—in
theory—match everyone up
with their soul mates in a few
decades. (I modeled a few
simple systems to estimate
how quickly people would
pair off and drop out of the
singles pool. If you want to
try to work through the math
for a particular setup, you
might start by looking at
derangement problems.)
In the real world, many
people have trouble finding
any time at all for romance
—few could devote two
decades to it. So maybe only
rich kids would be able to
afford to sit around on
SoulMateRoulette.
Unfortunately
for
the
proverbial 1 percent, most of
their soul mates would be
found in the other 99 percent.
If only 1 percent of the
wealthy used the service, then
1 percent of that 1 percent
would find their match
through this system—one in
10,000.
The other 99 percent of the
1 percent2 would have an
incentive to get more people
into the system. They might
sponsor charitable projects to
get computers to the rest of
the world—a cross between
One Laptop Per Child and
OKCupid.
Careers
like
“cashier” and “police officer in
Times Square” would become
high-status prizes because of
the eye contact potential.
People would flock to cities
and public gathering places to
find love—just as they do
now.
But even if a bunch of us
spent
years
on
SoulMateRoulette, another
bunch of us managed to hold
jobs that offered constant eye
contact with strangers, and
the rest of us just hoped for
luck, only a small minority of
us would ever find true love.
The rest of us would be out of
luck.
Given all the stress and
pressure, some people would
fake it. They’d want to join
the club, so they’d get
together with another lonely
person and stage a fake soul
mate
encounter.
They’d
marry, hide their relationship
problems, and struggle to
present a happy face to their
friends and family.
A world of random soul
mates would be a lonely one.
Let’s hope that’s not what we
live in.
1 xkcd, “Dating pools,”
http://xkcd.com/314.
2 “We are the zero point nine
nine percent!”
LASER
POINTER
Q. If every
person on
Earth aimed a
laser pointer
at the Moon
at the same
time, would it
change color?
—Peter Lipowicz
A. NOT
IF WE USED
regular laser pointers.
The first thing to consider
is that not everyone can see
the Moon at once. We could
gather everyone in one spot,
but let’s just pick a time when
the Moon is visible to as
many people as possible.
Since about 75 percent of the
world’s
population
lives
between 0°E and 120°E, we
should try this while the
Moon is somewhere over the
Arabian Sea.
We could try to illuminate
either a new moon or a full
moon. The new moon is
darker, making it easier to see
our lasers. But the new moon
is a trickier target, because it’s
mostly visible during the day
—washing out the effect.
Let’s pick a quarter moon,
so we can compare the effect
of our lasers on the dark and
light sides.
Here’s our target.
The typical red laser pointer
is about 5 milliwatts, and a
good one would have a tight
enough beam to hit the
Moon—though it’d be spread
out over a large fraction of the
surface when it got there. The
atmosphere would distort the
beam a bit, and absorb some
of it, but most of the light
would make it.
Let’s assume everyone has
steady enough aim to hit the
Moon, but no more than
that, and the light spreads
evenly across the surface.
Half an hour after midnight
(GMT), everyone aims and
presses the button.
This is what happened:
Well, that’s disappointing.
It makes sense, though.
Sunlight bathes the Moon in
a bit over a kilowatt of energy
per square meter. Since the
Moon’s cross-sectional area is
around 1013 square meters, it’s
bathed in about 1016 watts of
sunlight—10 petawatts, or 2
megawatts per person—far
outshining our 5-milliwatt
laser pointers. There are
varying efficiencies in each
part of this system, but none
of it changes that basic
equation.
A
1-watt
laser
is
an
extremely dangerous thing.
It’s not just powerful enough
to blind you—it’s capable of
burning skin and setting
things on fire. Obviously,
they’re not legal for consumer
purchase in the US.
Just kidding! You can pick
one up for $300. Just do a
search for “1-watt handheld
laser.”
So, suppose we spend the
$2 trillion to buy 1-watt
green lasers for everyone.
(Memo
to
presidential
candidates: This policy would
win my vote.) In addition to
being more powerful, green
laser light is nearer to the
middle
of
the
visible
spectrum, so the eye is more
sensitive to it and it seems
brighter.
Here’s the effect:
Dang.
The laser pointers we’re
using put out about 150
lumens of light (more than
most flashlights) in a beam 5
arc-minutes wide. This lights
up the surface of the Moon
with about half a lux of
illumination—compared to
about 130,000 lux from the
sun. (Even if we aimed them
all perfectly, it would result in
only half a dozen lux over
about 10 percent of the
Moon’s face.)
By comparison, the full
moon lights up the Earth’s
surface with about 1 lux of
illumination—which means
that not only would our lasers
be too weak to see from
Earth, but if you were
standing on the Moon, the
laser light on the landscape
would be fainter than
moonlight is to us on Earth.
With advances in lithium
batteries
and
LED
technology over the last ten
years, the high-performance
flashlight
market
has
exploded. But it’s clear that
flashlights aren’t gonna cut it.
So let’s skip past all of that
and give everyone a Nightsun.
You may not recognize the
name, but chances are you’ve
seen one in operation: It’s the
searchlight
mounted
on
police and Coast Guard
helicopters. With an output
on the order of 50,000
lumens, it’s capable of turning
a patch of ground from night
to day.
The beam is several degrees
wide, so we would want some
focusing lenses to get it down
to the half-degree needed to
hit the Moon.
Here’s the effect:
It’s hard to see, but we’re
making progress! The beam is
providing
20
lux
of
illumination, outshining the
ambient light on the night
half by a factor of two!
However, it’s quite hard to
see, and it certainly hasn’t
affected the light half.
Let’s
swap
out
each
Nightsun for an IMAX
projector array—a 30,000watt pair of water-cooled
lamps with a combined
output of over a million
lumens.
Still barely visible.
At the top of the Luxor
Hotel in Las Vegas is the
most powerful spotlight on
Earth. Let’s give one of them
to everyone.
Oh, and let’s add a lens
array to each so the entire
beam is focused on the
Moon:
Our light is definitely
visible, so we’ve accomplished
our goal! Good job, team.
Well . . .
The
Department
of
Defense
has
developed
megawatt lasers, designed for
destroying incoming missiles
in mid-flight.
The Boeing YAL-1 was a
megawatt-class
chemical
oxygen iodine laser mounted
in a 747. It was an infrared
laser, so it wasn’t directly
visible, but we can imagine
building a visible-light laser
with similar power.
Finally, we’ve managed to
match the brightness of
sunlight!
We’re also drawing 5
petawatts of power, which is
double the world’s average
electricity consumption.
Okay,
let’s
mount
a
megawatt laser on every
square meter of Asia’s surface.
Powering this array of 50
trillion lasers would use up
Earth’s oil reserves in
approximately two minutes,
but for those two minutes,
the Moon would look like
this:
The Moon would shine as
brightly as the midmorning
sun, and by the end of the
two minutes, the lunar
regolith would be heated to a
glow.
Okay, let’s step even more
firmly outside the realm of
plausibility.
The most powerful laser on
Earth is the confinement
beam at the National Ignition
Facility, a fusion research
laboratory. It’s an ultraviolet
laser with an output of 500
terawatts. However, it fires
only in single pulses lasting a
few nanoseconds, so the total
energy delivered is equivalent
to about a quarter-cup of
gasoline.
Let’s imagine we somehow
found a way to power and fire
it continuously, gave one to
everyone, and pointed them
all
at
the
Moon.
Unfortunately,
the
laser
energy flow would turn the
atmosphere
to
plasma,
instantly igniting the Earth’s
surface and killing us all. But
let’s assume that the lasers
somehow pass through the
atmosphere
without
interacting.
Under those circumstances,
it turns out Earth would still
catch fire. The reflected light
from the Moon would be four
thousand times brighter than
the noonday sun. Moonlight
would become bright enough
to boil away Earth’s oceans in
less than a year.
But forget the Earth—what
would happen to the Moon?
The laser itself would exert
enough radiation pressure to
accelerate the Moon at about
one ten millionth of a gee.
This acceleration wouldn’t be
noticeable in the short term,
but over the years, it would
add up to enough to push it
free from Earth orbit . . .
. . . if radiation pressure
were the only force involved.
Forty megajoules of energy
is enough to vaporize a
kilogram of rock. Assuming
Moon rocks have an average
density of about 3 kg/liter,
the lasers would pump out
enough energy to vaporize 4
meters of lunar bedrock per
second:
However, the actual lunar
rock wouldn’t evaporate that
fast—for a reason that turns
out to be very important.
When a chunk of rock is
vaporized, it doesn’t just
disappear. The surface layer
of the Moon becomes a
plasma, but that plasma
would still block the path of
the beam.
Our laser would keep
pouring more and more
energy into the plasma, and
the plasma would keep
getting hotter and hotter.
The particles would bounce
off each other, slam into the
surface of the Moon, and
eventually blast into space at a
terrific speed.
This flow of material
effectively turns the entire
surface of the Moon into a
rocket
engine—and
a
surprisingly efficient one, too.
Using lasers to blast off
surface material like this is
called laser ablation, and it
turns out to be a promising
method
for
spacecraft
propulsion.
The Moon is massive, but
slowly and surely the rock
plasma jet would begin to
push it away from the Earth.
(The jet would also scour the
face of the Earth clean and
destroy the lasers, but we’re
pretending
that
they’re
invulnerable.) The plasma
would also physically tear
away the lunar surface, a
complicated interaction that’s
tricky to model.
But if we make the wild
guess that the particles in the
plasma exit at an average
speed of 500 kilometers per
second, then it will take a few
months for the Moon to be
pushed out of range of our
laser. It would keep most of
its mass, but escape Earth’s
gravity and enter a lopsided
orbit around the sun.
Technically, the Moon
wouldn’t become a new
planet, under the IAU
definition of a planet. Since
its new orbit would cross
Earth’s,
it
would
be
considered a dwarf planet like
Pluto. This Earth-crossing
orbit would lead to periodic
unpredictable
orbital
perturbation. Eventually it
would either be slingshotted
into the Sun, ejected toward
the outer solar system, or
slammed into one of the
planets—quite possibly ours.
I think we can all agree that
in this case, we’d deserve it.
Scorecard:
And that, at last, would be
enough power.
PERIODIC
WALL OF
THE
ELEMENTS
Q. What
would
happen if you
made a
periodic table
out of cubeshaped
bricks, where
each brick
was made of
the
corresponding
element?
—Andy Connolly
A. THERE
ARE PEOPLE
WHO collect elements.
These collectors try to gather
physical samples of as many
of the elements as possible
into
periodic-table-shaped
display cases.1
Of the 118 elements, 30 of
them—like helium, carbon,
aluminum,
iron,
and
ammonia—can be bought in
pure form in local retail
stores. Another few dozen
can be scavenged by taking
things apart (you can find
tiny americium samples in
smoke detectors). Others can
be ordered over the Internet.
All in all, it’s possible to get
samples of about 80 of the
elements—90,
if
you’re
willing to take some risks
with your health, safety, and
arrest record. The rest are too
radioactive or short-lived to
collect more than a few atoms
of them at once.
But what if you did?
The periodic table of the
elements has seven rows.2
You could stack the
top two rows without
much trouble.
The third row would
burn you with fire.
The fourth row
would kill you with
toxic smoke.
The fifth row would
do all that stuff
PLUS give you a
mild dose of
radiation.
The sixth row would
explode violently,
destroying the
building in a cloud of
radioactive,
poisonous fire and
dust.
Do not build the
seventh row.
We’ll start from the top.
The first row is simple, if
boring:
The cube of hydrogen
would rise upward and
disperse, like a balloon
without a balloon. The same
goes for helium.
The second row is trickier.
The
lithium
would
immediately tarnish. The
beryllium is pretty toxic, so
you should handle it carefully
and avoid getting any dust in
the air.
The oxygen and nitrogen
drift
around,
slowly
dispersing. The neon floats
away.3
The pale yellow fluorine gas
would spread across the
ground. Fluorine is the most
reactive, corrosive element in
the periodic table. Almost any
substance exposed to pure
fluorine will spontaneously
catch fire.
I spoke to organic chemist
Derek Lowe about this
scenario.4 He said that the
fluorine wouldn’t react with
the neon, and “would observe
a sort of armed truce with the
chlorine, but everything else,
sheesh.” Even with the later
rows, the fluorine would
cause problems as it spread,
and if it came in contact with
any moisture, it would form
corrosive hydrofluoric acid.
If you breathed even a trace
amount, it would seriously
damage or destroy your nose,
lungs, mouth, eyes, and
eventually the rest of you.
You would definitely need a
gas mask. Keep in mind that
fluorine eats through a lot of
potential mask materials, so
you would want to test it first.
Have fun!
On to the third row!
Half of the data here is from the CRC
Handbook of Chemistry and Physics
and the other half is from Look
Around You.
The big troublemaker here
is
phosphorus.
Pure
phosphorus comes in several
forms. Red phosphorus is
reasonably safe to handle.
White
phosphorus
spontaneously ignites on
contact with air. It burns with
hot,
hard-to-extinguish
flames and is, in addition,
quite poisonous.5
The sulfur wouldn’t be a
problem
under
normal
circumstances; at worst, it
would smell bad. However,
our sulfur is sandwiched
between burning phosphorus
on the left . . . and the
fluorine and chlorine on the
right. When exposed to pure
fluorine gas, sulfur—like
many
substances—catches
fire.
The inert argon is heavier
than air, so it would just
spread out and cover the
ground. Don’t worry about
the argon. You have bigger
problems.
The fire would produce all
kinds of terrifying chemicals
with names like sulfur
hexafluoride. If you’re doing
this inside, you’d be choked
by toxic smoke and your
building might burn down.
And that’s only row three.
On to row four!
“Arsenic” sounds scary. The
reason it sounds scary is a
good one: It’s toxic to
virtually all forms of complex
life.
Sometimes this kind of
panic over scary chemicals is
disproportionate; there are
trace amounts of natural
arsenic in all our food and
water, and we handle those
fine. This is not one of those
times.
The burning phosphorus
(now joined by burning
potassium, which is similarly
prone
to
spontaneous
combustion) could ignite the
arsenic,
releasing
large
amounts of arsenic trioxide.
That stuff is pretty toxic.
Don’t inhale.
This row would also
produce hideous odors. The
selenium and bromine would
react vigorously, and Lowe
says that burning selenium
“can make sulfur smell like
Chanel.”
If the aluminum survived
the fire, a strange thing would
happen to it. The melting
gallium under it would soak
into
the
aluminum,
disrupting its structure and
causing it to become as soft
and weak as wet paper.6
The burning sulfur would
spill into the bromine.
Bromine is liquid at room
temperature, a property it
shares with only one other
element—mercury. It’s also
pretty nasty stuff. The range
of toxic compounds that
would be produced by this
blaze is, at this point,
incalculably large. However,
if you did this experiment
from a safe distance, you
might survive.
The fifth row contains
something
interesting:
technetium-99, our first
radioactive brick.
Technetium is the lowest-
numbered element that has
no stable isotopes. The dose
from a 1-liter cube of the
metal wouldn’t be enough to
be lethal in our experiment,
but it’s still substantial. If you
spent all day wearing it as a
hat—or breathed it in as dust
—it could definitely kill you.
Techneteium aside, the
fifth row would be a lot like
the fourth.
On to the sixth row! No
matter how careful you are,
the sixth row would definitely
kill you.
This version of the periodic table is a
little wider than you might be used
to, since we’re inserting the
lanthanide and actinide elements into
rows 6 and 7. (These elements are
normally shown separately from the
main table to avoid making it too
wide.)
The sixth row of the
periodic table contains several
radioactive
elements,
including
promethium,
polonium,7 astatine, and
radon. Astatine is the bad
one.8
We don’t know what
astatine looks like, because, as
Lowe put it, “that stuff just
doesn’t want to exist.” It’s so
radioactive (with a half-life
measured in hours) that any
large piece of it would be
quickly vaporized by its own
heat. Chemists suspect that it
has a black surface, but no
one really knows.
There’s no material safety
data sheet for astatine. If
there were, it would just be
the word “NO” scrawled over
and over in charred blood.
Our cube would, briefly,
contain more astatine than
has ever been synthesized. I
say “briefly” because it would
immediately turn into a
column of superheated gas.
The heat alone would give
third-degree burns to anyone
nearby, and the building
would be demolished. The
cloud of hot gas would rise
rapidly into the sky, pouring
out heat and radiation.
The explosion would be just
the right size to maximize the
amount of paperwork your
lab would face. If the
explosion were smaller, you
could potentially cover it up.
If it were larger, there would
be no one left in the city to
submit paperwork to.
Dust and debris coated in
astatine, polonium, and other
radioactive products would
rain
from
the
cloud,
rendering the downwind
neighborhood
completely
uninhabitable.
The radiation levels would
be incredibly high. Given that
it takes a few hundred
milliseconds to blink, you
would literally get a lethal
dose of radiation in the blink
of an eye.
You would die from what
we might call “extremely
acute
radiation
poisoning”—that is, you
would be cooked.
The seventh row would be
much worse.
There are a whole bunch of
weird elements along the
bottom of the periodic table
called transuranic elements.
For a long time, many of
them had placeholder names
like
“unununium,”
but
gradually
they’re
being
assigned permanent names.
There’s no rush, though,
because most of these
elements are so unstable that
they can be created only in
particle accelerators and don’t
exist for more than a few
minutes. If you had 100,000
atoms
of
Livermorium
(element 116), after a second
you’d have one left—and a
few hundred milliseconds
later, that one would be gone,
too.
Unfortunately
for
our
project,
the
transuranic
elements don’t vanish quietly.
They decay radioactively.
And most of them decay into
things that also decay. A cube
of any of the highestnumbered elements would
decay
within
seconds,
releasing
a
tremendous
amount of energy.
The result wouldn’t be like
a nuclear explosion—it would
be a nuclear explosion.
However, unlike a fission
bomb, it wouldn’t be a chain
reaction—just a reaction. It
would all happen at once.
The flood of energy would
instantly turn you—and the
rest of the periodic table—to
plasma. The blast would be
similar to that of a mediumsized nuclear detonation, but
the radioactive fallout would
be much, much worse—a
veritable salad of everything
on the periodic table turning
into everything else as fast as
possible.
A mushroom cloud would
rise over the city. The top of
the plume would reach up
through the stratosphere,
buoyed by its own heat. If you
were in a populated area, the
immediate casualties from the
blast would be staggering, but
the long-term contamination
from the fallout would be
even worse.
The fallout wouldn’t be
normal, everyday radioactive
fallout9—it would be like a
nuclear bomb that kept
exploding. The debris would
spread around the world,
releasing thousands of times
more radioactivity than the
Chernobyl disaster. Entire
regions would be devastated;
the cleanup would stretch on
for centuries.
While collecting things is
certainly fun, when it comes
to chemical elements, you do
not want to collect them all.
1 Think of the elements as
dangerous, radioactive, shortlived Pokémon.
2 An eighth row may be added
by the time you read this. And
if you’re reading this in the year
2038, the periodic table has ten
rows but all mention or
discussion of it is banned by the
robot overlords.
3 That is, assuming that they’re
in diatomic form (e.g. O2 and
N2). If the cube is in the form
of single atoms, they’ll instantly
combine, heating to thousands
of degrees as they do.
4 Lowe is the author of the
great drug research blog In the
Pipeline.
5 A property that has led to its
controversial use in incendiary
artillery shells.
6 Search YouTube for “gallium
infiltration” to see how strange
this is.
7 In 2006, an umbrella tipped
with polonium-210 was used to
murder former KGB officer
Alexander Litvinenko.
8 Radon is the cute one.
9 You know, the stuff we all
shrug off.
EVERYBODY
JUMP
Q. What
would
happen if
everyone on
Earth stood
as close to
each other as
they could
and jumped,
everyone
landing on
the ground at
the same
instant?
—Thomas Bennett (and
many others)
A. THIS
IS ONE OF the
most popular questions
submitted
through
my
website. It’s been examined
before,
including
by
ScienceBlogs
and
The
Straight Dope. They cover
the kinematics pretty well.
However, they don’t tell the
whole story.
Let’s take a closer look.
At the start of the scenario,
the entire Earth’s population
has
been
magically
transported together into one
place.
This crowd takes up an area
the size of Rhode Island. But
there’s no reason to use the
vague phrase “an area the size
of Rhode Island.” This is our
scenario; we can be specific.
They’re actually in Rhode
Island.
At the stroke of noon,
everyone jumps.
As discussed elsewhere, it
doesn’t really affect the
planet. Earth outweighs us by
a factor of over ten trillion.
On average, we humans can
vertically jump maybe half a
meter on a good day. Even if
the Earth were rigid and
responded instantly, it would
be pushed down by less than
an atom’s width.
Next, everyone falls back to
the ground.
Technically, this delivers a
lot of energy into the Earth,
but it’s spread out over a large
enough area that it doesn’t do
much more than leave
footprints in a lot of gardens.
A slight pulse of pressure
spreads through the North
American continental crust
and dissipates with little
effect. The sound of all those
feet hitting the ground creates
a loud, drawn-out roar lasting
many seconds.
Eventually, the air grows
quiet.
Seconds pass. Everyone
looks around.
There are a lot of
uncomfortable
glances.
Someone coughs.
A cell phone comes out of a
pocket. Within seconds, the
rest of the world’s five billion
phones follow. All of them—
even those compatible with
the region’s towers—are
displaying some version of
“NO SIGNAL.” The cell
networks have all collapsed
under the unprecedented
load. Outside Rhode Island,
abandoned machinery begins
grinding to a halt.
The T. F. Green Airport in
Warwick, Rhode Island,
handles a few thousand
passengers a day. Assuming
they got things organized
(including
sending
out
scouting missions to retrieve
fuel), they could run at 500
percent capacity for years
without making a dent in the
crowd.
The addition of all the
nearby
airports
doesn’t
change the equation much.
Nor does the region’s light
rail system. Crowds climb on
board container ships in the
deep-water
port
of
Providence, but stocking
sufficient food and water for a
long sea voyage proves a
challenge.
Rhode Island’s half-million
cars are commandeered.
Moments later, I-95, I-195,
and I-295 become the sites of
the largest traffic jam in the
history of the planet. Most of
the cars are engulfed by the
crowds, but a lucky few get
out and begin wandering the
abandoned road network.
Some make it past New
York or Boston before
running out of fuel. Since the
electricity is probably not on
at this point, rather than find
a working gas pump, it’s
easier to just abandon the car
and steal a new one. Who can
stop you? All the cops are in
Rhode Island.
The edge of the crowd
spreads
outward
into
southern Massachusetts and
Connecticut. Any two people
who meet are unlikely to have
a language in common, and
almost nobody knows the
area. The state becomes a
chaotic
patchwork
of
coalescing and collapsing
social hierarchies. Violence is
common.
Everybody
is
hungry and thirsty. Grocery
stores are emptied. Fresh
water is hard to come by and
there’s no efficient system for
distributing it.
Within
weeks,
Rhode
Island is a graveyard of
billions.
The survivors spread out
across the face of the world
and struggle to build a new
civilization atop the pristine
ruins of the old. Our species
staggers
on,
but
our
population has been greatly
reduced. Earth’s orbit is
completely
unaffected—it
spins along exactly as it did
before our species-wide jump.
But at least now we know.
A MOLE OF
MOLES
Q. What
would
happen if you
were to
gather a mole
(unit of
measurement)
of moles (the
small furry
critter) in one
place?
—Sean Rice
A.
THINGS GET A BIT
gruesome.
First, some definitions.
A mole is a unit. It’s not a
typical unit, though. It’s really
just a number—like “dozen”
or “billion.” If you have a
mole of something, it means
you
have
602,214,129,000,000,000,000,0
of them (usually written
6.022 × 1023). It’s such a big
number1 because it’s used for
counting
numbers
of
molecules, which there are a
lot of.
A mole is also a type of
burrowing mammal. There
are a handful of types of
moles, and some of them are
truly horrifying.2
So what would a mole of
moles
—602,214,129,000,000,000,00
animals—look like?
First, let’s start with wild
approximations. This is an
example of what might go
through my head before I
even pick up a calculator,
when I’m just trying to get a
sense of the quantities—the
kind of calculation where 10,
1, and 0.1 are all close enough
that we can consider them
equal:
A mole (the animal) is
small enough for me to pick
up and throw.[citation needed ]
Anything I can throw weighs
1 pound. One pound is 1
kilogram.
The
number
602,214,129,000,000,000,000,0
looks about twice as long as a
trillion, which means it’s
about a trillion trillion. I
happen to remember that a
trillion trillion kilograms is
how much a planet weighs.
. . . if anyone asks, I did not tell you
it was okay to do math like this.
That’s enough to tell us that
we’re talking about a pile of
moles on the scale of a planet.
It’s a pretty rough estimate,
since it could be off by a
factor of thousands in either
direction.
Let’s get some better
numbers.
An eastern mole (Scalopus
aquaticus) weighs about 75
grams, which means a mole
of moles weighs:
That’s a little over half the
mass of our moon.
Mammals are largely water.
A kilogram of water takes up
a liter of volume, so if the
moles weigh 4.52 × 1022
kilograms, they take up about
4.52 × 1022 liters of volume.
You might notice that we’re
ignoring the pockets of space
between the moles. In a
moment, you’ll see why.
The cube root of 4.52 ×
1022 liters is 3562 kilometers,
which means we’re talking
about a sphere with a radius
of 2210 kilometers, or a cube
2213 miles on each edge.3
If these moles were released
onto the Earth’s surface,
they’d fill it up to 80
kilometers deep—just about
to the (former) edge of space:
This smothering ocean of
high-pressure meat would
wipe out most life on the
planet, which could—to
reddit’s horror—threaten the
integrity of the DNS system.
So doing this on Earth is
definitely not an option.
Instead, let’s gather the
moles in interplanetary space.
Gravitational
attraction
would pull them into a
sphere.
Meat
doesn’t
compress very well, so it
would undergo only a little
bit
of
gravitational
contraction, and we’d end up
with a mole planet slightly
larger than the Moon.
The moles would have a
surface gravity of about onesixteenth of Earth’s—similar
to that of Pluto. The planet
would start off uniformly
lukewarm—probably a bit
over room temperature—and
the gravitational contraction
would heat the deep interior
by a handful of degrees.
But this is where it gets
weird.
The mole planet would be a
giant sphere of meat. It would
have a lot of latent energy
(there are enough calories in
the mole planet to support
the
Earth’s
current
population for 30 billion
years).
Normally,
when
organic matter decomposes, it
releases much of that energy
as heat. But throughout the
majority of the planet’s
interior, the pressure would
be over 100 megapascals,
which is high enough to kill
all bacteria and sterilize the
mole remains—leaving no
microorganisms to break
down the mole tissue.
Closer to the surface, where
the pressure would be lower,
there would be another
obstacle to decomposition—
the interior of a mole planet
would be low in oxygen.
Without oxygen, the usual
decomposition
couldn’t
happen, and the only bacteria
that would be able to break
down the moles would be
those that don’t require
oxygen. While inefficient,
this anaerobic decomposition
can unlock quite a bit of heat.
If continued unchecked, it
would heat the planet to a
boil.
But the decomposition
would be self-limiting. Few
bacteria can survive at
temperatures above about
60°C, so as the temperature
went up, the bacteria would
die
off,
and
the
decomposition would slow.
Throughout the planet, the
mole bodies would gradually
break down into kerogen, a
mush of organic matter that
would—if the planet were
hotter—eventually form oil.
The outer surface of the
planet would radiate heat into
space and freeze. Because the
moles form a literal fur coat,
when frozen they would
insulate the interior of the
planet and slow the loss of
heat to space. However, the
flow of heat in the liquid
interior would be dominated
by convection. Plumes of hot
meat and bubbles of trapped
gases like methane—along
with the air from the lungs of
the deceased moles—would
periodically rise through the
mole
crust
and
erupt
volcanically from the surface,
a geyser of death blasting
mole bodies free of the
planet.
Eventually, after centuries
or millennia of turmoil, the
planet would calm and cool
enough that it would begin to
freeze all the way through.
The deep interior would be
under such high pressure that
as it cooled, the water would
crystallize out into exotic
forms of ice such as ice III
and ice V, and eventually ice
II and ice IX.4
All told, this is a pretty
bleak picture. Fortunately,
there’s a better approach.
I don’t have any reliable
numbers for global mole
population (or small mammal
biomass in general), but we’ll
take a shot in the dark and
estimate that there are at least
a few dozen mice, rats, voles,
and other small mammals for
every human.
There might be a billion
habitable planets in our
galaxy. If we colonized them,
we’d certainly bring mice and
rats with us. If just one in a
hundred were populated with
small mammals in numbers
similar to Earth’s, after a few
million years—not long, in
evolutionary time—the total
number that have ever lived
would surpass Avogadro’s
number.
If you want a mole of
moles, build a spaceship.
1 “One mole” is close to the
number of atoms in a gram of
hydrogen. It’s also, by chance, a
decent ballpark guess for the
number of grains of sand on
Earth.
2
http://en.wikipedia.org/wiki/File
3 That’s a neat coincidence I’ve
never noticed before — a cubic
mile happens to be almost
exactly 4/3π cubic kilometers,
so a sphere with a radius of X
kilometers has the same volume
as a cube that’s X miles on each
side.
4 No relation.
HAIR DRYER
Q. What
would
happen if a
hair dryer
with
continuous
power were
turned on and
put in an
airtight 1 × 1
× 1-meter
box?
—Dry Paratroopa
A. A
TYPICAL
HAIR
DRYER draws 1875
watts of power.
All 1875 watts have to go
somewhere. No matter what
happens inside the box, if it’s
using 1875 watts of power,
eventually there will be 1875
watts of heat flowing out.
This is true of any device
that uses power, which is a
handy thing to know. For
example, people worry about
leaving disconnected chargers
plugged into the wall for fear
that they’re draining power.
Are they right? Heat flow
analysis provides a simple rule
of thumb: If an unused
charger isn’t warm to the
touch, it’s using less than a
penny of electricity a day. For
a small smartphone charger, if
it’s not warm to the touch, it’s
using less than a penny a year.
This is true of almost any
powered device.1
But back to the box.
Heat will flow from the hair
dryer out into the box. If we
assume
the
dryer
is
indestructible, the interior of
the box will keep getting
hotter until the outer surface
reaches about 60°C (140°F).
At that temperature, the box
will be losing heat to the
outside as fast as the hair
dryer is adding it inside, and
the system will be in
equilibrium.
It’s warmer than my parents! It’s my
new parents.
The
equilibrium
temperature will be a bit
cooler if there’s a breeze, or if
the box is sitting on a wet or
metallic surface that conducts
away heat quickly.
If the box is made of metal,
it will be hot enough to burn
your hand if you touch it for
more than five seconds. If it’s
wood, you can probably touch
it for a while, but there’s a
danger that parts of the box
in contact with the mouth of
the hair dryer will catch fire.
The inside of the box will
be like an oven. The
temperature it reaches will
depend on the thickness of
the box wall; the thicker and
more insulating the wall, the
higher the temperature. It
wouldn’t take a very thick box
to create temperatures high
enough to burn out the hair
dryer.
But let’s assume it’s an
indestructible hair dryer. And
if we have something as cool
as an indestructible hair dryer,
it seems like a shame to limit
it to 1875 watts.
With 18,750 watts flowing
out of the hair dryer, the
surface of the box reaches
over 200°C (475°F), as hot as
a skillet on low-medium.
I wonder how high this dial
goes.
There’s a distressing amount of
space left on the dial.
The surface of the box is
now 600°C, hot enough to
glow a dim red.
If it’s made of aluminium,
the inside is starting to melt.
If it’s made of lead, the
outside is starting to melt. If
it’s on a wood floor, the house
is on fire. But it doesn’t
matter what’s happening
around it; the hair dryer is
indestructible.
Two megawatts pumped
into a laser is enough to
destroy missiles.
At 1300°C, the box is now
about the temperature of lava.
One more notch.
This hair dryer is probably not up to
code.
Now 18 megawatts are
flowing into the box.
The surface of the box
reaches 2400°C. If it were
steel, it would have melted by
now. If it’s made of
something like tungsten, it
might conceivably last a little
longer.
Just one more, then we’ll
stop.
This much
megawatts—is
power—187
enough to
make the box glow white.
Not a lot of materials can
survive these conditions, so
we’ll have to assume the box
is indestructible.
The floor is made of lava.
Unfortunately, the floor
isn’t.
Before it can burn its way
through the floor, someone
throws a water balloon under
it. The burst of steam
launches the box out the front
door and onto the sidewalk.2
We’re at 1.875 gigawatts (I
lied
about
stopping).
According to Back to the
Future, the hair dryer is now
drawing enough power to
travel back in time.
The box is blindingly
bright, and you can’t get
closer than a few hundred
meters due to the intense
heat. It sits in the middle of a
growing pool of lava.
Anything within 50–100
meters bursts into flame. A
column of heat and smoke
rise high into the air. Periodic
explosions of gas beneath the
box launch it into the air, and
it starts fires and forms a new
lava pool where it lands.
We keep turning the dial.
At 18.7 gigawatts, the
conditions around the box are
similar to those on the pad
during a space shuttle launch.
The box begins to be tossed
around by the powerful
updrafts it’s creating.
In 1914, H. G. Wells
imagined devices like this in
his book The World Set Free.
He wrote of a type of bomb
that, instead of exploding
once, exploded continuously,
a slow-burn inferno that
started inextinguishable fires
in the hearts of cities. The
story eerily foreshadowed the
development, 30 years later,
of nuclear weapons.
The box is now soaring
through the air. Each time it
nears
the
ground,
it
superheats the surface, and
the plume of expanding air
hurls it back into the sky.
The outpouring of 1.875
terawatts is like a house-sized
stack of TNT going off every
second.
A trail of firestorms
—massive conflagrations that
sustain themselves by creating
their own wind systems
—winds its way across the
landscape.
A new milestone: The hair
dryer is now, impossibly,
consuming more power than
every other electrical device
on the planet combined.
The box, soaring high
above the surface, is putting
out energy equivalent to three
Trinity tests every second.
At this point, the pattern is
obvious. This thing is going
to
skip
around
the
atmosphere until it destroys
the planet.
Let’s
try
something
different.
We turn the dial to zero as
the box is passing over
northern Canada. Rapidly
cooling, it plummets to
Earth, landing in Great Bear
Lake with a plume of steam.
And then . . .
In this case, that’s 11
petawatts.
A brief story:
The official record for the
fastest manmade object is the
Helios 2 probe, which
reached about 70 km/s in a
close swing around the Sun.
But it’s possible the actual
holder of that title is a twoton metal manhole cover.
The cover sat atop a shaft at
an underground nuclear test
site operated by Los Alamos
as
part
of
Operation
Plumbbob. When the 1kiloton nuke went off below,
the facility effectively became
a nuclear potato cannon,
giving the cap a gigantic kick.
A high-speed camera trained
on the lid caught only one
frame of it moving upward
before it vanished—which
means it was moving at a
minimum of 66 km/s. The
cap was never found.
Now, 66 km/s is about six
times escape velocity, but
contrary
to
common
speculation, it’s unlikely the
cap ever reached space.
Newton’s
impact
depth
approximation suggests that it
was
either
destroyed
completely by impact with
the air or slowed and fell back
to Earth.
When we turn it back on,
our reactivated hair dryer box,
bobbing in lake water,
undergoes a similar process.
The heated steam below it
expands outward, and as the
box rises into the air, the
entire surface of the lake turns
to steam. The steam, heated
to a plasma by the flood of
radiation, accelerates the box
faster and faster.
Photo courtesy of Commander
Hadfield
Rather than slam into the
atmosphere like the manhole
cover, the box flies through a
bubble of expanding plasma
that offers little resistance. It
exits the atmosphere and
continues away, slowly fading
from second sun to dim star.
Much of the Northwest
Territories is burning, but the
Earth has survived.
However, a few may wish
we hadn’t.
1 Though not necessarily those
plugged into a second device. If
a charger is connected to
something, like a smartphone
or laptop, power can be flowing
from the wall through the
charger into the device.
2 Note: If you’re ever trapped
with me in a burning building,
and I suggest an idea for how
we could escape the situation,
it’s probably best to ignore me.
WEIRD
(AND
WORRYING)
QUESTIONS
FROM
THE
WHAT IF?
INBOX, #2
Q. Would
dumping antimatter into the
Chernobyl
reactor when it
was melting
down stop the
meltdown?
—AJ
Q.
Is it
possible to cry
so much you
dehydrate
yourself?
—Karl Wildermuth
THE LAST
HUMAN
LIGHT
Q. If every
human
somehow
simply
disappeared
from the face
of the Earth,
how long
would it be
before the
last artificial
light source
would go
out?
—Alan
A. THERE
WOULD BE A
lot of contenders for the
“last light” title.
The superb 2007 book The
World Without Us, by Alan
Weisman, explored in great
detail what would happen to
Earth’s
houses,
roads,
skyscrapers,
farms,
and
animals if humans suddenly
vanished. A 2008 TV series
called Life After People
investigated
the
same
premise. However, neither of
them answered this particular
question.
We’ll start with the
obvious: Most lights wouldn’t
last long, because the major
power grids would go down
relatively fast. Fossil fuel
plants, which supply the vast
majority of the world’s
electricity, require a steady
supply of fuel, and their
supply chains do involve
humans making decisions.
Without people, there
would be less demand for
power, but our thermostats
would still be running. As
coal and oil plants started
shutting down in the first few
hours, other plants would
need to take up the slack.
This kind of situation is
difficult to handle even with
human guidance. The result
would be a rapid series of
cascade failures, leading to a
blackout of all the major
power grids.
However,
plenty
of
electricity comes from sources
not tied to the major power
grids. Let’s take a look at a
few of those, and when each
one might turn off.
Diesel generators
Many remote communities,
like those on far-flung
islands, get their power from
diesel generators. These can
continue to operate until they
run out of fuel, which in most
cases could be anywhere from
days to months.
Geothermal plants
Generating stations that don’t
need a human-provided fuel
supply would be in better
shape. Geothermal plants,
which are powered by the
Earth’s internal heat, can run
for some time without human
intervention.
According
to
the
maintenance manual for the
Svartsengi Island geothermal
plant in Iceland, every six
months the operators must
change the gearbox oil and
regrease all electric motors
and
couplings.
Without
humans to perform these
sorts
of
maintenance
procedures,
some
plants
might run for a few years, but
they’d all succumb to
corrosion eventually.
Wind turbines
People relying on wind power
would be in better shape than
most. Turbines are designed
so that they don’t need
constant maintenance, for the
simple reason that there are a
lot of them and they’re a pain
to climb.
Some windmills can run for
a long time without human
intervention. The Gedser
Wind Turbine in Denmark
was installed in the late
1950s, and generated power
for
11
years
without
maintenance.
Modern
turbines are typically rated to
run for 30,000 hours (three
years) without servicing, and
there are no doubt some that
would run for decades. One
of them would no doubt have
at least a status LED in it
somewhere.
Eventually, most of the
wind turbines would be
stopped by the same thing
that would destroy the
geothermal plants: Their
gearboxes would seize up.
Hydroelectric dams
Generators
that
convert
falling water into electricity
will keep working for quite a
while. The History Channel
show Life After People spoke
with an operator at the
Hoover Dam, who said that if
everyone walked out, the
facility would continue to run
on autopilot for several years.
The dam would probably
succumb to either clogged
intakes or the same kind of
mechanical failure that would
hit the wind turbines and
geothermal plants.
Batteries
Battery-powered lights will
all be off in a decade or two.
Even without anything using
their
power,
batteries
gradually
self-discharge.
Some types last longer than
others, but even batteries
advertised as having long
shelf lives typically hold their
charge only for a decade or
two.
There are a few exceptions.
In the Clarendon Library at
Oxford University sits a
battery-powered bell that has
been ringing since the year
1840. The bell “rings” so
quietly it’s almost inaudible,
using only a tiny amount of
charge with every motion of
the clapper. Nobody knows
exactly what kind of batteries
it uses because nobody wants
to take it apart to figure it
out.
Sadly, there’s
hooked up to it.
no
light
Nuclear reactors
Nuclear reactors are a little
tricky. If they settle into lowpower mode, they can
continue running
indefinitely;
the
density of their fuel
that high. As a
webcomic put it:
Unfortunately,
almost
energy
is just
certain
although
there’s enough fuel, the
reactors
wouldn’t
keep
running for long. As soon as
something went wrong, the
core would go into automatic
shutdown.
This
would
happen quickly; many things
can trigger it, but the most
likely culprit would be a loss
of external power.
It may seem strange that a
power plant would require
external power to run, but
every part of a nuclear
reactor’s control system is
designed so that a failure
causes it to rapidly shut
down, or “SCRAM.”1 When
outside power is lost, either
because the outside power
plant shuts down or the onsite backup generators run out
of fuel, the reactor would
SCRAM.
Space probes
Out of all human artifacts,
our spacecraft might be the
longest-lasting. Some of their
orbits will last for millions of
years, although their electrical
power typically won’t.
Within centuries, our Mars
rovers will be buried by dust.
By then, many of our
satellites will have fallen back
to Earth as their orbits
decayed. GPS satellites, in
distant orbits, will last longer,
but in time, even the most
stable orbits will be disrupted
by the Moon and Sun.
Many
spacecraft
are
powered by solar panels, and
others by radioactive decay.
The Mars rover Curiosity, for
example, is powered by the
heat from a chunk of
plutonium it carries in a
container on the end of a
stick.
Curiosity could continue
receiving electrical power
from the RTG for over a
century.
Eventually
the
voltage will drop too low to
keep the rover operating, but
other parts will probably wear
out before that happens.
So
Curiosity
looks
promising.
There’s
one
problem: no lights.
Curiosity has lights; it uses
them to illuminate samples
and perform spectroscopy.
However, these lights are
turned on only when it’s
taking measurements. With
no human instructions, it will
have no reason to turn them
on.
Unless they have humans
on board, spacecraft don’t
need a lot of lights. The
Galileo probe, which explored
Jupiter in the 1990s, had
several
LEDs
in
the
mechanism of its flight data
recorder. Since they emitted
infrared rather than visible
light, calling them “lights” is a
stretch—and in any case,
Galileo
was
deliberately
crashed into Jupiter in 2003.2
Other satellites carry LEDs.
Some GPS satellites use, for
example, UV LEDs to
control charge buildup in
some of their equipment, and
they’re powered by solar
panels; in theory they can
keep running as long as the
Sun is shining. Unfortunately,
most won’t even last as long
as
Curiosity;
eventually,
they’ll succumb to space
debris impacts.
But solar panels aren’t used
just in space.
Solar power
Emergency call boxes, often
found along the side of the
road in remote locations, are
frequently
solar-powered.
They usually have lights on
them,
which
provide
illumination every night.
Like wind turbines, they’re
hard to service, so they’re
built to last for a long time.
As long as they’re kept free of
dust and debris, solar panels
will generally last as long as
the electronics connected to
them.
A solar panel’s wires and
circuits
will
eventually
succumb to corrosion, but
solar panels in a dry place,
with well-built electronics,
could
easily
continue
providing power for a century
if they’re kept free of dust by
occasional breezes or rain on
the exposed panels.
If we follow a strict
definition of lighting, solarpowered lights in remote
locations could conceivably be
the last surviving human light
source.3
But
there’s
another
contender, and it’s a weird
one.
Cherenkov radiation
Radioactivity isn’t usually
visible.
Watch dials used to be
coated in radium, which
made them glow. However,
this glow didn’t come from
the radioactivity itself. It
came
from
the
phosphorescent paint on top
of the radium, which glowed
when it was irradiated. Over
the years, the paint has
broken down. Although the
watch
dials
are
still
radioactive, they no longer
glow.
Watch dials, however, are
not our only radioactive light
source.
When radioactive particles
travel through materials like
water or glass, they can emit
light through a sort of optical
sonic boom. This light is
called Cherenkov radiation,
and it’s seen in the distinctive
blue glow of nuclear reactor
cores.
Some of our radioactive
waste products, such as
cesium-137, are melted and
mixed with glass, then cooled
into a solid block that can be
wrapped in more shielding so
they can be safely transported
and stored.
In the dark, these glass
blocks glow blue.
Cesium-137 has a half-life
of thirty years, which means
that two centuries later,
they’ll still be glowing with 1
percent of their original
radioactivity. Since the color
of the light depends only on
the decay energy, and not the
amount of radiation, it will
fade in brightness over time
but keep the same blue color.
And thus, we arrive at our
answer: Centuries from now,
deep in concrete vaults, the
light from our most toxic
waste will still be shining.
1 When Enrico Fermi built the
first nuclear reactor, he
suspended the control rods
from a rope tied to a balcony
railing. In case something went
wrong, next to the railing was
stationed a distinguished
physicist with an axe. This led
to the probably apocryphal
story that SCRAM stands for
“Safety Control Rod Axe
Man.”
2 The purpose of the crash was
to safely incinerate the probe so
it wouldn’t accidentally
contaminate the nearby moons,
such as the watery Europa, with
Earth bacteria.
3 The USSR built some
lighthouses powered by
radioactive decay, but none are
still in operation.
MACHINEGUN
JETPACK
Q. Is it
possible to
build a
jetpack using
downwardfiring
machine
guns?
—Rob B
A. I
WAS SORT OF
surprised to find that the
answer was yes! But to really
do it right, you’ll want to talk
to the Russians.
The principle here is pretty
simple. If you fire a bullet
forward, the recoil pushes you
back. So if you fire
downward, the recoil should
push you up.
The first question we have
to answer is “can a gun even
lift its own weight?” If a
machine gun weighs 10
pounds but produces only 8
pounds of recoil when firing,
it won’t be able to lift itself
off the ground, let alone lift
itself plus a person.
In the engineering world,
the ratio between a craft’s
thrust and the weight is
called, appropriately, thrust-
to-weight ratio. If it’s less
than 1, the vehicle can’t lift
off. The Saturn V had a
takeoff thrust-to-weight ratio
of about 1.5.
Despite growing up in the
South, I’m not really a
firearms expert, so to help
answer this question, I got in
touch with an acquaintance in
Texas.1
Note: Please, PLEASE do
not try this at home.
As it turns out, the AK-47
has a thrust-to-weight ratio
of around 2. This means if
you stood it on end and
somehow taped down the
trigger, it would rise into the
air while firing.
This isn’t true of all
machine guns. The M60, for
example,
probably
can’t
produce enough recoil to lift
itself off the ground.
The
amount
of
thrust
created by a rocket (or firing
machine gun) depends on (1)
how much mass it’s throwing
out behind it, and (2) how
fast it’s throwing it. Thrust is
the product of these two
amounts:
If an AK-47 fires ten 8gram bullets per second at
715 meters per second, its
thrust is:
Since the AK-47 weighs
only 10.5 pounds when
loaded, it should be able to
take off and accelerate
upward.
In practice, the actual thrust
would turn out to be up to
around 30 percent higher.
The reason for this is that the
gun isn’t spitting out just
bullets—it’s also spitting out
hot gas and explosive debris.
The amount of extra force
this adds varies by gun and
cartridge.
The overall efficiency also
depends on whether you eject
the shell casings out of the
vehicle or carry them with
you. I asked my Texan
acquaintances if they could
weigh some shell casings for
my calculations. When they
had trouble finding a scale, I
helpfully suggested that given
the size of their arsenal, really
they just need to find
someone else who owned a
scale.2
So what does all this mean
for our jetpack?
Well, the AK-47 could take
off, but it doesn’t have
enough spare thrust to lift
anything weighing
more than a squirrel.
much
We can try using multiple
guns. If you fire two guns at
the ground, it creates twice
the thrust. If each gun can lift
5 pounds more than its own
weight, two can lift 10.
At this point, it’s clear
where we’re headed:
You will not go to space today.
If we add enough rifles, the
weight of the passenger
becomes irrelevant; it’s spread
over so many guns that each
one barely notices. As the
number of rifles increases,
since the contraption is
effectively many individual
rifles flying in parallel, the
craft’s thrust-to-weight ratio
approaches that of a single,
unburdened rifle:
But there’s a problem:
ammunition.
An AK-47 magazine holds
30 rounds. At 10 rounds per
second, this would provide a
measly three seconds of
acceleration.
We can improve this with a
larger magazine—but only up
to a point. It turns out there’s
no advantage to carrying
more than about 250 rounds
of ammunition. The reason
for this is a fundamental and
central problem in rocket
science: Fuel makes you
heavier.
Each bullet weighs 8 grams,
and the cartridge (the “whole
bullet”) weighs over 16 grams.
If we added more than about
250 rounds, the AK-47
would be too heavy to take
off.
This suggests our optimal
craft would comprise a large
number of AK-47s (a
minimum of 25 but ideally at
least 300) carrying 250
rounds of ammunition each.
The largest versions of this
craft could accelerate upward
to vertical speeds approaching
100 meters per second,
climbing over half a kilometer
into the air.
So we’ve answered Rob’s
question.
With
enough
machine guns, you could fly.
But our AK-47 rig is clearly
not a practical jetpack. Can
we do better?
My Texas friends suggested
a series of machine guns, and
I ran the numbers on each
one. Some did pretty well; the
MG-42, a heavier machine
gun, had a marginally higher
thrust-to-weight ratio than
the AK-47.
Then we went bigger.
The GAU-8 Avenger fires
up to 60 1-pound bullets a
second. It produces almost 5
tons of recoil force, which is
crazy considering that it’s
mounted in a type of plane
(the A-10 “Warthog”) whose
two engines produce only 4
tons of thrust each. If you put
two of them in one aircraft,
and fired both guns forward
while opening up the throttle,
the guns would win and you’d
accelerate backward.
To put it another way: If I
mounted a GAU-8 on my
car, put the car in neutral, and
started firing backward from
a standstill, I would be
breaking the interstate speed
limit in less than three
seconds.
“Actually, what I’m confused about is
how.”
As good as this gun would
be as a rocket pack engine,
the Russians built one that
would work even better. The
Gryazev-Shipunov GSh-6-30
weighs half as much as the
GAU-8 and has an even
higher fire rate. Its thrust-toweight ratio approaches 40,
which means if you pointed
one at the ground and fired,
not only would it take off in a
rapidly expanding spray of
deadly metal fragments, but
you would experience 40 gees
of acceleration.
This is way too much. In
fact, even when it was firmly
mounted in an aircraft, the
acceleration was a problem:
[T]he recoil . . . still had a
tendency to inflict damage
on the aircraft. The rate of
fire was reduced to 4,000
rounds a minute but it
didn’t help much. Landing
lights almost always broke
after firing . . . Firing
more than about 30
rounds in a burst was
asking for trouble from
overheating . . .
— Greg Goebel,
airvectors.net
But if you somehow braced
the human rider, made the
craft strong enough to survive
the acceleration, wrapped the
GSh-6-30 in an aerodynamic
shell, and made sure it was
adequately cooled . . .
. . . you could jump
mountains.
1 Judging by the amount of
ammunition they had lying
around their house ready to
measure and weigh for me,
Texas has apparently become
some kind of Mad Max–esque
post-apocalyptic war zone.
2 Ideally someone with less
ammo.
RISING
STEADILY
Q. If you
suddenly
began rising
steadily at 1
foot per
second, how
exactly would
you die?
Would you
freeze or
suffocate
first? Or
something
else?
—Rebecca B
A. DID
YOU BRING A
COAT?
A foot per second isn’t that
fast; it’s substantially slower
than a typical elevator. It
would take you 5-7 seconds
to rise out of arm’s reach,
depending how tall your
friends are.
After 30 seconds, you’d be
30 feet—9 meters—off the
ground. If you skip ahead to
page 168, you’ll learn that this
is your last chance for a friend
to throw you a sandwich or
water bottle or something.1
After a minute or two you
would be above the trees. For
the most part, you’d still be
about as comfortable as you
were on the ground. If it’s a
breezy day, it would probably
get chillier thanks to the
steadier wind above the tree
line.2
After 10 minutes you would
be above all but the tallest
skyscrapers, and after 25
minutes you’d pass the spire
of the Empire State Building.
The air at these heights is
about 3 percent thinner than
it is at the surface.
Fortunately,
your
body
handles air pressure changes
like that all the time. Your
ears might pop, but you
wouldn’t
really
notice
anything else.
Air
pressure
changes
quickly
with
height.
Surprisingly, when you’re
standing on the ground, air
pressure changes measurably
within just a few feet. If your
phone has a barometer in it,
as a lot of modern phones do,
you can download an app and
actually see the pressure
difference between your head
and your feet.
A foot per second is pretty
close to a kilometer per hour,
so after an hour, you’ll be
about a kilometer off the
ground. At this point, you
definitely start to get chilly. If
you have a coat, you’ll still be
OK, though you might also
notice the wind picking up.
At about two hours and two
kilometers, the temperature
would drop below freezing.
The wind would also, most
likely, be picking up. If you
have any exposed skin, this is
where frostbite would start to
become a concern.
At this point, the air
pressure would fall below
what you’d experience in an
airliner cabin,3 and the effects
would start to become more
significant. However, unless
you had a warm coat, the
temperature would be a
bigger problem.
Over the next two hours,
the air would drop to belowzero
temperatures.4,5
Assuming for a moment that
you survived the oxygen
deprivation, at some point
you’d
succumb
to
hypothermia. But when?
The scholarly authorities on
freezing to death seem to be,
unsurprisingly,
Canadians.
The most widely used model
for human survival in cold air
was developed by Peter
Tikuisis and John Frim for
the Defence and Civil
Institute of Environmental
Medicine in Ontario.
According to their model,
the main factor in the cause
of death would be your
clothes. If you were nude,
you’d probably succumb to
hypothermia
somewhere
around the five-hour mark,
before your oxygen ran out.6
If you were bundled up, you
may be frostbitten, but you
would probably survive . . .
. . . long enough to reach
the Death Zone.
Above 8000 meters—above
the tops of all but the highest
mountains—the
oxygen
content in the air is too low
to support human life. Near
this
zone,
you
would
experience a range of
symptoms, possibly including
confusion,
dizziness,
clumsiness, impaired vision,
and nausea.
As you approach the Death
Zone, your blood oxygen
content would plummet.
Your veins are supposed to
bring low-oxygen blood back
to your lungs to be refilled
with oxygen. But in the
Death Zone, there’s so little
oxygen in the air that your
veins lose oxygen to the air
instead of gaining it.
The result would be a rapid
loss of consciousness and
death. This would happen
around the seven-hour mark;
the chances are very slim that
you would make it to eight.
She died as she lived—rising at a foot
per second. I mean, as she lived for
the last few hours.
And two million years later,
your frozen body, still moving
along steadily at a foot per
second, would pass through
the
heliopause
into
interstellar space.
Clyde Tombaugh, the
astronomer who discovered
Pluto, died in 1997. A
portion of his remains were
placed on the New Horizons
spacecraft, which will fly past
Pluto and then continue out
of the solar system.
It’s
true
that
your
hypothetical foot-per-second
trip
would
be
cold,
unpleasant, and rapidly fatal.
But when the Sun becomes a
red giant in four billion years
and consumes the Earth, you
and Clyde would be the only
ones to escape.
So there’s that.
1 It won’t help you survive, but
...
2 For this answer, I’m going to
assume a typical atmosphere
temperature profile. It can, of
course, vary quite a bit.
3 . . . which are typically kept
pressurized at about 70 percent
to 80 percent of sea level
pressure, judging from the
barometer in my phone.
4 Either unit.
5 Not Kelvin, though.
6 And frankly, this “nude”
scenario raises more questions
than it answers.
WEIRD
(AND
WORRYING)
QUESTIONS
FROM
THE
WHAT IF?
INBOX, #3
Q.
Given
humanity’s
current
knowledge and
capabilities, is
it possible to
build a new
star?
—Jeff Gordon
Q.
What sort
of logistic
anomalies
would you
encounter in
trying to raise
an army of
apes?
—Kevin
Q.
If people
had wheels
and could fly,
how would we
differentiate
them from
airplanes?
—Anonymous
ORBITAL
SUBMARINE
Q. How long
could a
nuclear
submarine
last in orbit?
—Jason Lathbury
A. THE
SUBMARINE
WOULD BE fine, but
the crew would be in trouble.
The submarine wouldn’t
burst. Submarine hulls are
strong enough to withstand
50 to 80 atmospheres of
external pressure from water,
so they’d have no problem
containing 1 atmosphere of
internal pressure from air.
The hull would likely be
airtight. Although watertight
seals don’t necessarily hold
back air, the fact that water
can’t find a way through the
hull under 50 atmospheres of
pressure suggests that air
won’t escape quickly. There
may be a few specialized oneway valves that would let air
out, but in all likelihood, the
submarine would remain
sealed.
The big problem the crew
would face would be the
obvious one: air.
Nuclear submarines use
electricity to extract oxygen
from water. In space, there’s
no water,[citation needed ] so
they wouldn’t be able to
manufacture more air. They
carry enough oxygen in
reserve to survive for a few
days, at least, but eventually
they’d be in trouble.
To stay warm, they could
run their reactor, but they’d
have to be very careful how
much they ran it—because
the ocean is colder than
space.
Technically, that’s not really
true. Everyone knows that
space is very cold. The reason
spacecraft can overheat is that
space isn’t as thermally
conductive as water, so heat
builds up more quickly in
spacecraft than in boats.
But if you’re even more
pedantic, it is true. The ocean
is colder than space.
Interstellar space is very
cold, but space near the Sun
—and near Earth—is actually
incredibly hot! The reason it
doesn’t seem that way is that
in space, the definition of
“temperature” breaks down a
little bit. Space seems cold
because it’s so empty.
Temperature is a measure
of the average kinetic energy
of a collection of particles. In
space, individual molecules
have a high average kinetic
energy, but there are so few of
them that they don’t affect
you.
When I was a kid, my dad
had a machine shop in our
basement, and I remember
watching him use a metal
grinder. Whenever metal
touched the grinding wheel,
sparks
flew
everywhere,
showering his hands and
clothes. I couldn’t understand
why they didn’t hurt him
—after all, the glowing sparks
were
several
thousand
degrees.
I later learned that the
reason the sparks didn’t hurt
him was that they were tiny;
the heat they carried could be
absorbed into the body
without warming anything
more than a tiny patch of
skin.
The hot molecules in space
are like the sparks in my dad’s
machine shop; they might be
hot or cold, but they’re so
small that touching them
doesn’t
change
your
temperature much.1 Instead,
your heating and cooling is
dominated by how much heat
you produce and how quickly
it pours out of you into the
void.
Without
a
warm
environment around you
radiating heat back to you,
you lose heat by radiation
much faster than normal. But
without air around you to
carry heat from your surface,
you also don’t lose much heat
by convection.2 For most
human-carrying spacecraft,
the latter effect is more
important; the big problem
isn’t staying warm, it’s
keeping cool.
A nuclear submarine is
clearly able to maintain a
livable temperature inside
when the outer hull is cooled
to 4°C by the ocean.
However, if the submarine’s
hull needed to hold this
temperature while in space, it
would lose heat at a rate of
about 6 megawatts while in
the shadow of the Earth. This
is more than the 20 kilowatts
supplied by the crew—and
the few hundred kilowatts of
apricity3 when in direct
sunlight—so they’d need to
run the reactor just to stay
warm.4
To get out of orbit, a
submarine would need to
slow down enough that it hit
the atmosphere. Without
rockets, it has no way to do
this.
Okay—technically,
a
submarine does have rockets.
Unfortunately, the rockets
are pointing the wrong way to
give the submarine a push.
Rockets are self-propelling,
which means they have very
little recoil. When a gun fires
a bullet, it’s pushing the bullet
up to speed. With a rocket,
you just light it and let go.
Launching missiles won’t
propel a submarine forward.
But not launching them
could.
If the ballistic missiles
carried by a modern nuclear
submarine were taken from
their tubes, turned around,
and placed in the tubes
backward, they could each
change the submarine’s speed
by about 4 meters per second.
A
typical
de-orbiting
maneuver requires in the
neighborhood of 100 m/s of
delta-v (speed change), which
means that the 24 Trident
missiles carried by an Ohioclass submarine could be just
enough to get it out of orbit.
Now,
because
the
submarine has no heat-
dissipating ablative tiles, and
because
it’s
not
aerodynamically stable at
hypersonic velocities, it would
inevitably tumble and break
up in the air.
If you tucked yourself into
the right crevice in the
submarine—and
were
strapped into an acceleration
couch—there’s a tiny, tiny,
tiny chance that you could
survive the rapid deceleration.
Then you’d need to jump out
of the wreckage with a
parachute before it hit the
ground.
If you ever try this, and I
suggest you don’t, I have one
piece of advice that is
absolutely critical:
Remember to disable the
detonators on the missiles.
1 This is why, even though
matches and torches are about
the same temperature, you see
tough guys in movies extinguish
matches by pinching them but
never see them do the same
with torches.
2 Or conduction.
3 This is my single favorite
word in the English language.
It means the warmth of
sunlight in winter.
4 When they moved into the
Sun, the sub’s surface would
warm, but they’d still be losing
heat faster than they’d be
gaining it.
SHORTANSWER
SECTION
Q. If my
printer could
literally print
out money,
would it have
that big an
effect on the
world?
—Derek O’Brien
A. YOU
CAN FIT FOUR
bills on an 8.5" × 11"
sheet of paper.
If your printer can manage
one page (front and back) of
full-color
high-quality
printing per minute, that’s
$200 million dollars a year.
This is enough to make you
very rich, but not enough to
put any kind of dent in the
world economy. Since there
are 7.8 billion $100 bills in
circulation, and the lifetime
of a $100 bill is about 90
months, that means there are
about a billion produced each
year. Your extra two million
bills a year would barely be
enough to notice.
Q. What
would
happen if you
set off a
nuclear bomb
in the eye of a
hurricane?
Would the
storm cell be
immediately
vaporized?
—Rupert
Bainbridge (and
hundreds of
others)
A. THIS
QUESTION
GETS SUBMITTED a
lot.
It turns out the National
Oceanic and Atmospheric
Administration—the agency
that runs the National
Hurricane Center—gets it a
lot, too. In fact, they’re asked
about it so often that they’ve
published a response.
I recommend you read the
whole thing,1 but I think the
last sentence of the first
paragraph says it all:
“Needless to say, this is not
a good idea.”
It makes me happy that an
arm of the US government
has, in some official capacity,
issued an opinion on the
subject of firing nuclear
missiles at hurricanes.
Q. If
everyone put
little turbine
generators on
the
downspouts
of their
houses and
businesses,
how much
power would
we generate?
Would we
ever generate
enough
power to
offset the cost
of the
generators?
—Damien
A. A
HOUSE IN A very
rainy place, like the
Alaska panhandle, might
receive close to 4 meters of
rain per year. Water turbines
can be pretty efficient. If the
house has a footprint of 1500
square feet and gutters 5
meters off the ground, it
would generate an average of
less than a watt of power
from rainfall, and the
maximum electricity savings
would be:
The rainiest hour on record
as of 2014 occurred in 1947
in Holt, Missouri, where
about 30 centimeters of rain
fell in 42 minutes. For those
42 minutes, our hypothetical
house could generate up to
800 watts of electricity, which
might be enough to power
everything inside it. For the
rest of the year, it wouldn’t
come close.
If the generator rig cost
$100, residents of the rainiest
place in the US—Ketchikan,
Alaska—could
potentially
offset the cost in under a
century.
Q. Using only
pronounceable
letter
combinations,
how long
would names
have to be to
give each star
in the
universe a
unique oneword name?
—Seamus
Johnson
A. THERE
ARE ABOUT
300,000,000,000,000,000,00
stars in the universe. If you
make a word pronounceable
by alternating vowels and
consonants (there are better
ways to make pronounceable
words, but this will do for an
approximation), then every
pair of letters you add lets you
name 105 times as many stars
(21 consonants times 5
vowels). Since numbers have
a similar information density
—100
possibilities
per
character
—this suggests the name will
end up being about as long as
the total number of stars:
The stars are named Joe Biden.
I like doing math that
involves
measuring
the
lengths of numbers written
out on the page (which is
really just a way of loosely
estimating log10x). It works,
but it feels so wrong.
Q. I bike to
class
sometimes.
It’s annoying
biking in the
wintertime,
because it’s
so cold. How
fast would I
have to bike
for my skin to
warm up the
way a
spacecraft
heats up
during
reentry?
—David Nai
A. REENTERING
SPACECRAFT HEAT
UP
because
they’re
compressing the air in front
of them (not, as is commonly
believed, because of air
friction).
To increase the temperature
of the air layer in front of
your body by 20 degrees
Celsius (enough to go from
freezing
to
room
temperature), you would need
to be biking at 200 meters per
second.
The fastest human-powered
vehicles at sea levels are
recumbent bicycles enclosed
in streamlined aerodynamic
shells. These vehicles have an
upper speed limit near 40 m/s
—the speed at which the
human can just barely
produce enough thrust to
balance the drag force from
the air.
Since drag increases with
the square of the speed, this
limit would be pretty hard to
push any further. Biking at
200 m/s would require at least
25 times the power output
needed to go 40 m/s.
At those speeds, you don’t
really have to worry about the
heating from the air—a quick
back-of-the-envelope
calculation suggests that if
your body were doing that
much work, your core
temperature would reach fatal
levels in a matter of seconds.
Q. How
much
physical
space does
the Internet
take up?
—Max L
A. THERE ARE A
LOT of
ways to estimate the
amount of information stored
on the Internet, but we can
put an interesting upper
bound on the number just by
looking at how much storage
space we (as a species) have
purchased.
The
storage
industry
produces in the neighborhood
of 650 million hard drives per
year. If most of them are 3.5inch drives, that’s 8 liters (2
gallons) of hard drive per
second.
This means the last few
years
of
hard-drive
production—which, thanks to
increasing size, represents the
majority of global storage
capacity—would just about
fill an oil tanker. So, by that
measure, the Internet is
smaller than an oil tanker.
Q. What if
you strapped
C4 to a
boomerang?
Could this be
an effective
weapon, or
would it be as
stupid as it
sounds?
—Chad
Macziewski
A. AERODYNAMICS
ASIDE, I’M CURIOUS
what tactical advantage you’re
expecting to gain by having
the high explosive fly back at
you if it misses the target.
1 Search for “Why don’t we try
to destroy tropical cyclones by
nuking them?” by Chris
Landsea.
LIGHTNING
Before we go any further, I
want
to
emphasize
something: I am not an
authority
on
lightning
safety.
I am a guy who draws
pictures on the Internet. I like
it when things catch fire and
explode, which means I do
not have your best interests in
mind. The authorities on
lightning safety are the folks
at the US National Weather
Service:
http://www.lightningsafety.
Okay. With that out of the
way . . .
To answer the questions
that follow, we need to get an
idea of where lightning is
likely to go. There’s a cool
trick for this, and I’ll give it
away right here at the start:
Roll an imaginary 60-meter
sphere across the landscape
and look at where it touches.1
In this section, I answer a few
different questions about
lightning.
They say lightning strikes
the tallest thing around.
That’s
the
kind
of
maddeningly
inexact
statement that immediately
sparks all kinds of questions.
How far is “around”? I mean,
not all lightning hits Mount
Everest. But does it find the
tallest person in a crowd? The
tallest person I know is
probably
Ryan
North.2
Should I try to hang around
him for lightning safety
reasons? What about other
reasons? Maybe I should stick
to answering questions rather
than asking them.
So how does lightning pick
its targets?
The strike starts with a
branching bundle of charge—
the
“leader”—descending
from the cloud. It spreads
downward at speeds of tens to
hundreds of kilometers per
second, covering the few
kilometers to the ground in a
few dozen milliseconds.
The
leader
carries
comparatively little current
—on the order of 200 amps.
That’s still enough to kill you,
but it’s nothing compared to
what happens next. Once the
leader makes contact with the
ground, the cloud and the
ground equalize with a
massive discharge of more
like 20,000 amps. This is the
blinding flash you see. It races
back up the channel at a
significant fraction of the
speed of light, covering the
distance
in
under
a
millisecond .3
The place on the ground
where we see a bolt “strike” is
the spot where the leader first
made contact with the
surface. The leader moves
down through the air in little
jumps. It’s ultimately making
its way toward the (usually)
positive charge in the ground.
However, it “feels” charges
within only a few tens of
meters of its tip when it’s
deciding where to jump next.
If
there’s
something
connected to the ground
within that distance, the bolt
will jump to it. Otherwise, it
jumps out in a semi-random
direction and repeats the
process.
This is where the 60-meter
sphere comes in. It’s a way to
imagine what spots might be
the first thing the leader
senses—the places it might
jump to in its next (final)
step.
To figure out where
lightning is likely to hit, you
roll the imaginary 60-meter
sphere across the landscape.4
This sphere climbs up over
trees and buildings without
passing through anything (or
rolling it up). Places the
surface
makes
contact
—treetops, fence posts, and
golfers
in
fields—are
potential lightning targets.
This means you can
calculate a lightning “shadow”
around an object of height h
on a flat surface.
The shadow is the area
where the leader is likely to
hit the tall object instead of
the ground around it:
Now, that doesn’t mean
you’re safe within the shadow
—often, it means the
opposite. After the current
hits the tall object, it flows
out into the ground. If you’re
touching the ground nearby,
it can travel through your
body. Of the 28 people killed
by lightning in the US in
2012, 13 were standing under
or near trees.
With all this in mind, let’s
look at possible lightning
paths for the scenarios in the
following questions.
Q. How
dangerous is
it, really, to
be in a pool
during a
thunderstorm?
A. PRETTY
DANGEROUS.
WATER IS conductive, but
that’s not the biggest problem
—the biggest problem is that
if you’re swimming, your
head is poking up from a
large flat surface. But
lightning striking the water
near you would still be bad.
The 20,000 amps spread
outward—mostly over the
surface—but how much of a
jolt it will give you at what
distance is hard to calculate.
My guess is that you’d be in
significant danger anywhere
within a minimum of a dozen
meters—and farther in fresh
water, because the current
will be happier to take a
shortcut through you.
What would happen if you
were taking a shower when
you were struck by lightning?
Or
standing
under
a
waterfall?
You’re not in danger from
the spray—it’s just a bunch of
droplets of water in the air.
It’s the tub under your feet,
and the puddle of water in
contact with the plumbing,
that’s the real threat.
Q. What
would
happen if you
were in a
boat or a
plane that got
hit by
lightning? Or
a submarine?
A. A
BOAT WITHOUT A
cabin is about as safe as a
golf course. A boat with a
closed cabin and a lightning
protection system is about as
safe as a car. A submarine is
about as safe as a submarine
safe (a submarine safe is not
to be confused with a safe in a
submarine—a safe in a
submarine is substantially
safer than a submarine safe).
Q. What if
you were
changing the
light at the
top of a radio
tower, and
lightning
struck? Or
what if you
were doing a
backflip? Or
standing in a
graphite
field? Or
looking
straight up at
the bolt?
A.
Q. What
would
happen if
lightning
struck a
bullet in
midair?
A. THE
BULLET WON’T
AFFECT the path the
lightning takes. You’d have to
somehow time the shot so the
bullet was in the middle of
the bolt when the return
stroke happened.
The core of a lightning bolt
is a few centimeters in
diameter. A bullet fired from
an AK-47 is about 26 mm
long and moves at about 700
millimeters every millisecond.
The bullet has a copper
coating over a lead core.
Copper is a fantastically good
conductor of electricity, and
much of the 20,000 amps
could easily take a shortcut
through the bullet.
Surprisingly, the bullet
would handle it pretty well. If
it were sitting still, the
current would quickly heat
and melt the metal. But since
it would be moving along so
quickly, it would exit the
channel before it could be
warmed by more than a few
degrees. It would continue on
to its target relatively
unaffected. There would be
some curious electromagnetic
forces
created
by
the
magnetic field around the
bolt and the current flow
through the bullet, but none
of the ones I examined would
change the overall picture
very much.
Q. What if
you were
flashing your
BIOS during a
thunderstorm
and you got
hit by
lightning?
A.
1 Or a real one, for that matter.
2 Paleontologists estimate he
stood nearly 5 meters tall at the
shoulder.
3 While it’s called a “return
stroke,” charge is still flowing
downward. However, the
discharge appears to propagate
upward. This effect is similar to
how when a traffic light turns
green, the cars in front start
moving, then the cars in back,
so the movement appears to
spread backward.
4 For safety reasons, do not use
a real sphere.
WEIRD
(AND
WORRYING)
QUESTIONS
FROM
THE
WHAT IF?
INBOX, #4
Q. Would it be
possible to
stop a volcano
eruption by
placing a bomb
(thermobaric or
nuclear)
underneath the
surface?
—Tomasz Gruszka
Q.
A friend of
mine is
convinced that
there is sound
in space. There
isn’t, right?
—Aaron Smith
HUMAN
COMPUTER
Q. How
much
computing
power could
we could
achieve if the
entire world
population
stopped
whatever we
are doing
right now and
started doing
calculations?
How would it
compare to a
modern-day
computer or
smartphone?
—Mateusz Knorps
A. ON
ONE
HAND,
HUMANS and computers do
very different types of
thinking, so comparing them
is like comparing apples and
oranges.
On the other hand, apples
are better.1 Let’s try directly
comparing
humans
and
computers at the same tasks.
It’s easy, though getting
harder every day, to invent
tasks that a single human can
do faster than all the
computers in the world.
Humans, for example, are
probably still far better at
looking at a picture of a scene
and guessing what just
happened:
To test this theory, I sent
this picture to my mother and
asked her what she thought
had
happened.
She
immediately replied,2 “The
kid knocked over the vase and
the cat is investigating.”
She
cleverly
rejected
alternate
hypotheses,
including:
The cat knocked over
the vase.
The cat jumped out
of the vase at the kid.
The kid was being
chased by the cat and
tried to climb up the
dresser with a rope to
escape.
There’s a wild cat in
the house, and
someone threw a vase
at it.
The cat was
mummified in the
vase, but arose when
the kid touched it
with a magic rope.
The rope holding the
vase broke and the
cat is trying to put it
back together.
The vase exploded,
attracting a child and
a cat. The child put
on the hat for
protection from
future explosions.
The kid and cat are
running around
trying to catch a
snake. The kid finally
caught it and tied a
knot in it.
All the computers in the
world couldn’t figure out the
correct answer faster than any
one parent could. But that’s
because computers haven’t
been programmed to figure
that kind of thing out,3
whereas brains have been
trained by millions of years of
evolution to be good at
figuring out what other brains
around them are doing and
why.
So we could choose a task
to give the humans an
advantage, but that’s no fun;
computers are limited by our
ability to program them, so
we’ve
got
a
built-in
advantage.
Instead, let’s see how we
compete on their turf.
The complexity of
microchips
Rather than making up a new
task, we’ll simply apply the
same benchmark tests to
humans that we do to
computers. These usually
consist of things like floating
point math, saving and
recalling
numbers,
manipulating
strings
of
letters, and basic logical
calculations.
According to computer
scientist Hans Moravec, a
human running through
computer chip benchmark
calculations by hand, using
pencil and paper, can carry
out the equivalent of one full
instruction every minute and
a half.4
By this measure, the
processor in a midrange
mobile phone could do
calculations about 70 times
faster than the entire world
population. A new high-end
desktop PC chip would
increase that ratio to 1500.
So, what year did a single
typical desktop computer
surpass
the
combined
processing
power
of
humanity?
1994.
In
1992,
the
world
population was 5.5 billion
people, which means their
combined computing power
by our benchmark test was
about 65 MIPS (million
instructions per second).
That same year, Intel
released the popular 486DX,
which
in
its
default
configuration achieved about
55 or 60 MIPS. By 1994,
Intel’s new Pentium chips
were achieving benchmark
scores in the 70s and 80s,
leaving humanity in the dust.
You might argue that we’re
being a little unfair to the
computers. After all, these
comparisons
are
one
computer against all humans.
How do all humans stack up
against all computers?
This is tough to calculate.
We can easily come up with
benchmark scores for various
types of computers, but how
do
you
measure
the
instructions per second of,
say, the chip in a Furby?
Most of the transistors in
the world are in microchips
not designed to run these
tests. If we’re assuming that
all
humans
are
being
modified (trained) to carry
out
the
benchmark
calculations, how much effort
should we spend to modify
each computer chip so it can
run the benchmark?
To avoid this problem, we
can instead estimate the
aggregate power of all the
world’s computing devices by
counting transistors. It turns
out that processors from the
1980s and processors from
today have a roughly similar
ratio of transistors to MIPS
—about 30 transistors per
instruction per second, give or
take an order of magnitude.
A paper by Gordon Moore
(of Moore’s law fame) gives
figures for the total number
of transistors manufactured
per year since the 1950s. It
looks something like this:
Using our ratio, we can
convert the number of
transistors to a total amount
of computing power. This
tells us that a typical modern
laptop,
which
has
a
benchmark score in the tens
of thousands of MIPS, has
more computing power than
existed in the entire world in
1965. By that measure, the
year when the combined
power of computers finally
pulled ahead of the combined
computing power of humans
was 1977.
The complexity of
neurons
Again, making people do
pencil-and-paper
CPU
benchmarks
is
a
phenomenally silly way to
measure human computing
power.
Measured
by
complexity, our brains are
more sophisticated than any
supercomputer. Right?
Right. Mostly.
There are projects that
attempt
to
use
supercomputers
to
fully
simulate a brain at the level of
individual synapses.5 If we
look at how many processors
and how much time these
simulations require, we can
come up with a figure for the
number
of
transistors
required
to
equal
the
complexity of the human
brain.
The numbers from a 2013
run of the Japanese K
supercomputer suggest a
figure of 1015 transistors per
human brain.6 By this
measure, it wasn’t until the
year 1988 that all the logic
circuits in the world added up
to the complexity of a single
brain . . . and the total
complexity of all our circuits
is still dwarfed by the total
complexity of all brains.
Under Moore’s law–based
projections, and using these
simulation figures, computers
won’t pull ahead of humans
until the year 2036.7
Why this is ridiculous
These
two
ways
of
benchmarking the brain
represent opposite ends of a
spectrum.
One, the pencil-and-paper
Dhrystone benchmark, asks
humans to manually simulate
individual operations on a
computer chip, and finds
humans perform about 0.01
MIPS.
The
other,
the
supercomputer
neuron
simulation
project,
asks
computers
to
simulate
individual neurons firing in a
human brain, and finds
humans perform about the
equivalent of 50,000,000,000
MIPS.
A slightly better approach
might be to combine the two
estimates.
This
actually
makes a strange sort of sense.
If we assume our computer
programs are about as
inefficient
at
simulating
human brain activity as
human
brains
are
at
simulating computer chip
activity, then maybe a more
fair brain power rating would
be the geometric mean of the
two numbers.
The
combined
figure
suggests human brains clock
in at about 30,000 MIPS—
right about on par with the
computer on which I’m
typing these words. It also
suggests that the year when
Earth’s digital complexity
overtook
its
human
neurological complexity was
2004.
Ants
In his paper “Moore’s Law at
40,” Gordon Moore makes an
interesting observation. He
points out that, according to
biologist E. O. Wilson, there
are 1015 to 1016 ants in the
world. By comparison, in
2014 there were about 1020
transistors in the world, or
tens
of
thousands
of
transistors per ant.8
An ant’s brain might
contain a quarter of a million
neurons, and thousands of
synapses per neuron, which
suggests that the world’s ant
brains have a combined
complexity similar to that of
the world’s human brains.
So we shouldn’t worry too
much about when computers
will catch up with us in
complexity. After all, we’ve
caught up to ants, and they
don’t seem too concerned.
Sure, we seem like we’ve
taken over the planet, but if I
had to bet on which one of us
would still be around in a
million
years—primates,
computers, or ants—I know
who I’d pick.
1 Except Red Delicious apples,
whose misleading name is a
travesty.
2 Our house had a lot of vases
when I was a kid.
3 Yet.
4 This figure comes from a list
(http://www.frc.ri.cmu.edu/users
in Hans Moravec’s book Robot:
Mere Machine to Transcendent
Mind.
5 Although even this might not
capture everything that’s going
on. Biology is tricky.
6 Using 82,944 processors with
about 750 million transistors
each, K spent 40 minutes
simulating one second of brain
activity in a brain with 1
percent of the number of
connections as a human’s.
7 If it’s past the year 2036 right
now while you’re reading this,
hello from the distant past! I
hope things are better in the
future. P.S. Please figure out a
way to come get us.
8 “TPA.”
LITTLE
PLANET
Q. If an
asteroid was
very small but
supermassive,
could you
really live on
it like the
Little Prince?
—Samantha Harper
“Did you eat my rose?” “Maybe.”
A. THE
LITTLE PRINCE,
BY Antoine de Saint-
Exupéry,
traveler
asteroid.
and
is a story about a
from a distant
It’s simple and sad
poignant
and
memorable.1 It’s ostensibly a
children’s book, but it’s hard
to pin down who the
intended audience is. In any
case, it certainly has found an
audience; it’s among the bestselling books in history.
It was written in 1942.
That’s an interesting time to
write about asteroids, because
in 1942 we didn’t actually
know what asteroids looked
like. Even in our best
telescopes,
the
largest
asteroids were visible only as
points of light. In fact, that’s
where their name comes from
—the word asteroid means
“starlike.”
We
got
our
first
confirmation
of
what
asteroids looked like in 1971,
when Mariner 9 visited Mars
and snapped pictures of
Phobos and Deimos. These
moons, believed to be
captured asteroids, solidified
the modern image of
asteroids as cratered potatoes.
Before the 1970s, it was
common for science fiction to
assume small asteroids would
be round, like planets.
The Little Prince took this
a step further, imagining an
asteroid as a tiny planet with
gravity, air, and a rose.
There’s no point in trying to
critique the science here,
because (1) it’s not a story
about asteroids, and (2) it
opens with a parable about
how foolish adults are for
looking at everything too
literally.
Rather than using science
to chip away at the story, let’s
see what strange new pieces it
can add. If there really were a
superdense asteroid with
enough surface gravity to
walk around on, it would
have some pretty remarkable
properties.
If the asteroid had a radius
of 1.75 meters, then in order
to have Earthlike gravity at
the surface, it would need to
have a mass of about 500
million tons. This is roughly
equal to the combined mass
of every human on Earth.
If you stood on the surface,
you’d experience tidal forces.
Your feet would feel heavier
than your head, which you’d
feel as a gentle stretching
sensation. It would feel like
you were stretched out on a
curved rubber ball, or were
lying on a merry-go-round
with your head near the
center.
The escape velocity at the
surface would be about 5
meters per second. That’s
slower than a sprint, but still
pretty fast. As a rule of
thumb, if you can’t dunk a
basketball, you wouldn’t be
able to escape this asteroid by
jumping.
However, the weird thing
about escape velocity is that it
doesn’t
matter
which
direction you’re going.2 If
you go faster than the escape
speed, as long as you don’t
actually go toward the planet,
you’ll escape. That means you
might be able to leave our
asteroid
by
running
horizontally and jumping off
the end of a ramp.
If you didn’t go fast enough
to escape the planet, you’d go
into orbit around it. Your
orbital speed would be
roughly 3 meters per second,
which is a typical jogging
speed.
But this would be a weird
orbit.
Tidal forces would act on
you in several ways. If you
stretched your arm down
toward the planet, it would be
pulled much harder than the
rest of you. And when you
reach down with one arm, the
rest of you gets pushed
upward, which means other
parts of your body feel even
less gravity. Effectively, every
part of your body would be
trying to go in a different
orbit.
A large orbiting object
under these kinds of tidal
forces—say, a moon—will
generally break apart into
rings.3 This wouldn’t happen
to you. However, your orbit
would become chaotic and
unstable.
These types of orbits were
investigated in a paper by
Radu D. Rugescu and
Daniele
Mortari.
Their
simulations showed that
large, elongated objects follow
strange paths around their
central bodies. Even their
centers of mass don’t move in
the traditional ellipses; some
adopt pentagonal orbits,
while
others
tumble
chaotically and crash into the
planet.
This type of analysis could
actually
have
practical
applications. There have been
various proposals over the
years to use long, whirling
tethers to move cargo in and
out of gravity wells—a sort of
free-floating space elevator.
Such tethers could transport
cargo to and from the surface
of the Moon, or to pick up
spacecraft from the edge of
the Earth’s atmosphere. The
inherent instability of many
tether orbits poses a challenge
for such a project.
As for the residents of our
superdense asteroid, they’d
have to be careful; if they ran
too fast, they’d be in serious
danger of entering orbit,
going into a tumble and
losing their lunch.
Fortunately, vertical jumps
would be fine.
Cleveland-area fans of French
children’s literature were
disappointed by the Prince’s decision
to sign with the Miami Heat.
1 Although not everyone sees it
this way. Mallory Ortberg,
writing on the-toast.net,
characterized the story of The
Little Prince as a wealthy child
demanding that a plane crash
survivor draw him pictures,
then critiquing his drawing
style.
2 . . . which is why it should
really be called “escape speed”
— the fact that it has no
direction (which is the
distinction between “speed” and
“velocity”) is unexpectedly
significant here.
3 This is presumably what
happened to Sonic the
Hedgehog.
STEAK DROP
Q. From what
height would
you need to
drop a steak
for it to be
cooked when
it hit the
ground?
—Alex Lahey
A. I HOPE YOU LIKE your
steaks Pittsburgh Rare. And
you may need to defrost it
after you pick it up.
Things get really hot when
they come back from space.
As they enter the atmosphere,
the air can’t move out of the
way fast enough, and gets
squished in front of the object
—and compressing air heats
it up. As a rule of thumb, you
start to notice compressive
heating above about Mach 2
(which is why the Concorde
had heat-resistant material on
the leading edge of its wings).
When
skydiver
Felix
Baumgartner jumped from 39
kilometers, he hit Mach 1 at
around 30 kilometers. This
was enough to heat the air by
a few degrees, but the air was
so far below freezing that it
didn’t make a difference.
(Early in his jump, it was
about minus 40 degrees,
which is that magical point
where you don’t have to
clarify whether you mean
Fahrenheit or Celsius—it’s
the same in both.)
As far as I know, this steak
question originally came up in
a lengthy 4chan thread,
which quickly disintegrated
into poorly informed physics
tirades
intermixed
with
homophobic slurs. There was
no clear conclusion.
To try to get a better
answer, I decided to run a
series of simulations of a steak
falling from various heights.
An 8-ounce steak is about
the size and shape of a hockey
puck, so I based my steak’s
drag coefficients on those
given on page 74 of The
Physics of Hockey (which
author Alain Haché actually
measured personally using
some lab equipment). A steak
isn’t a hockey puck, but the
precise drag coefficient turned
out not to make a big
difference in the result.
Since
answering
these
questions often includes
analyzing unusual objects in
extreme
physical
circumstances, often the only
relevant research I can find is
US military studies from the
Cold War era. (Apparently,
the US government was
shoveling tons of money at
anything even loosely related
to weapons research.) To get
an idea of how the air would
heat the steak, I looked at
research papers on the
heating of ICBM nose cones
as
they
reenter
the
atmosphere. Two of the most
useful were “Predictions of
Aerodynamic Heating on
Tactical Missile Domes” and
“Calculation of ReentryVehicle
Temperature
History.”
Lastly, I had to figure out
exactly how quickly heat
spreads through a steak. I
started by looking at some
papers from industrial food
production that simulated
heat flow through various
pieces of meat. It took me a
while to realize there was a
much easier way to learn what
combinations of time and
temperature will effectively
heat the various layers of a
steak: Check a cookbook.
Jeff Potter’s excellent book
Cooking for Geeks provides a
great introduction to the
science of cooking meat, and
explains what ranges of heat
produce what effects in steak
and why. Cook’s The Science
of Good Cooking was also
helpful.
Putting it all together, I
found that the steak will
accelerate quickly until it
reaches an altitude of about
30–50 kilometers, at which
point the air gets thick
enough to start slowing it
back down.
The falling steak’s speed
would steadily drop as the air
gets thicker. No matter how
fast it was going when it
reached the lower layers of
the atmosphere, it would
quickly slow down to
terminal velocity. No matter
the starting height, it always
takes six or seven minutes to
drop from 25 kilometers to
the ground.
For much of those 25
kilometers,
the
air
temperature is below freezing
—which means the steak will
spend six or seven minutes
subjected to a relentless blast
of subzero, hurricane-force
winds. Even if it’s cooked by
the fall, you’ll probably have
to defrost it when it lands.
When the steak does finally
hit the ground, it will be
traveling at terminal velocity
—about 30 meters per
second. To get an idea of
what this means, imagine a
steak flung at the ground by a
major-league pitcher. If the
steak is even partially frozen,
it could easily shatter.
However, if it lands in the
water, mud, or leaves, it will
probably be fine.1
A steak dropped from 39
kilometers will, unlike Felix,
probably stay below the sound
barrier. It also won’t be
appreciably heated. This
makes sense—after all, Felix’s
suit wasn’t scorched when he
landed.
Steaks can probably survive
breaking the sound barrier. In
addition to Felix, pilots have
ejected at supersonic speeds
and lived to tell about it.
To break the sound barrier,
you’ll need to drop the steak
from about 50 kilometers.
But this still isn’t enough to
cook it.
We need to go higher.
If dropped from 70
kilometers, the steak will go
fast enough to be briefly
blasted
by
350°F
air.
Unfortunately, this blast of
thin, wispy air barely lasts a
minute—and anyone with
some basic kitchen experience
can tell you that a steak
placed in the oven at 350 for
60 seconds isn’t going to be
cooked.
From 100 kilometers—the
formally defined edge of
space—the
picture’s
not
much better. The steak
spends a minute and a half
over Mach 2, and the outer
surface will likely be singed,
but the heat is too quickly
replaced
by
the
icy
stratospheric blast for it to
actually be cooked.
At
supersonic
and
hypersonic
speeds,
a
shockwave forms around the
steak that helps protect it
from the faster and faster
winds.
The
exact
characteristics of this shock
front—and
thus
the
mechanical stress on the steak
—depend on how an
uncooked
8-ounce
filet
tumbles at hypersonic speeds.
I searched the literature, but
was unable to find any
research on this.
For the sake of this
simulation, I assume that at
lower speeds some type of
vortex shedding creates a
flipping tumble, while at
hypersonic
speeds
it’s
squished into a semi-stable
spheroid shape. However,
this is little more than a wild
guess. If anyone puts a steak
in a hypersonic wind tunnel
to get better data on this,
please, send me the video.
If you drop the steak from
250 kilometers, things start to
heat up; 250 kilometers puts
us in the range of low Earth
orbit. However, the steak,
since it’s dropped from a
standstill, isn’t moving nearly
as fast as an object reentering
from orbit.
In this scenario, the steak
reaches a top speed of Mach
6, and the outer surface may
even get pleasantly seared.
The inside, unfortunately, is
still uncooked. Unless, that is,
it goes into a hypersonic
tumble and explodes into
chunks.
From higher altitudes, the
heat starts to get really
substantial. The shockwave in
front of the steak reaches
thousands
of
degrees
(Fahrenheit or Celsius; it’s
true in both). The problem
with this level of heat is that
it burns the surface layer
completely, converting it to
little more than carbon. That
is, it becomes charred.
Charring is a normal
consequence of dropping
meat in a fire. The problem
with charring meat at
hypersonic speeds is that the
charred layer doesn’t have
much structural integrity, and
is blasted off by the wind
—exposing a new layer to be
charred. (If the heat is high
enough, it will simply blast
the surface layer off as it
flash-cooks it. This is referred
to in the ICBM papers as the
“ablation zone.”)
Even from those heights,
the steak still doesn’t spend
enough time in the heat to
get cooked all the way
through.2 We can try higher
and higher speeds, and we
might lengthen the exposure
time via dropping it at an
angle, from orbit.
But if the temperature is
high enough or the burn time
long enough, the steak will
slowly disintegrate as the
outer layer is repeatedly
charred and blasted off. If
most of the steak makes it to
the ground, the inside will
still be raw.
Which is why we should
drop
the
steak
over
Pittsburgh.
As the probably apocryphal
story goes, steelworkers in
Pittsburgh would cook steaks
by slapping them on the
glowing
metal
surfaces
coming out of the foundry,
searing the outside while
leaving the inside raw. This
is, supposedly, the origin of
the term “Pittsburgh Rare.”
So drop your steak from a
suborbital rocket, send out a
collection team to recover it,
brush it off, reheat it, cut
away any badly charred
sections, and dig in.
Just
watch
out
for
salmonella.
And
Andromeda Strain.
the
1 I mean, intact. Not
necessarily fine to eat.
2 I know what some of you are
probably thinking, and the
answer is no — it doesn’t spend
enough time in the Van Allen
belts to be sterilized by
radiation.
HOCKEY
PUCK
Q. How hard
would a puck
have to be
shot to be
able to knock
the goalie
himself
backward
into the net?
—Tom
A. THIS
CAN’T REALLY
HAPPEN.
It’s not just a problem of
hitting the puck hard enough.
This book isn’t concerned
with that kind of limitation.
Humans with sticks can’t
make a puck go much faster
than about 50 meters per
second, but we can assume
this puck is launched by a
hockey robot or an electric
sled or a hypersonic light gas
gun.
The problem, in a nutshell,
is that hockey players are
heavy and pucks are not. A
goalie in full gear outweighs a
puck by a factor of about 600.
Even the fastest slap shot has
less momentum than a tenyear-old skating along at a
mile per hour.
Hockey players can also
brace pretty hard against the
ice. A player skating at full
speed can stop in the space of
a few meters, which means
the force they’re exerting on
the ice is pretty substantial.
(It also suggests that if you
started to slowly rotate a
hockey rink, it could tilt up to
50 degrees before the players
would all slide to one end.
Clearly, experiments are
needed to confirm this.)
From estimates of collision
speeds in hockey videos, and
some guidance from a hockey
player, I estimated that the
165-gram puck would have to
be
moving
somewhere
between Mach 2 and Mach 8
to knock the goalie backward
into the goal—faster if the
goalie is bracing against the
hit, and slower if the puck
hits at an upward angle.
Firing an object at Mach 8
is not, in itself, very hard.
One of the best methods for
doing
so
is
the
aforementioned hypersonic
gas gun, which is—at its core
—the same mechanism a BB
gun uses to fire BBs.1
But a hockey puck moving
at Mach 8 would have a lot of
problems, starting with the
fact that the air ahead of the
puck would be compressed
and heated very rapidly. It
wouldn’t be going fast
enough to ionize the air and
leave a glowing trail like a
meteor, but the surface of the
puck would (given a long
enough flight) start to melt or
char.
The air resistance, however,
would slow the puck down
very quickly, so a puck going
at Mach 8 when it leaves the
launcher might be going a
fraction of that when it
arrives at the goal. And even
at Mach 8, the puck probably
wouldn’t pass through the
goalie’s body. Instead, it
would burst apart on impact
with the power of a large
firecracker or small stick of
dynamite.
If you’re like me, when you
first saw this question, you
might’ve imagined the puck
leaving
a
cartoon-style
hockey-puck-shaped
hole.
But that’s because our
intuitions are shaky about
how materials react at very
high speeds.
Instead, a different mental
picture might be more
accurate: Imagine throwing a
ripe tomato—as hard as you
can—at a cake.
That’s about what would
happen.
1 Though it uses hydrogen
instead of air, and when you
shoot your eye out, you really
shoot your eye out.
COMMON
COLD
Q. If
everyone on
the planet
stayed away
from each
other for a
couple of
weeks,
wouldn’t the
common cold
be wiped
out?
— Sarah Ewart
A. WOULD
IT
BE
WORTH IT?
The common cold is caused
by a variety of viruses,1 but
rhinoviruses are the most
common culprit.2 These
viruses take over the cells in
your nose and throat and use
them to produce more
viruses. After a few days, your
immune system notices and
destroys it,3 but not before
you infect, on average, one
other person.4 After you fight
off the infection, you are
immune to that particular
rhinovirus
strain—an
immunity that lasts for years.
If Sarah put us all in
quarantine, the cold viruses
we carry would have no fresh
hosts to run to. Could our
immune systems then wipe
out every copy of the virus?
Before we answer that
question, let’s consider the
practical consequences of this
kind of quarantine. The
world’s total annual economic
output is in the neighborhood
of $80 trillion, which suggests
that interrupting all economic
activity for a few weeks would
cost many trillions of dollars.
The shock to the system from
the worldwide “pause” could
easily cause a global economic
collapse.
The world’s total food
reserves are probably large
enough to cover us for four or
five weeks of quarantine, but
the food would have to be
evenly
parceled
out
beforehand. Frankly, I’m not
sure what I’d do with a 20day grain reserve while
standing alone in a field
somewhere.
A global quarantine brings
us to another question: How
far apart can we actually get
from one another? The world
is big,[citation needed ] but there
are
a
lot
of
people.
[citation needed ]
If we divide up the world’s
land area evenly, there’s
enough room for each of us to
have a little over 2 hectares
each, with the nearest person
77 meters away.
While 77 meters is probably
enough separation to block
the
transmission
of
rhinoviruses, that separation
would come at a cost. Much
of the world’s land is not
pleasant to stand around on
for five weeks. A lot of us
would be stuck standing in
the Sahara Desert,5 or central
Antarctica.6
A more practical—though
not
necessarily
cheaper
—solution would be to give
everyone biohazard suits.
That way, we could walk
around and interact, even
allowing
some
normal
economic activity to continue:
But let’s set aside the
practicality
and
address
Sarah’s
actual
question:
Would it work?
To help figure out the
answer, I talked to Professor
Ian M. Mackay, a virology
expert from the Australian
Infectious Diseases Research
Centre at the University of
Queensland.7
Dr. Mackay said that this
idea is actually somewhat
reasonable, from a purely
biological point of view. He
said that rhinoviruses—and
other RNA respiratory viruses
—are completely eliminated
from the body by the immune
system; they do not linger
after infection. Furthermore,
we don’t seem to pass any
rhinoviruses back and forth
with animals, which means
there are no other species that
can serve as reservoirs of our
colds. If rhinoviruses don’t
have enough humans to move
between, they die out.
We’ve actually seen this
viral extinction in action in
isolated populations. The
remote islands of St. Kilda,
far to the northwest of
Scotland, for centuries hosted
a population of about 100
people. The islands were
visited by only a few boats a
year, and suffered from an
unusual syndrome called the
cnatan-na-gall, or “stranger’s
cough.” For several centuries,
the cough swept the island
like clockwork every time a
new boat arrived.
The exact cause of the
outbreaks is unknown,8 but
rhinoviruses were probably
responsible for many of them.
Every time a boat visited, it
would introduce new strains
of virus. These strains would
sweep the islands, infecting
virtually everyone. After
several weeks, all the residents
would have fresh immunity to
those strains, and with
nowhere to go, the viruses
would die out.
The same viral clearing
would likely happen in any
small and isolated population
—for example, shipwreck
survivors.
If all humans were isolated
from one another, the St.
Kilda scenario would play out
on a species-wide scale. After
a week or two, our colds
would run their course, and
healthy immune systems
would have plenty of time to
clear the viruses.
Unfortunately, there’s one
catch, and it’s enough to
unravel the whole plan: We
don’t all have healthy
immune systems.
In
most
people,
rhinoviruses are fully cleared
from the body within about
ten days. The story is
different for those with
severely weakened immune
systems.
In
transplant
patients, for example, whose
immune systems have been
artificially
suppressed,
common
infections
—including
rhinoviruses
—can linger for weeks,
months, or conceivably years.
This small group of
immunocompromised people
would serve as safe havens for
rhinoviruses. The hope of
eradicating them is slim; they
would need to survive in only
a few hosts in order to sweep
out and retake the world.
In addition to probably
causing the collapse of
civilization, Sarah’s plan
wouldn’t
eradicate
rhinoviruses.9 However, this
might be for the best!
While colds are no fun,
their absence might be worse.
In his book A Planet of
Viruses, author Carl Zimmer
says that children who aren’t
exposed to rhinoviruses have
more immune disorders as
adults. It’s possible that these
mild infections serve to train
and calibrate our immune
systems.
On the other hand, colds
suck. And in addition to
being
unpleasant,
some
research says infections by
these viruses also weaken our
immune systems directly and
can open us up to further
infections.
All in all, I wouldn’t stand
in the middle of a desert for
five weeks to rid myself of
colds forever. But if they ever
come up with a rhinovirus
vaccine, I’ll be first in line.
1 “Virii” is used occasionally but
discouraged. “Viræ” is definitely
wrong.
2 Any upper respiratory
infection can actually be the
cause of the “common cold.”
3 The immune response is
actually the cause of your
symptoms, not the virus itself.
4 Mathematically, this must be
true. If the average were less
than one, the virus would die
out. If it were more than one,
eventually everyone would have
a cold all the time.
5 (450 million people).
6 (650 million people).
7 I first tried to take the
question to Boing Boing’s Cory
Doctorow, but he patiently
explained to me that he’s not
actually a doctor.
8 The residents of St. Kilda
correctly identified the boats as
the trigger for the outbreaks.
The medical experts of the
time, however, dismissed these
claims, instead blaming the
outbreaks on the way the
islanders stood around outdoors
in the cold when a boat arrived,
and on their celebrating the
new arrivals by drinking too
much.
9 Unless we ran out of food
during the quarantine and all
starved to death; in that case,
human rhinoviruses would die
with us.
GLASS HALF
EMPTY
Q. What if a
glass of water
was, all of a
sudden,
literally half
empty?
—Vittorio Iacovella
A. THE
PESSIMIST IS
PROBABLY more right
about how it would turn out
than the optimist.
When people say “glass half
empty,” they usually mean a
glass containing equal parts
water and air.
Traditionally, the optimist
sees the glass as half full while
the pessimist sees it as half
empty. This has spawned a
zillion joke variants—for
example, the engineer sees a
glass that’s twice as big as it
needs to be, the surrealist sees
a giraffe eating a necktie, etc.
But what if the empty half
of the glass were actually
empty—a vacuum?1 The
vacuum would definitely not
last long. But exactly what
happens depends on a key
question that nobody usually
bothers to ask: Which half is
empty?
For our scenario, we’ll
imagine three different halfempty glasses, and follow
what happens to them
microsecond by microsecond.
In the middle is the
traditional air/water glass. On
the right is a glass like the
traditional one, except the air
is replaced by a vacuum. The
glass on the left is half full of
water and half empty—but
it’s the bottom half that’s
empty.
We’ll imagine the vacuums
appear at time t=0.
For the first handful of
microseconds,
nothing
happens. On this timescale,
even the air molecules are
nearly stationary.
For the most part, air
molecules jiggle around at
speeds of a few hundred
meters per second. But at any
given time, some happen to
be moving faster than others.
The fastest few are moving at
over 1000 meters per second.
These are the first to drift
into the vacuum in the glass
on the right.
The vacuum on the left is
surrounded by barriers, so air
molecules can’t easily get in.
The water, being a liquid,
doesn’t expand to fill the
vacuum in the same way air
does. However, in the
vacuum of the glasses, it does
start to boil, slowly shedding
water vapor into the empty
space.
While the water on the
surface in both glasses starts
to boil away, in the glass on
the right, the air rushing in
stops it before it really gets
going. The glass on the left
continues to fill with a very
faint mist of water vapor.
After a few hundred
microseconds, the air rushing
into the glass on the right fills
the vacuum completely and
rams into the surface of the
water, sending a pressure
wave through the liquid. The
sides of the glass bulge
slightly, but they contain the
pressure and do not break. A
shockwave
reverberates
through the water and back
into the air, joining the
turbulence already there.
The shockwave from the
vacuum collapse takes about a
millisecond to spread out
through the other two glasses.
The glass and water both flex
slightly as the wave passes
through them. In a few more
milliseconds, it reaches the
humans’ ears as a loud bang.
Around this time, the glass
on the left starts to visibly lift
into the air.
The air pressure is trying to
squeeze the glass and water
together. This is the force we
think of as suction. The
vacuum on the right didn’t
last long enough for the
suction to lift the glass, but
since air can’t get into the
vacuum on the left, the glass
and the water begin to slide
toward each other.
The boiling water has filled
the vacuum with a very small
amount of water vapor. As
the space gets smaller, the
buildup of water vapor slowly
increases the pressure on the
water’s surface. Eventually,
this will slow the boiling, just
like higher air pressure would.
However, the glass and
water are now moving too
fast for the vapor buildup to
matter. Less than ten
milliseconds after the clock
started, they’re flying toward
each other at several meters
per second. Without a
cushion of air between them
—only a few wisps of vapor
—the water smacks into the
bottom of the glass like a
hammer.
Water is very nearly
incompressible, so the impact
isn’t spread out over time—it
comes as a single sharp shock.
The momentary force on the
glass is immense, and it
breaks.
This “water hammer” effect
(which is also responsible for
the “clunk” you sometimes
hear in old plumbing when
you turn off the faucet) can be
seen in the well-known party
trick of smacking the top of a
glass bottle to blow out the
bottom.
When the bottle is struck,
it’s
pushed
suddenly
downward. The liquid inside
doesn’t respond to the suction
(air pressure) right away
—much like in our scenario
—and a gap briefly opens up.
It’s a small vacuum—a few
fractions of an inch thick
—but when it closes, the
shock breaks the bottom of
the bottle.
In our situation, the forces
would be more than enough
to destroy even the heaviest
drinking glasses.
The bottom is carried
downward by the water and
thunks against the table. The
water splashes around it,
spraying droplets and glass
shards in all directions.
Meanwhile, the detached
upper portion of the glass
continues to rise.
After half a second, the
observers, hearing a pop, have
begun to flinch. Their heads
lift involuntarily to follow the
rising movement of the glass.
The glass has just enough
speed to bang against the
ceiling,
breaking
into
fragments . . .
. . . which, their
momentum now spent, return
to the table.
The lesson: If the optimist
says the glass is half full, and
the pessimist says the glass is
half empty, the physicist
ducks.
1 Even a vacuum arguably isn’t
truly empty, but that’s a
question for quantum
semantics.
WEIRD
(AND
WORRYING)
QUESTIONS
FROM
THE
WHAT IF?
INBOX, #5
Q. If global
warming puts
us in danger
through
temperature
rise, and
super-volcanos
put us into
danger of
global cooling,
shouldn’t those
two dangers
balance each
other out?
—Florian Seidl-Schulz
Q.
How fast
would a human
have to run in
order to be cut
in half at the
bellybutton by
a cheesecutting wire?
—Jon Merrill
ALIEN
ASTRONOMER
Q. Let’s
assume
there’s life on
the nearest
habitable
exoplanet
and that they
have
technology
comparable
to ours. If
they looked
at our star
right now,
what would
they see?
—Chuck H
A.
Let’s try a more complete
answer. We’ll start with . . .
Radio transmissions
Contact popularized the idea
of aliens listening in on our
broadcast media. Sadly, the
odds are against it.
Here’s the problem: Space
is really big.
You can work through the
physics of interstellar radio
attenuation,1 but the problem
is captured pretty well by
considering the economics of
the situation: If your TV
signals are getting to another
star, you’re wasting money.
Powering a transmitter is
expensive, and creatures on
other stars aren’t buying the
products
in
the
TV
commercials that pay your
power bill.
The full picture is more
complicated, but the bottom
line is that as our technology
has gotten better, less of our
radio traffic has been leaking
out into space. We’re closing
down the giant transmitting
antennas and switching to
cable, fiber, and tightly
focused cell-tower networks.
While our TV signals may
have been detectable—with
great effort—for a while, that
window is closing. Even in
the late 20th century, when
we were using TV and radio
to scream into the void at the
top of our lungs, the signal
probably
faded
to
undetectability after a few
light-years. The potentially
habitable exoplanets we’ve
spotted so far are dozens of
light-years away, so the odds
are
they
aren’t
currently
repeating our catchphrases.2
But
TV
and
radio
transmissions still weren’t
Earth’s most powerful radio
signal. They were outshone
by the beams from earlywarning radar.
Early-warning radar, a
product of the Cold War,
consisted of a bunch of
ground and airborne stations
scattered around the Arctic.
These stations swept the
atmosphere with powerful
radar beams 24/7, often
bouncing them off the
ionosphere,
and
people
obsessively monitored the
echos for any hints of enemy
movement.3
These radar transmissions
leaked into space, and could
probably be picked up by
nearby exoplanets if they
happened to be listening
when the beam swept over
their part of the sky. But the
same march of technological
progress that made the TV
broadcast towers obsolete has
had the same effect on earlywarning
radar.
Today’s
systems—where they exist at
all—are much quieter, and
may eventually be replaced
completely
technology.
by
new
Earth’s most powerful radio
signal is the beam from the
Arecibo
telescope.
This
massive dish in Puerto Rico
can function as a radar
transmitter, bouncing a signal
off nearby targets like
Mercury and the asteroid
belt.
It’s
essentially
a
flashlight that we shine on
planets to see them better.
(This is just as crazy as it
sounds.)
However, it transmits only
occasionally, and in a narrow
beam. If an exoplanet
happened to be caught in the
beam, and they were lucky
enough to be pointing a
receiving antenna at our
corner of the sky at the time,
all they would pick up would
be a brief pulse of radio
energy, then silence.4
So
hypothetical
aliens
looking at Earth probably
wouldn’t pick us up with
radio antennas.
But there’s also . . .
Visible light
This is more promising. The
Sun
is
really
bright,
[citation needed ]
and its light
illuminates
the
Earth.
[citation needed ]
Some of that
light is reflected back into
space as “Earthshine.” Some
of it skims close to our planet
and passes through our
atmosphere before continuing
on to the stars. Both of these
effects could potentially be
detected from an exoplanet.
They wouldn’t tell you
anything
about
humans
directly, but if you watched
the Earth for long enough,
you could figure out a lot
about our atmosphere from
the reflectivity. You could
probably figure out what our
water cycle looked like, and
our oxygen-rich atmosphere
would give you a hint that
something weird was going
on.
So in the end, the clearest
signal from Earth might not
be from us at all. It might be
from the algae that have been
terraforming the planet—and
altering the signals we send
into space—for billions of
years.
Heeeey, look at the time. Gotta run.
Of course, if we wanted to
send a clearer signal, we
could. A radio transmission
has the problem that they
have to be paying attention
when it arrives.
Instead, we could make
them pay attention. With ion
drives, nuclear propulsion, or
just clever use of the Sun’s
gravity well, we could
probably send a probe out of
the solar system fast enough
to reach a given nearby star in
a few dozen millennia. If we
can figure out how to make a
guidance system that survives
the trip (which would be
tough), we could use it to
steer toward any inhabited
planet.
To land safely, we’d have to
slow down. But slowing down
takes even more fuel. And,
hey, the whole point of this
was for them to notice us,
right?
So maybe if those aliens
looked toward our solar
system, this is what they
would see:
1 I mean, if you want.
2 Contrary to the claims made
by certain unreliable
webcomics.
3 I wasn’t alive during most of
this period, but from what I
hear, the mood was tense.
4 Which is exactly what we saw
once, in 1977. The source of
this blip (dubbed the “Wow
Signal”) has never been
identified.
NO MORE
DNA
Q. This may
be a bit
gruesome,
but . . . if
someone’s
DNA
suddenly
vanished,
how long
would that
person last?
—Nina Charest
A. IF
YOU LOST YOUR
DNA, you would instantly
be about a third of a pound
lighter.
Losing a third of a
pound
I don’t recommend this
strategy. There are easier
ways to lose a third of a
pound, including:
Taking off your shirt
Peeing
Cutting your hair (if
you have very long
hair)
Donating blood, but
putting a kink in the
IV once they drain
150 mL and refusing
to let them take any
more
Holding a 3-footdiameter balloon full
of helium
Removing your
fingers
You’ll also lose a third of a
pound if you take a trip from
the polar regions to the
tropics. This happens for two
reasons: One, the Earth is
shaped like this:
If you stand on the North
Pole, you’re 20 kilometers
closer to the center of the
Earth than if you stand on
the equator, and you feel a
stronger pull from gravity.
Furthermore, if you’re on
the equator, you’re being
flung outward by centrifugal
force.1
The result of these two
phenomena is that if you
move between polar regions
and equatorial ones, you
might lose or gain up to
about half a percent of your
body weight.
The reason I’m focusing on
weight is that if your DNA
disappeared, the physical loss
of the matter wouldn’t be the
first thing you might notice.
It’s possible you’d feel
something—a tiny, uniform
shockwave as every cell
contracted
slightly—but
maybe not.
If you were standing up
when you lost your DNA,
you might twitch slightly.
When you stand, your
muscles
are
constantly
working to keep you upright.
The force being exerted by
those muscle fibers wouldn’t
change, but the mass they’re
pulling
on—your
limbs
—would. Since F = ma,
various body parts would
accelerate slightly.
After that, you would
probably feel pretty normal.
For a while.
Destroying angel
Nobody has ever lost all their
DNA,2 so we can’t say for
sure what the precise
sequence
of
medical
consequences would be. But
to get an idea of what it
might be like, let’s turn to
mushroom poisonings.
Amanita bisporigera is a
species of mushroom found in
eastern
North
America.
Along with related species in
America and Europe, it’s
known by the common name
destroying angel.
Destroying angel is a small,
white,
inoccuous-looking
mushroom. If you’re like me,
you were told never to eat
mushrooms you found in the
woods. Amanita is the reason
why.3
If you eat a destroying
angel, for the rest of the day
you’ll feel fine. Later that
night, or the next morning,
you’ll start exhibiting choleralike
symptoms—vomiting,
abdominal pain, and severe
diarrhea. Then you start to
feel better.
At the point where you
start to feel better, the
damage
is
probably
irreversible.
Amanita
mushrooms
contain
amatoxin, which binds to an
enzyme that is used to read
information from DNA. It
hobbles
the
enzyme,
effectively interrupting the
process by which cells follow
DNA’s instructions.
Amatoxin
causes
irreversible
damage
to
whatever cells it collects in.
Since most of your body is
made of cells,4 this is bad.
Death is generally caused by
liver or kidney failure, since
those are the first sensitive
organs in which the toxin
accumulates.
Sometimes
intensive care and a liver
transplant can be enough to
save a patient, but a sizable
percentage of those who eat
Amanita mushrooms die.
The frightening thing about
Amanita poisoning is the
“walking ghost” phase—the
period where you seem to be
fine (or getting better), but
your cells are accumulating
irreversible
and
lethal
damage.
This pattern is typical of
DNA damage, and we’d
likely see something like it in
someone who lost their
DNA.
The picture is even more
vividly illustrated by two
other examples of DNA
damage: chemotherapy and
radiation.
Radiation and
chemotherapy
Chemotherapy drugs
are
blunt instruments. Some are
more precisely targeted than
others, but many simply
interrupt cell division in
general. The reason that this
selectively kills cancer cells,
instead of harming the
patient and the cancer
equally, is that cancer cells are
dividing all the time, whereas
most normal cells divide only
occasionally.
Some human cells do divide
constantly. The most rapidly
dividing cells are found in the
bone marrow, the factory that
produces blood.
Bone marrow is also central
to the human immune
system. Without it, we lose
the ability to produce white
blood cells, and our immune
system
collapses.
Chemotherapy causes damage
to the immune system, which
makes
cancer
patients
vulnerable
to
stray
infections.5
There are other types of
rapidly dividing cells in the
body. Our hair follicles and
stomach lining also divide
constantly, which is why
chemotherapy can cause hair
loss and nausea.
Doxorubicin, one of the
most common and potent
chemotherapy drugs, works
by linking random segments
of DNA to one another to
tangle them. This is like
dripping superglue on a ball
of yarn; it binds the DNA
into a useless tangle.6 The
initial
side
effects
of
doxorubicin, in the few days
after treatment, are nausea,
vomiting,
and
diarrhea
—which makes sense, since
the drug kills cells in the
digestive tract.
A loss of DNA would cause
similar cell death, and
probably similar symptoms.
Radiation
Large doses of gamma
radiation also harm you by
damaging
your
DNA;
radiation
poisoning
is
probably the kind of real-life
injury that most resembles
Nina’s scenario. The cells
most sensitive to radiation
are, as with chemotherapy,
those in your bone marrow,
followed by those in your
digestive tract.7
Radiation poisoning, like
destroying angel mushroom
toxicity, has a latent period—
a “walking ghost” phase. This
is the period where the body
is still working, but no new
proteins can be synthesized
and the immune system is
collapsing.
In cases of severe radiation
poisoning,
the
immune
system collapse is the primary
cause of death. Without a
supply of white blood cells,
the body can’t fight off
infections,
and
ordinary
bacteria can get into the body
and run wild.
The end result
Losing your DNA would
most
likely
result
in
abdominal pain, nausea,
dizziness, rapid immune
system collapse, and death
within days or hours from
either rapid systemic infection
or systemwide organ failure.
On the other hand, there
would be at least one silver
lining. If we ever end up in a
dystopian
future
where
Orwellian
governments
collect
our
genetic
information and use it to
track and control us . . .
. . . you’d be invisible.
1 Yes, “centrifugal.” I will fight
you.
2 I don’t have a citation for this,
but I feel like we would have
heard about it.
3 There are several members of
the Amanita genus called
“destroying angel,” and —
along with another Amanita
called “death cap” — they are
responsible for the vast majority
of fatal mushroom poisonings.
4 Citation: I got one of your
friends to sneak into your room
with a microscope while you
were sleeping and check.
5 Immune boosters like
pegfilgrastim (Neulasta) make
frequent doses of chemotherapy
safer. They stimulate white
blood cell production by, in
effect, tricking the body into
thinking that it has a massive
E. coli infection that it needs to
fight off.
6 Although it’s a little different;
if you drip superglue on cotton
thread, it will catch fire.
7 Extremely high radiation
doses kill people quickly, but
not because of DNA damage.
Instead, they physically dissolve
the blood-brain barrier,
resulting in rapid death from
cerebral hemorrhage (brain
bleeding).
INTERPLANET
CESSNA
Q. What
would
happen if you
tried to fly a
normal Earth
airplane
above
different solar
system
bodies?
—Glen Chiacchieri
A. HERE’S
AIRCRAFT:1
OUR
We have to use an electric
motor because gas engines
work only near green plants.
On worlds without plants,
oxygen doesn’t stay in the
atmosphere—it
combines
with other elements to form
things like carbon dioxide and
rust. Plants undo this by
stripping the oxygen back out
and pumping it into the air.
Engines need oxygen in the
air to run.2
Here’s our pilot:
Here’s what would happen
if our aircraft were launched
above the surface of the 32
largest solar system bodies:
In most cases, there’s no
atmosphere, and the plane
would fall straight to the
ground. If it were dropped
from 1 kilometer or less, in a
few cases the crash would be
slow enough that the pilot
could survive—although the
life-support
equipment
probably wouldn’t.
There are nine solar system
bodies with atmospheres
thick enough to matter: Earth
—obviously—Mars, Venus,
the four gas giants, Saturn’s
moon Titan, and the Sun.
Let’s take a closer look at
what would happen to a plane
on each one.
The Sun: This would work
about as well as you’d
imagine. If the plane were
released close enough to the
Sun to feel its atmosphere at
all, it would be vaporized in
less than a second.
Mars: To see what would
happen to our aircraft on
Mars, we turn to X-Plane.
X-Plane is the most
advanced flight simulator in
the world. The product of 20
years of obsessive labor by a
hardcore
aeronautics
enthusiast3 and community
of
supporters,
it
actually
simulates the flow of air over
every piece of an aircraft’s
body as it flies. This makes it
a valuable research tool, since
it can accurately simulate
entirely new aircraft designs
—and new environments.
In particular, if you change
the X-Plane config file to
reduce gravity, thin the
atmosphere, and shrink the
radius of the planet, it can
simulate flight on Mars.
X-Plane tells us that flight
on Mars is difficult, but not
impossible. NASA knows
this, and has considered
surveying Mars by airplane.
The tricky thing is that with
so little atmosphere, to get
any lift, you have to go fast.
You need to approach Mach
1 just to get off the ground,
and once you get moving, you
have so much inertia that it’s
hard to change course—if you
turn, your plane rotates, but
keeps moving in the original
direction.
The
X-Plane
author compared piloting
Martian aircraft to flying a
supersonic ocean liner.
Our Cessna 172 wouldn’t
be up to the challenge. If
launched from 1 km, it
wouldn’t build up enough
speed to pull out of a dive,
and would plow into the
Martian terrain at over 60
m/s (135 mph). If dropped
from 4 or 5 kilometers, it
could gain enough speed to
pull up into a glide—at over
half the speed of sound. The
landing would not be
survivable.
Venus: Unfortunately, X-
Plane is not capable of
simulating
the
hellish
environment near the surface
of Venus. But physics
calculations give us an idea of
what flight there would be
like. The upshot is: Your
plane would fly pretty well,
except it would be on fire the
whole time, and then it would
stop flying, and then stop
being a plane.
The atmosphere on Venus
is over 60 times denser than
Earth’s. It’s thick enough that
a Cessna moving at jogging
speed would rise into the air.
Unfortunately, that air is hot
enough to melt lead. The
paint would start melting off
in seconds, the plane’s
components
would
fail
rapidly, and the plane would
glide gently into the ground
as it came apart under the
heat stress.
A much better bet would be
to fly above the clouds. While
Venus’s surface is awful, its
upper
atmosphere
is
surprisingly Earthlike. At 55
kilometers, a human could
survive with an oxygen mask
and a protective wetsuit; the
air is room temperature and
the pressure is similar to that
on Earth mountains. You
would need the wetsuit,
though, to protect you from
the sulfuric acid.4
The acid’s no fun, but it
turns out the area right above
the clouds is a great
environment for an airplane,
as long as it has no exposed
metal to be corroded away by
the sulfuric acid. And is
capable of flight in constant
category-5-hurricane-level
winds, which are another
thing I forgot to mention
earlier.
Venus is a terrible place.
Jupiter:
Our
Cessna
wouldn’t be able to fly on
Jupiter; the gravity is just too
strong. The power needed to
maintain level flight under
Jupiter’s gravity is three times
greater than that on Earth.
Starting from a friendly sealevel pressure, we’d accelerate
through the tumbling winds
into a 275 m/s (600 mph)
downward glide deeper and
deeper through the layers of
ammonia ice and water ice
until we and the aircraft were
crushed. There’s no surface to
hit;
Jupiter
transitions
smoothly from gas to liquid
as you sink deeper and
deeper.
Saturn: The picture here is
a little friendlier than on
Jupiter. The weaker gravity—
close to Earth’s, actually
—and slightly denser (but
still thin) atmosphere mean
that we’d be able to struggle
along a bit further before we
gave in to either the cold or
high winds and descended to
the same fate as on Jupiter.
Uranus: Uranus is a
strange, uniform bluish orb.
There are high winds and it’s
bitterly
cold.
It’s
the
friendliest of the gas giants to
our Cessna, and you could
probably fly for a little while.
But given that it seems to be
an
almost
completely
featureless planet, why would
you want to?
Neptune: If you’re going to
fly around one of the ice
giants, I would probably
recommend Neptune5 over
Uranus. It at least has some
clouds to look at before you
freeze to death or break apart
from the turbulence.
Titan: We’ve saved the best
for last. When it comes to
flying, Titan might be better
than Earth. Its atmosphere is
thick but its gravity is light,
giving it a surface pressure
only 50 percent higher than
Earth’s with air four times as
dense. Its gravity—lower than
that of the Moon—means
that flying is easy. Our
Cessna could get into the air
under pedal power.
In fact, humans on Titan
could fly by muscle power. A
human in a hang glider could
comfortably take off and
cruise around powered by
oversized swim-flipper boots
—or even take off by flapping
artificial wings. The power
requirements are minimal—it
would probably take no more
effort than walking.
The downside (there’s
always a downside) is the
cold. It’s 72 kelvin on Titan,
which
is
about
the
temperature
of
liquid
nitrogen. Judging from some
numbers
on
heating
requirements
for
light
aircraft, I estimate that the
cabin of a Cessna on Titan
would probably cool by about
2 degrees per minute.
The batteries would help to
keep themselves warm for a
little while, but eventually the
craft would run out of heat
and crash. The Huygens
probe, which descended with
batteries
nearly
drained,
taking fascinating pictures as
it fell, succumbed to the cold
after only a few hours on the
surface. It had enough time to
send back a single photo after
landing—the only one we
have from the surface of a
body beyond Mars.
If humans put on artificial
wings to fly, we might
become Titanian versions of
the Icarus story—our wings
could freeze, fall apart, and
send us tumbling to our
deaths.
But I’ve never seen the
Icarus story as a lesson about
the limitations of humans. I
see it as a lesson about the
limitations of wax as an
adhesive. The cold of Titan is
just an engineering problem.
With the right refitting, and
the right heat sources, a
Cessna 172 could fly on Titan
—and so could we.
1 The Cessna 172 Skyhawk,
probably the most common
plane in the world.
2 Also, our gasoline is MADE
of ancient plants.
3 Who uses capslock a lot when
talking about planes.
4 I’m not selling this well, am
I?
5 Motto: “The Slightly Bluer
One.”
WEIRD
(AND
WORRYING)
QUESTIONS
FROM
THE
WHAT IF?
INBOX, #6
Q . What is the
total
nutritional
value (calories,
fat, vitamins,
minerals, etc.)
of the average
human body?—
Justin Risner
Q.
What
temperature
would a
chainsaw (or
other cutting
implement)
need to be at
to instantly
cauterize any
injuries
inflicted with
it?
—Sylvia Gallagher
YODA
Q. How
much Force
power can
Yoda output?
—Ryan Finnie
A. I’M
GOING TO—of
course—ignore
the
prequels.
Yoda’s greatest display of
raw power in the original
trilogy came when he lifted
Luke’s X-wing from the
swamp. As far as physically
moving objects around goes,
this was easily the biggest
expenditure
of
energy
through the Force we saw
from anyone in the trilogy.
The energy it takes to lift
an object to a given height is
equal to the object’s mass
times the force of gravity
times the height it’s lifted.
The X-wing scene lets us use
this to put a lower limit on
Yoda’s peak power output.
First we need to know how
heavy the ship was. The Xwing’s mass has never been
canonically established, but
its length has—12.5 meters.
An F-22 is 19 meters long
and weighs 19,700 kg, so
scaling down from this gives
an estimate for the X-wing of
about 12,000
metric tons).
pounds
(5
Next, we need to know how
fast it was rising. I went over
footage of the scene and
timed the X-wing’s rate of
ascent as it was emerging
from the water.
The front landing strut rises
out of the water in about
three and a half seconds, and
I estimated the strut to be 1.4
meters long (based on a scene
in A New Hope where a crew
member squeezes past it),
which tells us the X-wing was
rising at 0.39 m/s.
Lastly, we need to know the
strength of gravity on
Dagobah. Here, I figure I’m
stuck, because while sci-fi
fans are obsessive, it’s not like
there’s gonna be a catalog of
minor
geophysical
characteristics for every planet
visited in Star Wars. Right?
Nope. I’ve underestimated
the fandom. Wookieepeedia
has just such a catalog, and
informs us that the surface
gravity on Dagobah is 0.9g.
Combining this with the Xwing mass and lift rate gives
us our peak power output:
That’s enough to power a
block of suburban homes. It’s
also equal to about 25
horsepower, which is about
the power of the motor in the
electric-model Smart Car.
At current electricity prices,
Yoda would be worth about
$2/hour.
But telekinesis is just one
type of Force power. What
about that lightning the
Emperor used to zap Luke?
The physical nature of it is
never made clear, but Tesla
coils that produce similar
displays draw something like
10 kilowatts—which would
put the Emperor roughly on
par with Yoda. (Those Tesla
coils typically use lots of very
short pulses. If the Emperor
is sustaining a continuous arc,
as in an arc welder, the power
could easily be in the
megawatts.)
What about Luke? I
examined the scene where he
used his nascent Force powers
to yank his lightsaber out of
the snow. The numbers are
harder to estimate here, but I
went through frame-by-frame
and came up with an estimate
of 400 watts for his peak
output. This is a fraction of
Yoda’s 19kW, and was
sustained for only a fraction
of a second.
So Yoda sounds like our
best bet as an energy source.
But with world electricity
consumption
pushing
2
terawatts, it would take a
hundred million Yodas to
meet our demands. All things
considered, switching to Yoda
power probably isn’t worth
the trouble—though it would
definitely be green.
FLYOVER
STATES
Q. Which US
state is
actually flown
over the
most?
—Jesse Ruderman
A. WHEN
PEOPLE SAY
“FLYOVER
states,”
they’re usually referring to the
big, square states out west
that people stereotypically
cross over while flying
between New York, LA, and
Chicago, but don’t actually
land in.
But what state do the
largest number of planes
actually fly over? There are a
lot of flights up and down the
East Coast; it would be easy
to imagine that people fly
over New York more often
than Wyoming.
To figure out what the real
flyover states are, I looked at
over 10,000 air traffic routes,
determining which states
each flight passed over.
Surprisingly, the state with
the most planes flying over it
—without taking off or
landing—is . . .
. . . Virginia.
This result surprised me. I
grew up in Virginia, and I
certainly never thought of it
as a “flyover state.”
It’s
surprising
because
Virginia has several major
airports; two of the airports
serving DC are actually
located
in
Virginia
(DCA/Reagan
and
IAD/Dulles). This means
most flights to DC don’t
count toward flights over
Virginia, since those flights
land in Virginia.
Here’s a map of US states
colored by number of daily
flyovers:
Close behind Virginia are
Maryland, North Carolina,
and Pennsylvania. These
states have substantially more
daily flyovers than any other.
So why Virginia?
There are a number of
factors, but one of the biggest
is
Hartsfield-Jackson
Atlanta
International
Airport.
Atlanta’s airport is the
busiest in the world, with
more passengers and flights
than Tokyo, London, Beijing,
Chicago, or Los Angeles. It’s
the main hub airport for
Delta
Air
Lines—until
recently the world’s largest
airline—which
means
passengers
taking
Delta
flights will often connect
through Atlanta.
Thanks to the large volume
of flights from Atlanta to the
northeast US, 20 percent of
all Atlanta flights cross
Virginia and 25 percent cross
North Carolina, contributing
substantially to the totals for
each state.
However, Atlanta isn’t the
biggest
contributor
to
Virginia’s totals. The airport
with the most flights over
Virginia was a surprise to me.
Toronto
Pearson
International Airport (YYZ)
seems an unlikely source of
Virginia-crossing flights, but
Canada’s
largest
airport
contributes more flights over
Virginia than New York’s
JFK and LaGuardia airports
combined.
Part of the reason for
Toronto’s dominance is that
it has many direct flights to
the Caribbean and South
America, which cross US
airspace on the way to their
destinations.1 In addition to
Virginia, Toronto is also the
chief source of flights over
West Virginia, Pennsylvania,
and New York.
This map shows, for each
state, which airport is the
source of the most flights over
it:
Flyover states by ratio
Another possible definition of
“flyover state” is the state that
has the highest ratio of flights
over it to flights to it. By this
measure, the flyover states
are, for the most part, simply
the least dense states. The top
ten include, predictably,
Wyoming, Alaska, Montana,
Idaho, and the Daktoas.
The state with the highest
ratio
of
flights-over-toflights-to, however, is a
surprise: Delaware.
A little digging turned up
the
very
straightforward
reason: Delaware has no
airports.
Now, that’s not quite true.
Delaware has a number of
airfields, including Dover Air
Force Base (DOV) and New
Castle Airport (ILG). New
Castle Airport is the only one
that might qualify as a
commercial airport, but after
Skybus Airlines shut down in
2008, the airport had no
airlines serving it.2
Least flown-over state
The least flown-over state is
Hawaii, which makes sense.
It consists of tiny islands in
the middle of the world’s
biggest ocean; you have to try
pretty hard to hit it.
Of the 49 non-island
states,3 the least flown-over
state is California. This came
as a surprise to me, since
California is long and skinny,
and it seems like a lot of
flights over the Pacific would
need to pass over it.
However, since jet-fuelladen planes were used as
weapons on 9/11, the FAA
has tried to limit the number
of unnecessarily fuel-heavy
flights crossing the US, so
most international travelers
who might otherwise travel
over California instead take a
connecting flight from one of
the airports there.
Fly-under states
Lastly, let’s answer a slightly
stranger question: What is
the most flown-under state?
That is, what state has the
most flights on the opposite
side of the Earth pass directly
under its territory?
The answer turns out to be
Hawaii.
The reason such a tiny state
wins in this category is that
most of the US is opposite
the Indian Ocean, which has
very few commercial flights
over it. Hawaii, on the other
hand, is opposite Botswana in
Central Africa. Africa doesn’t
have a high volume of flights
over it compared to most
other continents, but it’s
enough to win Hawaii the top
spot.
Poor Virginia
As someone who grew up
there, it’s hard for me to
accept Virginia’s status as the
most flown-over state. If
nothing else, when I’m back
home with family, I’ll try to
remember—once in a while
—to look up and wave.
(And if you find yourself on
Arik Air Flight 104 from
Johannesburg, South Africa
to Lagos, Nigeria—daily
service, departing at 9:35 A.M.
—remember to look down
and say “Aloha!”)
1 It helps that Canada, unlike
the US, has extensive
commercial flight service to
Cuba.
2 This changed in 2013, when
Frontier Airlines began
operating a route between New
Castle Airport and Fort Myers,
Florida. This wasn’t included in
my data set, and it’s possible
Frontier will bump Delaware
down the list.
3 I’m including Rhode Island
here, although it seems wrong
to.
FALLING
WITH
HELIUM
Q. What if I
jumped out of
an airplane
with a couple
of tanks of
helium and
one huge, uninflated
balloon?
Then, while
falling, I
release the
helium and
fill the
balloon. How
long of a fall
would I need
in order for
the balloon to
slow me
enough that I
could land
safely?
—Colin Rowe
A. AS
RIDICULOUS AS
IT sounds, this is—sort of
—plausible.
Falling from great heights is
dangerous.[citation needed ] A
balloon could actually help
save you, although a regular
helium one from a party
obviously won’t do the trick.
If the balloon is large
enough, you don’t even need
the helium. A balloon will act
as a parachute, slowing your
fall to nonfatal speeds.
Avoiding a high-speed
landing is, unsurprisingly, the
key to survival. As one
medical paper put it . . .
It is, of course, obvious
that speed, or height of
fall, is not in itself
injurious . . . but a high
rate of change of velocity,
such as occurs after a 10
story fall onto concrete, is
another matter.
. . . which is just a wordy
version of the old saying “It’s
not the fall that kills you, it’s
the sudden stop at the end.”
To act as a parachute, a
balloon filled with air—rather
than helium—would have to
be 10 to 20 meters across, far
too big to be inflated with
portable tanks. A powerful
fan could be used to fill it
with ambient air, but at that
point, you may as well just
use a parachute.
Helium
The helium makes things
easier.
It doesn’t take too many
helium balloons to lift a
person. In 1982, Larry
Walters flew across Los
Angeles in a lawn chair lifted
by
weather
balloons,
eventually reaching several
miles in altitude. After
passing
through
LAX
airspace, he descended by
shooting some of the balloons
with a pellet gun.
On landing, Walters was
arrested,
although
the
authorities had some trouble
figuring out what to charge
him with. At the time, an
FAA safety inspector told the
New York Times, “We know
he broke some part of the
Federal Aviation Act, and as
soon as we decide which part
it is, some type of charge will
be filed.”
A relatively small helium
balloon—certainly
smaller
than a parachute—will suffice
to slow your fall, but it still
has to be huge by party
balloon
standards.
The
biggest
consumer
rental
helium tanks are about 250
cubic feet, and you would
need to empty at least ten of
them to put enough air in the
balloon to support your
weight.
You’d have to do it quickly.
Compressed helium cylinders
are smooth and often quite
heavy, which means they have
a high terminal velocity.
You’ll have only a few
minutes to use up all the
cylinders. (As soon as you
emptied one, you could drop
it.)
You can’t get around this
problem by moving your
starting point higher. As we
learned from the steak
incident, since the upper
atmosphere is pretty thin,
anything dropped from the
stratosphere or higher will
accelerate to very high speeds
until it hits the lower
atmosphere, then fall slowly
the rest of the way. This is
true of everything from small
meteors1
to
Felix
Baumgartner.
But if you inflated the
balloons quickly, possibly by
connecting many canisters to
it at once, you’d be able to
slow your fall. Just don’t use
too much helium, or you’ll
end up floating at 16,000 feet
like Larry Walters.
While researching this
answer, I managed to lock up
my copy of Mathematica
several times on balloonrelated differential equations,
and subsequently got my IP
address
banned
from
Wolfram|Alpha for making
too many requests. The banappeal form asked me to
explain what task I was
performing that necessitated
so many queries. I wrote,
“Calculating how many rental
helium tanks you’d have to
carry with you in order to
inflate a balloon large enough
to act as a parachute and slow
your fall from a jet aircraft.”
Sorry, Wolfram.
1 While researching impact
speeds for this answer, I came
across a discussion on the
Straight Dope Message Board
about survivable fall heights.
One poster compared a fall
from height to being hit by a
bus. Another user, a medical
examiner, replied that this was
a bad comparison:
“When hit by a car,
the vast majority of
people are not run
over; they are run
under. The lower
legs break, sending
them into the air.
They usually strike
the hood of the car,
often with the back
of the head
impacting the
windshield, ‘starring’
the windshield,
possibly leaving a
few hairs in the
glass. They then go
over the top of the
car. They are still
alive, although with
broken legs, and
maybe with head
pain from the
nonfatal windshield
impact. They die
when they hit the
ground. They die
from head injury.”
The lesson: Don’t mess with
medical examiners. They’re
apparently pretty hardcore.
EVERYBODY
OUT
Q. Is there
enough
energy to
move the
entire current
human
population
off-planet?
—Adam
A. THERE
ARE
A
BUNCH
of
science
fiction movies where, because
of pollution, overpopulation,
or nuclear war, humanity
abandons Earth.
But lifting people into space
is hard. Barring a massive
reduction in the population,
is launching the whole human
race into space physically
possible? Let’s not even worry
about where we’re headed—
we’ll assume we don’t have to
find a new home, but we can’t
stay here.
To figure out if this is
plausible, we can start with an
absolute baseline energy
requirement: 4 gigajoules per
person. No matter how we do
it, whether we use rockets or
a cannon or a space elevator
or a ladder, moving a 65kilogram
person—or
65
kilograms of anything—out
of the Earth’s gravity well
requires at least this much
energy.
How much is 4 gigajoules?
It’s about a megawatt-hour,
which is what a typical US
household
consumes
in
electricity in a month or two.
It’s equal to the amount of
stored energy in 90 kg of
gasoline or a cargo van full of
AA batteries.
Four gigajoules times seven
billion people gives us
2.8×1018 joules, or 8 petawatt-hours. This is about 5
percent of the world’s annual
energy consumption. A lot,
but
not
physically
implausible.
However, 4 gigajoules is
just a minimum. In practice,
everything would depend on
our means of transportation.
If we were using rockets, for
example, it would take a lot
more energy than that. This
is because of a fundamental
problem with rockets: They
have to lift their own fuel.
Let’s return for a moment
to those 90 kilograms of
gasoline (about 30 gallons),
because they help illustrate
this central problem in space
travel.
If we want to launch a 65kilogram spaceship, we need
the energy of around 90
kilograms of fuel. We load
that fuel on board—and now
our spaceship weighs 155
kilograms. A 155-kilogram
spaceship
requires
215
kilograms of fuel, so we load
another 125 kilograms on
board . . .
Fortunately, we’re saved
from an infinite loop—where
we add 1.3 kilograms for
every 1 kilogram we add—by
the fact that we don’t have to
carry that fuel all the way up.
We burn it as we go, so we
get lighter and lighter, which
means we need less and less
fuel. But we do have to lift
the fuel partway. The formula
for how much propellant we
need to burn to get moving at
a given speed is given by the
Tsiolkovsky Rocket equation:
and
are the total mass of the ship
plus the fuel before and after
the
burn,
and
is the “exhaust velocity” of the
fuel, a number that’s between
2.5 and 4.5 km/s for rocket
fuels.
What’s important is the
ratio between
, the speed we want to be
going,
and
, the speed that the propellant
exits our rocket. For leaving
Earth,
we
need
a
of upward of 13 km/s, and
is limited to about 4.5 km/s,
which gives a fuel-to-ship
ratio
of
at
least
. If that ratio is x, then to
launch a kilogram of ship, we
need ex kilograms of fuel.
As x grows, this amount
gets very large.
The upshot is that to
overcome Earth’s gravity
using traditional rocket fuels,
a 1-ton craft needs 20 to 50
tons of fuel. Launching all of
humanity
(total
weight:
around 400 million tons)
would therefore take tens of
trillions of tons of fuel. That’s
a lot; if we were using
hydrocarbon-based fuels, it
would represent a decent
chunk
of
the
world’s
remaining oil reserves. And
that’s not even worrying
about the weight of the ship
itself, food, water, or our
pets.1 We’d also need fuel to
produce all these ships, to
transport people to the launch
sites, and so forth. It’s not
necessarily
completely
impossible, but it’s certainly
outside
the
realm
of
plausibility.
But rockets aren’t our only
option. As crazy as it sounds,
we might be better off trying
to (1) literally climb into
space on a rope, or (2) blow
ourselves off the planet with
nuclear weapons. These are
actually serious—if audacious
—ideas for launch systems,
both of which have been
bouncing around since the
start of the Space Age.
The first approach is the
“space elevator” concept, a
favorite of science fiction
authors. The idea is that we
connect a tether to a satellite
orbiting far enough out that
the tether is held taut by
centrifugal force. Then we
can send climbers up the rope
using ordinary electricity and
motors, powered by solar
power, nuclear generators, or
whatever works best. The
biggest engineering hurdle is
that the tether would have to
be several times stronger than
anything we can currently
build. There are hopes that
carbon
nanotube-based
materials could provide the
required
strength—adding
this to the long list of
engineering problems that
can be waved away by tacking
on the prefix “nano-.”
The second approach is
nuclear pulse propulsion, a
surprisingly plausible method
for getting huge amounts of
material moving really fast.
The basic idea is that you toss
a nuclear bomb behind you
and ride the shockwave.
You’d think the spacecraft
would be vaporized, but it
turns out that if it has a welldesigned shield, the blast
would fling away before it has
a chance to disintegrate. If it
could be made reliable
enough, this system would in
theory be capable of lifting
entire city blocks into orbit,
and
could—potentially
—accomplish our goal.
The engineering principles
behind this were thought to
be solid enough that in the
1960s, under the guidance of
Freeman Dyson, the US
government actually tried to
build one of these spaceships.
The story of that effort,
dubbed Project Orion, is
detailed in the excellent book
of the same name by
Freeman’s
son,
George.
Advocates for nuclear pulse
propulsion
are
still
disappointed that the project
was cancelled before any
prototypes were built. Others
argue that when you think
about what they were trying
to do—put a gigantic nuclear
arsenal in a box, hurl it high
into the atmosphere, and
bomb it repeatedly—it’s
terrifying that it got as far as
it did.
So the answer is that while
sending one person into space
is easy, getting all of us there
would tax our resources to the
limit and possibly destroy the
planet. It’s a small step for a
man, but a giant leap for
mankind.
1 There are probably around a
million tons of pet dog in the
US alone.
WEIRD
(AND
WORRYING)
QUESTIONS
FROM
THE
WHAT IF?
INBOX, #7
Q. In Thor the
main character
is at one point
spinning his
hammer so fast
that he creates
a strong
tornado. Would
this be
possible in real
life?
—Davor
Q.
If you
saved a whole
life’s worth of
kissing and
used all that
suction power
on one single
kiss, how
much suction
force would
that single kiss
have?
—Jonatan Lindström
Q.
How many
nuclear
missiles would
have to be
launched at
the United
States to turn it
into a complete
wasteland?
—Anonymous
SELFFERTILIZATION
Q. I read
about some
researchers
who were
trying to
produce
sperm from
bone marrow
stem cells. If
a woman
were to have
sperm cells
made from
her own stem
cells and
impregnate
herself, what
would be her
relationship
to her
daughter?
—R Scott LaMorte
A. TO
MAKE A HUMAN,
you need to put together
two sets of DNA.
In humans, these two sets
are held in a sperm cell and
an egg cell, each of which
holds a random sample of the
parents’ DNA. (More on how
that randomization works in a
moment.) In humans, these
cells are from two different
people. However, that doesn’t
necessarily have to be the
case. Stem cells, which can
form any type of tissue, could
in principle be used to
produce sperm (or eggs).
So far, nobody has been
able to produce complete
sperm from stem cells. In
2007, a group of researchers
succeeded in turning bone
marrow stem cells into
spermatogonial stem cells.
These
cells
are
the
predecessors to sperm. The
researchers couldn’t get the
cells to fully develop into
sperm, but it was a step. In
2009, the same group
published a paper that
seemed to claim they’d made
the final step and produced
functioning sperm cells.
There were two problems.
First, they didn’t actually
say they had produced sperm
cells. They said they produced
sperm-like cells, but the
media generally glossed over
this. Second, the paper was
retracted by the journal that
published it. It turns out the
authors had plagiarized two
paragraphs of their article
from another paper.
Despite these problems, the
fundamental idea here is not
that far-fetched, and the
answer to R. Scott’s question
turns out to be a little bit
unsettling.
Keeping track of the flow of
genetic information can be
pretty tricky. To help
illustrate it, let’s take a look at
a highly simplified model that
may be familiar to fans of
role-playing games.
Chromosomes: D&D
edition
Human DNA is organized
into 23 segments, called
chromosomes, and each
person has two versions of
each chromosome—one from
their mother and one from
their father.
In our simplified version of
DNA,
instead
of
23
chromosomes, there will be
just seven. In humans, each
chromosome contains a huge
amount of genetic code, but
in
our
model
each
chromosome will control only
one thing.
We’ll use a version of of
D&D’s “d20” system of
character stats in which each
piece of DNA contains seven
chromosomes:
Six of these are the classic
character stats from role-
playing games: strength,
constitution,
dexterity,
charisma,
wisdom,
and
intelligence. The last one is
the
sex-determining
chromosome.
Here’s an example DNA
“strand”:
In
our
model,
each
chromosome contains one
piece of information. This
piece of information is either
a stat (a number, usually
between 1 and 18) or a
multiplier. The last one,
SEX, is the sex-determining
chromosome, which, as with
real human genetics, can be
“X” or “Y.”
Just like in real life, each
person has two sets of
chromosomes—one
from
their mother and one from
their father. Imagine that
your genes looked like this:
The combination of these
two sets of stats determines a
person’s
characteristics.
Here’s the simple rule for
combining stats in our
system:
If you have a number for
both
versions
of
a
chromosome, you get the
bigger number as your stat. If
you have a number on one
chromosome
and
a
multiplier on the other, your
stat is the number times the
multiplier. If you have a
multiplier on both sides, you
get a stat of 1.1
Here’s
how
our
hypothetical character from
earlier would turn out:
When
one
parent
contributes a multiplier and
the other contributes a
number, the result can be very
good!
This
character’s
constitution is a superhuman
24. In fact, other than a low
score in wisdom, this
character has great stats all
around.
Now, let’s say this character
(call her “Alice”) meets
someone else (“Bob”):
Bob also has stellar stats:
If they have a child, each
one will contribute a strand of
DNA. But the strand they
contribute will be a random
mix of their mother and
father strands. Every sperm
cell—and every egg cell—
contains
a
random
combination of chromosomes
from each strand. So let’s say
Bob and Alice make the
following sperm and egg:
If these sperm and egg
combine, the child’s stats will
look like this:
Alice has her mother’s
strength and her father’s
wisdom. She also has
superhuman
intelligence,
thanks to the very good 14
contributed by Alice and the
multiplier contributed by
Bob. Her constitution, on the
other hand, is much weaker
than either of her parents,
since her mother’s 2x
multiplier could only do so
much
with
the
“5”
contributed by her father.
Alice and Bob both had a
multiplier on their paternal
“charisma”
chromosome.
Since
two
multipliers
together result in a stat of 1,
if Alice and Bob had both
contributed their multiplier,
the child would have a rockbottom CHR. Fortunately,
the odds of this happening
were only 1 in 4.
If the child had multipliers
on both strands, the stat
would have been reduced to
1.
Fortunately,
since
multipliers are relatively rare,
the odds of them lining up in
two random people are low.
Now let’s look at what
would happen if Alice had a
child with herself.
First, she’d produce a pair
of sex cells, which would run
the random selection process
twice:
Then the selected strands
would be contributed to the
child:
The child is guaranteed to
be female, since there’s
nobody to contribute a Y
chromosome.
The child also has a
problem: For three of her
seven stats—INT, DEX, and
CON—she inherited the
same chromosome on both
sides. This isn’t a problem for
DEX and CON, since Alice
had a high score in those two
categories, but in CON,she
inherited a multiplier from
both sides, giving her a
constitution score of 1.
If someone produces a child
on their own, it dramatically
increases the likelihood that
the child will inherit the same
chromosome on both sides,
and thus a double multiplier.
The odds of Alice’s child
having a double multiplier are
58 percent—compared to the
25 percent chance for a child
with Bob.
In general, if you have a
child with yourself, 50
percent of your chromosomes
will have the same stat on
both sides. If that stat is a 1—
or if it’s a multiplier—the
child will be in trouble, even
though you might not have
been. This condition, having
the same genetic code on
both copies of a chromosome,
is called homozygosity.
Humans
In humans, probably the most
common genetic disorder
caused by inbreeding is spinal
muscular atrophy (SMA).
SMA causes the death of the
cells in the spinal cord, and is
often fatal or severely
disabling.
SMA is caused by an
abnormal version of a gene on
chromosome 5. About 1 in 50
people have this abnormality,
which means 1 in 100 people
will contribute it to their
children . . . and, therefore, 1
in 10,000 people (100 times
100) will inherit the defective
gene from both parents.2
If a parent has a child with
his- or herself, on the other
hand, the chance of SMA is 1
in 400—since if he or she has
a copy of the defective gene
(1 in 100), there’s a 1 in 4
chance it will be the child’s
only copy.
One in 400 may not sound
so bad, but SMA is only the
start.
DNA is complicated
DNA is source code for the
most complex machine in the
known
universe.
Each
chromosome
contains
a
staggering
amount
of
information,
and
the
interaction between DNA
and the cell machinery
around it is incredibly
complicated, with countless
moving parts and Mousetrapstyle feedback loops. Even
calling DNA “source code”
sells it short—compared to
DNA, our most complex
programming projects are like
pocket calculators.
In
humans,
each
chromosome affects many
things through a variety of
mutations and variations.
Some of these mutations, like
the one responsible for SMA,
seem to be entirely negative;
the mutation responsible has
no benefit. In our D&D
system,
it’s
like
a
chromosome having an STR
of 1. If your other
chromosome is normal, you’ll
have a normal character stat;
you’ll be a silent “carrier.”
Other mutations, like the
sickle-cell
gene
on
chromosome 11, can provide
a mix of benefit and harm.
People who have the sickle-
cell gene on both their copies
of the chromosome suffer
from sickle-cell anemia.
However, if they have the
gene on just one of their
chromosomes, they get a
surprise
benefit:
extra
resistance to malaria.
In the D&D system, this is
like a “2x” multiplier. One
copy of the gene can make
you stronger, but two copies
—double multipliers—lead to
a serious disorder.
These two diseases illustrate
one reason that genetic
diversity
is
important.
Mutations pop up all over the
place, but our redundant
chromosomes help blunt this
effect.
By
avoiding
inbreeding, a population
reduces the odds that rare and
harmful mutations will pop
up at the same place on both
sides of the chromosome.
Inbreeding coefficient
Biologists use a number called
the “inbreeding coefficient” to
quantify the percentage of
someone’s chromosomes that
are likely to be identical. A
child from unrelated parents
has an inbreeding coefficient
of 0, while one who has a
completely duplicated set of
chromosomes
has
an
inbreeding coefficient of 1.
This brings us to the answer
to the original question. A
child from a parent who selffertilized would be like a
clone of the parent with
severe genetic damage. The
parent would have all the
genes the child would, but the
child wouldn’t have all the
genes of the parent. Half the
child’s chromosomes would
have
their
“partner”
chromosomes replaced by a
copy of themselves.
This means the child would
have an inbreeding coefficient
of 0.50. This is very high; it’s
what you would expect in a
child of three generations of
consecutive sibling marriages.
According to D. S. Falconer’s
Introduction to Quantitative
Genetics,
an
inbreeding
coefficient of 0.50 would
result in an average of a 22point reduction in IQ and a
4-inch reduction in height at
age ten. There would be a
very good chance that the
resulting fetus would not
survive to birth.
This kind of inbreeding was
famously exhibited by royal
families attempting to keep
their bloodlines “pure.” The
European
House
of
Hapsburg, a family of
European rulers from the
mid-second millennium, was
marked by frequent cousin
marriages, culminating in the
birth of King Charles II of
Spain.
Charles had an inbreeding
coefficient of 0.254, making
him slightly more inbred than
a child of two siblings
(0.250). He suffered from
extensive
physical
and
emotional disabilities, and
was a strange (and largely
ineffective) king. In one
incident,
he
reportedly
ordered that the corpses of his
relatives be dug up so he
could look at them. His
inability to bear children
marked the end of that royal
bloodline.
Self-fertilization is a risky
strategy, which is why sex is
so popular among large and
complex organisms.3 There
are occasionally complex
animals
that
reproduce
asexually,4 but this behavior
is relatively rare. It typically
appears in environments
where
it’s
difficult
to
reproduce sexually, whether
due to resource scarcity,
population isolation . . .
Life finds a way.
. . . or overconfident theme
park operators.
1 Because 1 is the multiplicative
identity.
2 Some forms of SMA are
actually caused by a defect in
two genes, so in practice the
statistical picture is a little more
complicated.
3 Well, one of the reasons.
4 “Tremblay’s Salamander” is a
hybrid species of salamander
that reproduces exclusively by
self-fertilizing. These
salamanders are an all-female
species, and — strangely —
have three genomes instead of
two. To breed, they go through
a courtship ritual with male
salamanders of related species,
then lay self-fertilized eggs.
The male salamander gets
nothing out of it; he’s simply
used to stimulate egg-laying.
HIGH
THROW
Q. How high
can a human
throw
something?
—Irish Dave on the Isle of
Man
A. HUMANS
ARE GOOD
AT throwing things. In
fact, we’re great at it; no other
animal can throw stuff like we
can.
It’s true that chimpanzees
hurl feces (and, on rare
occasions, stones), but they’re
not nearly as accurate or
precise as humans. Antlions
throw sand, but they don’t
aim it. Archerfish hunt
insects by throwing water
droplets, but they use
specialized mouths instead of
arms. Horned lizards shoot
jets of blood from their eyes
for distances of up to 5 feet. I
don’t know why they do this
because whenever I reach the
phrase “shoot jets of blood
from their eyes” in an article I
just stop there and stare at it
until I need to lie down.
So while there are other
animals that use projectiles,
we’re just about the only
animal that can grab a
random object and reliably
nail a target. In fact, we’re so
good at it that some
researchers have suggested
that rock-throwing played a
central role in the evolution
of the modern human brain.
Throwing is hard.1 In order
to deliver a baseball to a
batter, a pitcher has to release
the ball at exactly the right
point in the throw. A timing
error of half a millisecond in
either direction is enough to
cause the ball to miss the
strike zone.
To put that in perspective,
it
takes
about
five
milliseconds for the fastest
nerve impulse to travel the
length of the arm. That
means that when your arm is
still rotating toward the
correct position, the signal to
release the ball is already at
your wrist. In terms of
timing, this is like a drummer
dropping a drumstick from
the tenth story and hitting a
drum on the ground on the
correct beat.
We seem to be much better
at throwing things forward
than throwing them upward.2
Since we’re going for
maximum height, we could
use projectiles that curve
upward when you throw them
forward; the Aerobie Orbiters
I had when I was a kid often
got stuck in the highest
treetops.3 But we could also
sidestep the whole problem
by using a device like this
one:
A mechanism for hitting yourself in
the head with a baseball after a foursecond delay
We
could
use
a
springboard, a greased chute,
or even a dangling sling
—anything that redirects the
object upward without adding
to or subtracting from its
speed. Of course, we could
also try this:
I ran through the basic
aerodynamic calculations for a
baseball thrown at various
speeds. I will give these
heights in units of giraffes:
The average person can
probably throw a baseball at
least three giraffes high:
Someone with a reasonably
good arm could manage five:
A pitcher with an 80 mph
fastball could manage ten
giraffes:
Aroldis Chapman, the
holder of the world record for
fastest recorded pitch (105
mph), could in theory launch
a baseball 14 giraffes high:
But what about projectiles
other than a baseball?
Obviously, with the aid of
tools like slings, crossbows, or
the curved xistera scoops in
jai alai, we can launch
projectiles much faster than
that. But for this question,
let’s assume we stick to barehanded throwing.
A baseball is probably not
the ideal projectile, but it’s
hard to find speed data on
other kinds of thrown objects.
Fortunately, a British javelin
thrower
named
Roald
Bradstock held a “random
object throwing competition,”
in which he threw everything
from dead fish to an actual
kitchen sink. Bradstock’s
experience gives us a lot of
useful data.4 In particular, it
suggests a potentially superior
projectile: a golf ball.
Few professional athletes
have been recorded throwing
golf
balls.
Fortunately,
Bradstock has, and he claims
a record throw of 170 yards.
This involved a running start,
but even so, it’s reason to
think that a golf ball might
work better than a baseball.
From a physics standpoint, it
makes sense; the limiting
factor in baseball pitches is
the torque on the elbow, and
the lighter golf ball might
allow the pitching arm to
move slightly faster.
The speed improvement
from using a golf ball instead
of a baseball would probably
not be very large, but it seems
plausible that a professional
pitcher with some time to
practice could throw a golf
ball faster than a baseball.
If so, based on aerodynamic
calculations,
Aroldis
Chapman could probably
throw a golf ball about sixteen
giraffes high:
This is probably about the
maximum possible altitude
for a thrown object.
. . . unless you count the
technique by which any fiveyear-old can beat all these
records easily.
1 Citation: my Little League
career.
2 Counterexample: my Little
League career.
3 Where they remained forever.
4 And a lot of other data, too.
LETHAL
NEUTRINOS
Q. How close
would you
have to be to
a supernova
to get a lethal
dose of
neutrino
radiation?
—Dr. Donald Spector
A. THE
PHRASE
“LETHAL DOSE of
neutrino radiation” is a weird
one. I had to turn it over in
my head a few times after I
heard it.
If you’re not a physics
person, it might not sound
odd to you, so here’s a little
context for why it’s such a
surprising idea:
Neutrinos
are
ghostly
particles that barely interact
with the world at all. Look at
your hand—there are about a
trillion neutrinos from the
Sun passing through it every
second.
Okay, you can stop looking at your
hand now.
The reason you don’t notice
the neutrino flood is that
neutrinos
mostly
ignore
ordinary matter. On average,
out of that massive flood,
only one neutrino will “hit”
an atom in your body every
few years.1
In fact, neutrinos are so
shadowy that the entire Earth
is transparent to them; nearly
all of the Sun’s neutrino
steam goes straight through it
unaffected.
To
detect
neutrinos, people build giant
tanks filled with hundreds of
tons of target material in the
hopes that they’ll register the
impact of a single solar
neutrino.
This means that when a
particle accelerator (which
produces neutrinos) wants to
send a neutrino beam to a
detector somewhere else in
the world, all it has to do is
point the beam at the
detector—even if it’s on the
other side of the Earth!
That’s why the phrase
“lethal dose of neutrino
radiation” sounds weird—it
mixes
scales
in
an
incongruous way. It’s like the
idiom “knock me over with a
feather” or the phrase
“football stadium filled to the
brim with ants.”2 If you have
a math background, it’s sort
of like seeing the expression
“ln(x)e”—it’s not that, taken
literally, it doesn’t make sense
—it’s that you can’t imagine a
situation
apply.3
where
it
would
Similarly, it’s hard to
produce enough neutrinos to
get even a single one of them
to interact with matter; it’s
strange to imagine a scenario
in which there’d be enough of
them to hurt you.
Supernovae provide that
scenario.4 Dr. Spector, the
Hobart and William Smith
Colleges physicist who asked
me this question, told me his
rule of thumb for estimating
supernova-related numbers:
However big you think
supernovae are, they’re bigger
than that.
Here’s a question to give
you a sense of scale. Which of
the following would be
brighter, in terms of the
amount of energy delivered to
your retina:
A supernova, seen from as
far away as the Sun is from
the Earth, or the detonation
of a hydrogen bomb pressed
against your eyeball?
Can you hurry up and set it off?
This is heavy.
Applying Dr. Spector’s rule
of thumb suggests that the
supernova is brighter. And
indeed, it is . . . by nine
orders of magnitude.
That’s why this is a neat
question—supernovae
are
unimaginably
huge
and
neutrinos are unimaginably
insubstantial. At what point
do these two unimaginable
things cancel out to produce
an effect on a human scale?
A paper by radiation expert
Andrew Karam provides an
answer. It explains that
during certain supernovae,
the collapse of a stellar core
into a neutron star, 1057
neutrinos can be released (one
for every proton in the star
that collapses to become a
neutron).
Karam calculates that the
neutrino radiation dose at a
distance of 1 parsec5 would
be around half a nanosievert,
or 1/500th the dose from
eating a banana.6
A fatal radiation dose is
about 4 sieverts. Using the
inverse-square law, we can
calculate the radiation dose:
That’s a little more than the
distance between the Sun and
Mars.
Core-collapse supernovae
happen to giant stars, so if
you observed a supernova
from that distance, you’d
probably be inside the outer
layers of the star that created
it.
GRB 080319B was the most violent
event ever observed—especially for
the people who were floating right
next to it with surfboards.
The idea of neutrino
radiation damage reinforces
just how big supernovae are.
If you observed a supernova
from 1 AU away—and you
somehow avoided being
incinerated, vaporized, and
converted to some type of
exotic plasma—even the flood
of ghostly neutrinos would be
dense enough to kill you.
If it’s going fast enough, a
feather can absolutely knock
you over.
1 Less often if you’re a child,
since you have fewer atoms to
be hit. Statistically, your first
neutrino interaction probably
happens somewhere around age
ten.
2 Which would still be less than
1 percent of the ants in the
world.
3 If you want to be mean to
first-year calculus students, you
can ask them to take the
derivative of ln(x)e dx. It looks
like it should be “1” or
something, but it’s not.
4 “Supernovas” is also fine.
“Supernovii” is discouraged.
5 3.262 light-years, or a little
less than the distance from here
to Alpha Centauri.
6 “Radiation Dose Chart,”
http://xkcd.com/radiation.
WEIRD
(AND
WORRYING)
QUESTIONS
FROM
THE
WHAT IF?
INBOX, #8
Q. A toxin
blocks the
ability of the
nephron tubule
reabsorption
but does not
affect filtration.
What are the
possible shortterm effects of
this toxin?
—Mary
Q.
If a Venus
fly trap could
eat a person,
about how
long would it
take for the
human to be
fully de-juiced
and absorbed?
—Jonathan Wang
SPEED
BUMP
Q. How fast
can you hit a
speed bump
while driving
and live?
—Myrlin Barber
A. SURPRISINGLY
FAST.
First, a disclaimer. After
reading this answer, don’t try
to drive over speed bumps at
high speeds. Here are some
reasons:
You could hit and kill
someone.
It can destroy your
tires, suspension, and
potentially your
entire car.
Have you read any of
the other answers in
this book?
If that’s not enough, here
are some quotes from medical
journals on spinal injury from
speed bumps.
Examination
of
the
thoracolumbar X-ray and
computed
tomography
displayed
compression
fractures
in
four
patients . . . Posterior
instrumentation
was
applied . . . All patients
recovered well except for
the one with cervical
fracture.
L1
was
the
most
frequently
fractured
vertebra (23 /52, 44.2
percent).
Incorporation of the
buttocks with realistic
properties diminished the
first
vertical
natural
frequency from ~12 to 5.5
Hz, in agreement with the
literature.
(That last one isn’t directly
related to speed bump
injuries, but I wanted to
include it anyway.)
Regular little speed
bumps probably won’t
kill you
Speed bumps are designed to
make drivers slow down.
Going over a typical speed
bump at 5 miles per hour
results in a gentle bounce,1
while hitting one at 20
delivers a sizable jolt. It’s
natural to assume that hitting
a speed bump at 60 would
deliver a proportionally larger
jolt, but it probably wouldn’t.
As those medical quotes
attest, it’s true that people are
occasionally injured by speed
bumps. However, nearly all of
those injuries happen to a
very specific category of
people: those sitting in hard
seats in the backs of buses,
riding on poorly maintained
roads.
When you’re driving a car,
the
two
main
things
protecting you from bumps in
the road are the tires and the
suspension. No matter how
fast you hit a speed bump,
unless the bump is large
enough to hit the frame of
the car, enough of the jolt will
be absorbed by these two
systems that you probably
won’t be hurt.
Absorbing the shock won’t
necessarily be good for those
systems. In the case of the
tires, they may absorb it by
exploding.2 If the bump is
large enough to hit the wheel
rims, it may permanently
damage a lot of important
parts of the car.
The typical speed bump is
between 3 and 4 inches tall.
That’s also about how thick
an average tire’s cushion is
(the separation between the
bottom of the rims and the
ground).3 This means that if
a car hits a small speed bump,
the rim won’t actually touch
the bump; the tire will just be
compressed.
The typical sedan has a top
speed of around 120 miles per
hour. Hitting a speed bump
at that speed would, in one
way or another, probably
result in losing control of the
car and crashing.4 However,
the jolt itself probably
wouldn’t be fatal.
If you hit a larger speed
bump—like a speed hump or
speed table—your car might
not fare so well.
How fast would you
have to go to definitely
die?
Let’s consider what would
happen if a car were going
faster than its top speed. The
average modern car is limited
to a top speed of around 120
mph, and the fastest can go
about 200.
While most passenger cars
have some kind of artificial
speed limits imposed by the
engine
computer,
the
ultimate physical limit to a
car’s top speed comes from air
resistance. This type of drag
increases with the square of
speed; at some point, a car
doesn’t have enough engine
power to push through the air
any faster.
If you did force a sedan to
go faster than its top speed
—perhaps by reusing the
magical accelerator from the
relativistic
baseball—the
speed bump would be the
least of your problems.
Cars generate lift. The air
flowing around a car exerts all
kinds of forces on it.
Where did all these arrows come
from?
The lift forces are relatively
minor at normal highway
speeds, but at higher speeds
they become substantial.
In a Formula One car
equipped with airfoils, this
force pushes downward,
holding the car against the
track. In a sedan, they lift it
up.
Among NASCAR fans,
there’s frequently talk of a
200-mph “liftoff speed” if the
car starts to spin. Other
branches of auto racing have
seen spectacular backflip
crashes
when
the
aerodynamics don’t work out
as planned.
The bottom line is that in
the range of 150–300 mph, a
typical sedan would lift off
the ground, tumble, and
crash . . . before you even hit
the bump.
BREAKING: Child, Unidentified
Creature in Bicycle Basket Hit and
Killed by Car
If you kept the car from
taking off, the force of the
wind at those speeds would
strip away the hood, side
panels, and windows. At
higher speeds, the car itself
would be disassembled, and
might even burn up like a
spacecraft reentering the
atmosphere.
What’s the ultimate
limit?
In the state of Pennsylvania,
drivers may see $2 added to
their speeding ticket for every
mile per hour by which they
break the speed limit.
Therefore, if you drove a
car over a Philadelphia speed
bump at 90 percent of the
speed of light, in addition to
destroying the city . . .
. . . you could expect a
speeding ticket of $1.14
billion.
1 Like anyone with a physics
background, I do all my
calculations in SI units, but I’ve
gotten too many US speeding
tickets to write this answer in
anything but miles per hour; it’s
just been burned into my brain.
Sorry!
2 Just Google “hit a curb at 60.”
3 There are cars everywhere.
Go outside with a ruler and
check.
4 At high speeds, you can easily
lose control even without
hitting a bump. Joey
Huneycutt’s 220-mph crash left
his Camaro a burned-out hulk.
LOST
IMMORTALS
Q. If two
immortal
people were
placed on
opposite
sides of an
uninhabited
Earthlike
planet, how
long would it
take them to
find each
other?
100,000
years?
1,000,000
years?
100,000,000,00
years?
—Ethan Lake
A. WE’LL
START WITH
THE simple, physicist-style1
answer: 3000 years.
That’s about how long it
would take two people to find
each other, assuming that
they were walking around at
random over a sphere for 12
hours per day and had to get
within a kilometer to see each
other.
We can immediately see
some problems with this
model.2
The
simplest
problem is the assumption
that you can always see
someone if they come within
a kilometer of you. That’s
possible under only the most
ideal circumstances; a person
walking along a ridge might
be visible from a kilometer
away, whereas in a thick
forest during a rainstorm, two
people could pass within a
few meters without seeing
each other.
We could try to calculate
the average visibility across all
parts of the Earth, but then
we run into another question:
Why would two people who
are trying to find each other
spend time in a thick jungle?
It would seem to make more
sense for both of them to stay
in flat, open areas where they
could easily see and be seen.3
Once we start considering
the psychology of our two
people,
our
sphericalimmortal-in-a-vacuum model
is in trouble.4 Why should we
assume our people will walk
around randomly at all? The
optimal strategy might be
something totally different.
What strategy would make
the most sense for our lost
immortals?
If they have time to plan
beforehand, it’s easy. They
can arrange to meet at the
North or South Pole, or—if
those turn out to be
unreachable—at the highest
point on land, or the mouth
of the longest river. If there’s
any ambiguity, they can just
travel between all the options
at random. They have plenty
of time.
If they don’t have a chance
to communicate beforehand,
things get a little harder.
Without knowing the other
person’s strategy, how do you
know what your strategy
should be?
There’s an old puzzle, from
before the days of cell phones,
that goes something like this:
Suppose you’re meeting a
friend in an American
town that neither of you
have been to before. You
don’t have a chance to
plan a meeting place
beforehand. Where do you
go?
The author of the puzzle
suggested that the logical
solution would be to go to the
town’s main post office and
wait at the main receiving
window, where out-of-town
packages arrive. His logic was
that it’s the only place that
every town in the US has
exactly one of, and which
everyone would know where
to find.
To me, that argument
seems a little weak. More
importantly, it doesn’t hold
up experimentally. I’ve asked
that question to a number of
people, and none of them
suggested the post office. The
original author of that puzzle
would be waiting in the
mailroom alone.
Our lost immortals have it
tougher, since they don’t
know anything about the
geography of the planet
they’re on.
Following the coastlines
seems like a sensible move.
Most people live near water,
and it’s much faster to search
along a line than over a plane.
If your guess turns out to be
wrong, you won’t have wasted
much time compared to
having searched the interior
first.
Walking around the average
continent would take about
five years, based on typical
width-to-coastline-length
ratios for Earth land masses.5
Let’s assume you and the
other person are on the same
continent. If you both walk
counterclockwise, you could
circle forever without finding
each other. That’s no good.
A different approach would
be to make a complete circle
counterclockwise, then flip a
coin. If it comes up heads,
circle counterclockwise again.
If tails, go clockwise. If you’re
both following the same
algorithm, this would give
you a high probability of
meeting within a few circuits.
The assumption that you’re
both
using
the
same
algorithm
is
probably
optimistic.
Fortunately,
there’s a better solution: Be
an ant.
Here’s the algorithm that I
would follow (if you’re ever
lost on a planet with me, keep
this in mind!):
If you have no information,
walk at random, leaving a
trail of stone markers, each
one pointing to the next. For
every day that you walk, rest
for three. Periodically mark
the date alongside the cairn.
It doesn’t matter how you do
this, as long as it’s consistent.
You could chisel the number
of days into a rock, or lay out
rocks to plot the number.
If you come across a trail
that’s newer than any you’ve
seen before, start following it
as fast as you can. If you lose
the trail and can’t recover it,
resume leaving your own trail.
You don’t have to come
across the other player’s
current location; you simply
have to come across a location
where they’ve been. You can
still chase one another in
circles, but as long as you
move more quickly when
you’re following a trail than
when you’re leaving one,
you’ll find each other in a
matter of years or decades.
And if your partner isn’t
cooperating—perhaps they’re
just sitting where they started
and waiting for you—then
you’ll get to see some neat
stuff.
1 Assuming a spherical
immortal human in a
vacuum . . .
2 Like, what happened to all
the other people? Are they
okay?
3 Although the visibility
calculation does sounds fun. I
know what I’m doing next
Saturday night!
4 Which is why we usually try
not to consider things like that.
5 Of course, some areas would
present a challenge. Louisiana’s
bayous, the Caribbean’s
mangrove forests, and Norway’s
fjords would all make for slower
walking than a typical beach.
ORBITAL
SPEED
Q. What if a
spacecraft
slowed down
on reentry to
just a few
miles per
hour using
rocket
boosters like
the Mars sky
crane? Would
it negate the
need for a
heat shield?
—Brian
Q. Is it
possible for a
spacecraft to
control its
reentry in
such a way
that it avoids
the
atmospheric
compression
and thus
would not
require the
expensive
(and relatively
fragile) heat
shield on the
outside?
—Christopher
Mallow
Q. Could a
(small) rocket
(with
payload) be
lifted to a
high point in
the
atmosphere
where it
would only
need a small
rocket to get
to escape
velocity?
—Kenny Van de
Maele
A. THE
ANSWERS TO
THESE questions all
hinge on the same idea. It’s
an idea I’ve touched on in
other answers, but right now
I want to focus on it
specifically:
The reason it’s hard to get
to orbit isn’t that space is
high up.
It’s hard to get to orbit
because you have to go so
fast.
Space isn’t like this:
Not actual size.
Space is like this:
You know what, sure, actual size.
Space
is
about
100
kilometers away. That’s far
away—I wouldn’t want to
climb a ladder to get there—
but it isn’t that far away. If
you’re in Sacramento, Seattle,
Canberra,
Kolkata,
Hyderabad, Phnom Penh,
Cairo, Beijing, central Japan,
central
Sri
Lanka,
or
Portland, space is closer than
the sea.
Getting to space is easy.1
It’s not, like, something you
could do in your car, but it’s
not a huge challenge. You
could get a person to space
with a rocket the size of a
telephone pole. The X-15
aircraft reached space just by
going fast and then steering
up.2,3
You will go to space today, and then
you will quickly come back.
But getting to space is easy.
The problem is staying there.
Gravity in low Earth orbit
is almost as strong as gravity
on the surface. The Space
Station hasn’t escaped Earth’s
gravity at all; it’s experiencing
about 90 percent the pull that
we feel on the surface.
To avoid falling back into
the atmosphere, you have to
go sideways really, really fast.
The speed you need to stay
in orbit is about 8 kilometers
per second.4 Only a fraction
of a rocket’s energy is used to
lift up out of the atmosphere;
the vast majority of it is used
to gain orbital (sideways)
speed.
This leads us to the central
problem of getting into orbit:
Reaching orbital speed takes
much more fuel than
reaching orbital height.
Getting a ship up to 8 km/s
takes a lot of booster rockets.
Reaching orbital speed is hard
enough; reaching orbital
speed while carrying enough
fuel to slow back down would
be completely impractical.5
These
outrageous
fuel
requirements are why every
spacecraft
entering
an
atmosphere has braked using
a heat shield instead of
rockets—slamming into the
air is the most practical way
to slow down. (And to answer
Brian’s
question,
the
Curiosity rover was no
exception to this; although it
used small rockets to hover
when it was near the surface,
it first used air-braking to
shed the majority of its
speed.)
How fast is 8 km/s,
anyway?
I think the reason for a lot of
confusion about these issues
is that when astronauts are in
orbit, it doesn’t seem like
they’re moving that fast; they
look like they’re drifting
slowly over a blue marble.
But 8 km/s is blisteringly
fast. When you look at the
sky near sunset, you can
sometimes see the ISS go
past . . . and then, 90 minutes
later, see it go past again.6 In
those 90 minutes, it’s circled
the entire world.
The ISS moves so quickly
that if you fired a rifle bullet
from one end of a football
field,7
the
International
Space Station could cross the
length of the field before the
bullet traveled 10 yards.8
Let’s imagine what it would
look like if you were speedwalking across the Earth’s
surface at 8 km/s.
To get a better sense of the
pace
at
which
you’re
traveling, let’s use the beat of
a song to mark the passage of
time.9 Suppose you started
playing the 1988 song by The
Proclaimers, “I’m Gonna Be
(500 Miles).” That song is
about 131.9 beats per minute,
so imagine that with every
beat of the song, you move
forward more than 2 miles.
In the time it took to sing
the first line of the chorus,
you could walk from the
Statue of Liberty all the way
to the Bronx.
You’d be moving at about
15 subway stops per minute.
It would take you about two
lines of the chorus (16 beats
of the song) to cross the
English Channel between
London and France.
The song’s length leads to
an odd coincidence. The
interval between the start and
the end of “I’m Gonna Be” is
3 minutes and 30 seconds,
and the ISS is moving at 7.66
km/s.
This means that if an
astronaut on the ISS listens to
“I’m Gonna Be,” in the time
between the first beat of the
song and the final lines . . .
. . . they will have traveled
just about exactly 1000 miles.
1 Specifically, low Earth orbit,
which is where the
International Space Station is
and where shuttles could go.
2 The X-15 reached 100 km on
two occasions, both when flown
by Joe Walker.
3 Make sure to remember to
steer up and not down, or you
will have a bad time.
4 It’s a little less if you’re in the
higher region of low Earth
orbit.
5 This exponential increase is
the central problem of rocketry:
The fuel required to increase
your speed by 1 km/s multiplies
your weight by about 1.4. To
get into orbit, you need to
increase your speed to 8 km/s,
which means you’ll need a lot of
fuel: 1.4 × 1.4 × 1.4 × 1.4 × 1.4
× 1.4 × 1.4 × 1.4 ≈ 15 times the
original weight of your ship.
Using a rocket to slow down
carries the same problem: Every
1 km/s decrease in speed
multiplies your starting mass by
that same factor of 1.4. If you
want to slow all the way down
to zero — and drop gently into
the atmosphere — the fuel
requirements multiply your
weight by 15 again.
6 There are some good apps
and online tools to help you
spot the station, along with
other neat satellites.
7 Either kind.
8 This type of play is legal in
Australian rules football.
9 Using song beats to help
measure the passage of time is a
technique also used in CPR
training, where the song
“Stayin’ Alive” is used.
FEDEX
BANDWIDTH
Q. When–if
ever–will the
bandwidth of
the Internet
surpass that
of FedEx?
—Johan Öbrink
Never underestimate the
bandwidth of a station
wagon full of tapes
hurtling down the
highway.
–Andrew Tanenbaum,
1981
A. IF
YOU WANT TO
transfer a few hundred
gigabytes
of
data,
it’s
generally faster to FedEx a
hard drive than to send the
files over the Internet. This
isn’t a new idea—it’s often
dubbed “SneakerNet”—and
it’s even how Google transfers
large amounts of data
internally.
But will it always be faster?
Cisco estimates that total
Internet traffic currently
averages 167 terabits per
second. FedEx has a fleet of
654 aircraft with a lift
capacity of 26.5 million
pounds daily. A solid-state
laptop drive weighs about 78
grams and can hold up to a
terabyte.
That means FedEx is
capable of transferring 150
exabytes of data per day, or
14 petabits per second
—almost a hundred times the
current throughput of the
Internet.
If you don’t care about cost,
this 10-kilogram shoebox can
hold a lot of Internet.
We can improve the data
density even further by using
microSD cards:
Those
thumbnail-sized
flakes have a storage density
of up to 160 terabytes per
kilogram, which means a
FedEx fleet loaded with
microSD cards could transfer
about 177 petabits per
second, or 2 zettabytes per
day—a thousand times the
Internet’s current traffic level.
(The infrastructure would be
interesting—Google would
need
to
build
huge
warehouses to hold a massive
card-processing operation.)
Cisco estimates Internet
traffic is growing at about 29
percent annually. At that rate,
we’ll hit the FedEx point in
2040. Of course, the amount
of data we can fit on a drive
will have gone up by then,
too. The only way to actually
reach the FedEx point is if
transfer rates grow much
faster than storage rates. In an
intuitive sense, this seems
unlikely, since storage and
transfer are fundamentally
linked—all that data is
coming from somewhere and
going
somewhere—but
there’s no way to predict
usage patterns for sure.
While FedEx is big enough
to keep up with the next few
decades of actual usage,
there’s
no
technological
reason we can’t build a
connection that beats them
on bandwidth. There are
experimental fiber clusters
that can handle over a petabit
per second. A cluster of 200
of those would beat FedEx.
If you recruited the entire
US freight industry to move
SD cards for you, the
throughput would be on the
order of 500 exabits—half a
zettabit—per second. To
match that transfer rate
digitally, you’d need to take
half a million of those petabit
cables.
So the bottom line is that
for raw bandwidth of FedEx,
the Internet will probably
never
beat
SneakerNet.
However,
the
virtually
infinite bandwidth of a
FedEx-based Internet would
come at the cost of
80,000,000-millisecond ping
times.
FREE FALL
Q. What
place on
Earth would
allow you to
free-fall the
longest by
jumping off
it? What
about using a
squirrel suit?
—Dhash Shrivathsa
A. THE
LARGEST
PURELY
VERTICAL
drop on Earth is the face of
Canada’s Mount Thor, which
is shaped like this:
Source:
AAAAAAAAAAAAAAAAAAAAAAAA
To make this scenario a
little less gruesome, let’s
suppose there’s a pit at the
bottom of the cliff filled with
something fluffy—like cotton
candy—to safely break your
fall.
Would this work? You’ll have to wait
for book two . . .
A human falling with arms
and legs outstretched has a
terminal velocity in the
neighborhood of 55 meters
per second. It takes a few
hundred meters to get up to
speed, so it would take you a
little over 26 seconds to fall
the full distance.
What can you do in 26
seconds?
For starters, it’s enough
time to get all the way
through the original Super
Mario World 1-1, assuming
you have perfect timing and
take the shortcut through the
pipe.
It’s also long enough to
miss a phone call. Sprint’s
ring cycle—the time the
phone rings before going to
voicemail—is 23 seconds.1
If someone called your
phone, and it started ringing
the moment you jumped, it
would go to voicemail three
seconds before you reached
the bottom.
On the other hand, if you
jumped off Ireland’s 210meter Cliffs of Moher, you
would be able to fall for only
about eight seconds—or a
little more, if the updrafts
were strong. That’s not very
long, but according to River
Tam,
given
adequate
vacuuming systems it might
be enough time to drain all
the blood from your body.
So far, we’ve assumed you’re
falling vertically. But you
don’t have to.
Even without any special
equipment, a skilled skydiver
—once he or she gets up to
full speed—can glide at
almost a 45-degree angle. By
gliding away from the base of
the
cliff,
you
could
conceivably extend your fall
substantially.
AAAAAAAAAAAAAAAAAAAAAAAA
::gasp::
AAAAAAAAAAAAAAAAAAAAAAAA
It’s hard to say exactly how
far; in addition to the local
terrain, it depends heavily on
your choice of clothes. As a
comment on a BASE
jumping records wiki puts it,
The record for longest
[fall time] without a
wingsuit is hard to find
since the line between
jeans and wingsuits has
blurred
since
the
introduction of more
advanced . . . apparel.
Which brings us to
wingsuits—the halfway point
between parachute pants and
parachutes.
Wingsuits let you fall much
more slowly. One wingsuit
operator posted tracking data
from a series of jumps. It
shows that in a glide, a
wingsuit can lose altitude as
slowly as 18 meters per
second—a huge improvement
over 55.
Even ignoring horizontal
travel, that would stretch out
our fall to over a minute.
That’s long enough for a
chess game. It’s also long
enough to sing the first verse
of—appropriately enough—
REM’s “It’s the End of the
World as We Know It,”
followed
by—less
appropriately—the
entire
breakdown from the end of
the Spice Girls’ “Wannabe.”
When we include the
higher cliffs opened up by
horizontal glides, the times
get even longer.
There are a lot of
mountains
that
could
probably support very long
wingsuit flights. For example,
Nanga Parbat, a mountain in
Pakistan, has a drop of more
than 3 kilometers at a fairly
steep angle. (Surprisingly, a
wingsuit still works fine in
such thin air, though the
jumper would need oxygen,
and it would glide a little
faster than normal.)
So far, the record for
longest wingsuit BASE jump
is held by Dean Potter, who
jumped from the Eiger—a
mountain in Switzerland
—and flew for three minutes
and twenty seconds.
What could you do with
three minutes and twenty
seconds?
Suppose we recruit Joey
Chestnut
and
Takeru
Kobayashi, the world’s top
competitive eaters.
If we can find a way for
them to operate wingsuits
while eating at full speed, and
they jumped from the Eiger,
they could—in theory—finish
as many as 45 hot dogs
between them before reaching
the ground . . .
. . . which would, if
nothing else, earn them what
just might be the strangest
world record in history.
1 For those keeping score, that
means Wagner’s is 2,350 times
longer.
WEIRD
(AND
WORRYING)
QUESTIONS
FROM
THE
WHAT IF?
INBOX, #9
Q. Could you
survive a tidal
wave by
submerging
yourself in an
in-ground
pool?
—Chris Muska
Q.
If you are
in free fall and
your parachute
fails, but you
have a Slinky
with extremely
convenient
mass, tension,
etc., would it
be possible to
save yourself
by throwing
the Slinky
upward while
holding on to
one end of it?
—Varadarajan
Srinivasan
SPARTA
Q. In the
movie 300
they shoot
arrows up
into the sky
and they
seemingly
blot out the
sun. Is this
possible, and
how many
arrows would
it take?
—Anna Newell
A. IT’S
PRETTY HARD
TO make this work.
Attempt 1
Longbow archers can fire
eight to ten arrows per
minute. In physics terms, a
longbow archer is an arrow
generator with a frequency of
150 millihertz.
Each arrow spends only a
few seconds in the air. If an
arrow’s average time over the
battlefield is three seconds,
then about 50 percent of all
archers have arrows in the air
at any given time.
Each arrow intercepts about
40 cm2 of sunlight. Since
archers have arrows in the air
only half the time, each
blocks an average of 20 cm2
of sunlight.
If the archers are packed in
rows, with two archers per
meter and a row every meter
and a half, and the archer
battery is 20 rows (30 meters)
deep, then for every meter of
width . . .
. . . there will be 18 arrows
in the air.
18 arrows will block only
about 0.1 percent of the Sun
from the firing range. We
need to improve on this.
Attempt 2
First, we can pack the archers
more tightly. If they stand
with the density of a mosh pit
crowd,1 we can triple the
number of archers per square
foot. Sure, it will make firing
awkward, but I’m sure they
can figure it out.
We can expand the depth
of the firing column to 60
meters. That gives us a
density of 130 archers per
meter.
How fast can they fire?
In the extended edition of
the 2001 film Lord of the
Rings: The Fellowship of the
Ring, there’s a scene where a
group of orcs2 charge at
Legolas, and Legolas draws
and fires arrows in rapid
succession,
felling
the
attackers with one shot each
before they reach him.
The actor playing Legolas,
Orlando Bloom, couldn’t
really fire arrows that quickly.
He was actually dry-firing an
empty bow; the arrows were
added using CGI. Since this
fire rate appeared, to the
audience, to be impressively
fast but not physically
implausible, it provides a
convenient upper limit for our
calculations.
Let’s assume we can train
our archers to replicate
Legolas’s fire rate of seven
arrows in eight seconds.
In that case, our column of
archers (firing an impossible
339 arrows per meter) will
still block out only 1.56
percent of the sunlight
passing through them.
Attempt 3
Let’s dispense with the bows
entirely and give our archers
arrow-firing Gatling bows. If
they can fire 70 arrows per
second, that adds up to 110
square meters of arrows per
100
square
meters
of
battlefield! Perfect.
But there’s a problem. Even
though the arrows have a
total cross-sectional area of
100 meters, some of them
shadow each other.
The formula for the
fraction of ground coverage
by a large number of arrows,
some of which overlap each
other, is this:
With 110 square meters of
arrows, you’ll cover only twothirds of the battlefield. Since
our eyes judge brightness on a
logarithmic scale, reducing
the Sun’s brightness to a third
of its normal value will be
seen as a slight dimming;
certainly not “blotting it out.”
With an even more
unrealistic fire rate, we could
make it work. If the guns
release 300 arrows per second,
they would block out 99
percent of the sunlight
reaching the battlefield.
But there’s an easier way.
Attempt 4
We’ve been making the
implicit assumption that the
Sun is directly overhead.
That’s certainly what the
movie shows. But perhaps the
famous boast was based on a
plan to attack at dawn.
If the Sun were low on the
eastern horizon, and the
archers were firing north,
then the light could have to
pass through the entire
column of arrows, potentially
multiplying the shadow effect
a thousandfold.
Of course, the arrows
wouldn’t be aimed anywhere
near the enemy soldiers. But,
to be fair, all they said was
that their arrows would blot
out the Sun. They never said
anything
about
hitting
anyone.
And who knows; maybe,
against the right enemy, that’s
all they need.
1 Rule of thumb: One person
per square meter is a light
crowd, four people per square
meter is a mosh pit.
2 Strictly speaking, they were
Uruk-Hai, not typical orcs. The
precise nature and origin of the
Uruk-Hai is a little tricky.
Tolkien suggested that they
were created by cross-breeding
humans with orcs. However, in
an earlier draft, published in
The Book of Lost Tales, he
instead suggests the Uruks had
been born from the
“subterranean heats and slimes
of the Earth.” Director Peter
Jackson, when deciding what to
show on-screen in his film
adaptation, wisely went with
the latter version.
DRAIN THE
OCEANS
Q. How
quickly would
the oceans
drain if a
circular portal
10 meters in
radius
leading into
space were
created at the
bottom of
Challenger
Deep, the
deepest spot
in the ocean?
How would
the Earth
change as the
water was
being
drained?
—Ted M
A. I
WANT TO GET one
thing out of the way first:
According to my rough
calculations, if an aircraft
carrier sank and got stuck
against the drain, the pressure
would easily be enough to
fold it up and suck it through.
Cooool.
Just how far away is this
portal? If we put it near the
Earth, the ocean would just
fall back down into the
atmosphere. As it fell, it
would heat up and turn to
steam, which would condense
and fall right back into the
ocean as rain. The energy
input into the atmosphere
alone would also wreak all
kinds of havoc with our
climate, as would the huge
clouds of high-altitude steam.
So let’s put the ocean-
dumping portal far away—
say, on Mars. (In fact, I vote
we put it directly above the
Curiosity rover; that way, it
will
finally
have
incontrovertible evidence of
liquid water on Mars’s
surface.)
What happens to the
Earth?
Not much. It would actually
take hundreds of thousands of
years for the ocean to drain.
Even though the opening is
wider than a basketball court,
and the water is forced
through at incredible speeds,
the oceans are huge. When
you started, the water level
would drop by less than a
centimeter per day.
There wouldn’t even be a
cool whirlpool at the surface
—the opening is too small
and the ocean is too deep.
(It’s the same reason you
don’t get a whirlpool in the
bathtub until the water is
more than halfway drained.)
But let’s suppose we speed
up the draining by opening
more drains,1 so the water
level starts to drop more
quickly.
Let’s take a look at how the
map would change.
Here’s how it looks at the
start:
This is a Plate Carrée projection (c.f.
xkcd.com/977).
And here’s the map after
the oceans drop 50 meters:
It’s pretty similar, but there
are a few small changes. Sri
Lanka, New Guinea, Great
Britain, Java, and Borneo are
now connected to their
neighbors.
And after 2000 years of
trying to hold back the sea,
the Netherlands are finally
high and dry. No longer
living with the constant
threat of a cataclysmic flood,
they’re free to turn their
energies toward outward
expansion. They immediately
spread out and claim the
newly exposed land.
When the sea level reaches
(minus) 100 meters, a huge
new island off the coast of
Nova Scotia is exposed—the
former site of the Grand
Banks.
You may start to notice
something odd: Not all the
seas are shrinking. The Black
Sea, for example, shrinks only
a little, then stops.
This is because these bodies
are no longer connected to
the ocean. As the water level
falls, some basins cut off from
the drain in the Pacific.
Depending on the details of
the sea floor, the flow of
water out of the basin might
carve a deeper channel,
allowing it to continue to
flow out. But most of them
will
eventually
become
landlocked and stop draining.
At 200 meters, the map is
starting to look weird. New
islands
are
appearing.
Indonesia is a big blob. The
Netherlands now control
much of Europe.
Japan is now an isthmus
connecting
the
Korean
peninsula with Russia. New
Zealand gains new islands.
The Netherlands expand
north.
New
Zealand
grows
dramatically. The Arctic
Ocean is cut off and its water
level stops falling. The
Netherlands cross the new
land bridge
America.
into
North
The sea has dropped by 2
kilometers. New islands are
popping up left and right.
The Caribbean Sea and the
Gulf of Mexico are losing
their connections with the
Atlantic. I don’t even know
what New Zealand is doing.
At 3 kilometers, many of
the peaks of the mid-ocean
ridge—the world’s long-est
mountain range—break the
surface. Vast swaths of rugged
new land emerge.
By this point, most of the
major oceans have become
disconnected and stopped
draining. The exact locations
and sizes of the various inland
seas are hard to predict; this is
only a rough estimate.
This is what the map looks
like when the drain finally
empties. There’s a surprising
amount of water left,
although much of it consists
of very shallow seas, with a
few trenches where the water
is as deep as 4 or 5
kilometers.
Vacuuming up half the
oceans would massively alter
the climate and ecosystems in
ways that are hard to predict.
At the very least, it would
almost certainly involve a
collapse of the biosphere and
mass extinctions at every
level.
But it’s possible—if unlikely
—that humans could manage
to survive. If we did, we’d
have this to look forward to:
1 Remember to clean the whale
filter every few days.
DRAIN THE
OCEANS:
PART II
Q. Supposing
you did drain
the oceans,
and dumped
the water on
top of the
Curiosity
rover, how
would Mars
change as the
water
accumulated?
—Iain
A. IN
THE
PREVIOUS
ANSWER, we opened a
portal at the bottom of the
Mariana Trench and let the
oceans drain out.
We didn’t worry too much
about where the oceans were
draining to. I picked Mars;
the Curiosity rover is working
so hard to find evidence of
water, so I figured we could
make things easier for it.
Curiosity is sitting in Gale
Crater, a round depression in
the Martian surface with a
peak, nicknamed Mount
Sharp, in the center.
There’s a lot of water on
Mars. The problem is, it’s
frozen. Liquid water doesn’t
last long there, because it’s
too cold and there’s too little
air.
If you set out a cup of warm
water on Mars, it’ll try to boil,
freeze,
and
sublimate,
practically all at once. Water
on Mars seems to want to be
in any state except liquid.
However, we’re dumping a
lot of water very fast (all of it
at a few degrees above 0°C),
and it won’t have much time
to freeze, boil, or sublimate.
If our portal is big enough,
the water will start to turn
Gale Crater into a lake, just
like it would on Earth. We
can use the excellent USGS
Mars Topographic Map to
chart the water’s progress.
Here’s Gale Crater at the
start of our experiment:
As the flow continues, the
lake fills in, burying Curiosity
under hundreds of meters of
water:
Eventually, Mount Sharp
becomes an island. However,
before the peak can disappear
completely, the water spills
over the north rim of the
crater and starts flowing out
across the sand.
There’s evidence that—due
to occasional heat waves—ice
in
the
Martian
soil
occasionally melts and flows
as a liquid. When this
happens, the trickle of water
quickly dries up before it can
get very far. However, we’ve
got a lot of ocean at our
disposal.
The water pools in the
North Polar Basin:
Gradually, it will fill the
basin:
However, if we look at a
map of the more equatorial
regions of Mars, where the
volcanoes are, we’ll see that
there’s still a lot of land far
from the water:
[Mercator projection; does not show
the poles.]
Frankly, I think this map is
kind of boring; there’s not a
lot going on. It’s just a big
empty swath of land with
some ocean at the top.
Would not buy again.
We haven’t come close to
running out of ocean yet
although there was a lot of
blue on the map of the Earth
at the end of our last answer,
the seas that remained were
shallow; most of the volume
of the oceans was gone.
And Mars is much smaller
than Earth, so the same
volume of water will make a
deeper sea.
At this point, the water fills
in the Valles Marineris,
creating
some
unusual
coastlines. The map is less
boring, but the terrain around
the great canyons makes for
some odd shapes.
The water now reaches and
swallows up Spirit and
Opportunity. Eventually, it
breaks into the Hellas Impact
Crater, the basin containing
the lowest point on Mars.
In my opinion, the rest of
the map is starting to look
pretty good.
As the water spreads across
the surface in earnest, the
map splits into several large
islands (and innumerable
smaller ones).
The water quickly finishes
covering most of the high
plateaus, leaving only a few
islands left.
And then, at last, the flow
stops; the oceans back on
Earth are drained.
Let’s take a closer look at
the main islands:
No rovers remain above water.
Olympus Mons, and a few
other volcanoes, remain above
water. Surprisingly, they
aren’t even close to being
covered. Olympus Mons still
rises well over 10 kilometers
above the new sea level. Mars
has some huge mountains.
Those crazy islands are the
result of water filling in
Noctis Labyrinthus (the
Labyrinth of the Night), a
bizarre set of canyons whose
origin is still a mystery.
The oceans on Mars
wouldn’t last. There might be
some transient greenhouse
warming, but in the end,
Mars is just too cold.
Eventually, the oceans will
freeze over, become covered
with dust, and gradually
migrate to the permafrost at
the poles.
However, it would take a
long time, and until it did,
Mars would be a much more
interesting place.
When you consider that
there’s a ready-made portal
system to allow transit
between the two planets, the
consequences are inevitable:
TWITTER
Q. How many
unique
English
tweets are
possible?
How long
would it take
for the
population of
the world to
read them all
out loud?
—Eric H, Hopatcong, NJ
High up in the North in
the land called Svithjod,
there stands a rock. It is a
hundred miles high and a
hundred miles wide. Once
every thousand years a
little bird comes to this
rock to sharpen its beak.
When the rock has thus
been worn away, then a
single day of eternity will
have gone by.
—Hendrik Willem Van
Loon
A. TWEETS
ARE 140
CHARACTERS
long.
There are 26 letters in
English—27 if you include
spaces. Using that alphabet,
there are 27140 ≈ 10200 possible
strings.
But Twitter doesn’t limit
you to those characters. You
have all of Unicode to play
with, which has room for over
a million different characters.
The way Twitter counts
Unicode
characters
is
complicated, but the number
of possible strings could be as
high as 10800.
Of course, almost all of
them would be meaningless
jumbles of characters from a
dozen different languages.
Even if you’re limited to the
26 English letters, the strings
would be full of meaningless
jumbles like “ptikobj.” Eric’s
question was about tweets
that actually say something in
English. How many of those
are possible?
This is a tough question.
Your first impulse might be
to allow only English words.
Then you could further
restrict it to grammatically
valid sentences.
But it gets tricky. For
example, “Hi, I’m Mxyztplk”
is a grammatically valid
sentence if your name
happens to be Mxyztplk.
(Come to think of it, it’s just
as grammatically valid if
you’re lying.) Clearly, it
doesn’t make sense to count
every string that starts with
“Hi, I’m . . . ” as a separate
sentence. To a normal
English speaker, “Hi, I’m
Mxyztplk”
is
basically
indistinguishable from “Hi,
I’m Mxzkqklt,” and shouldn’t
both count. But “Hi, I’m
xPoKeFaNx” is definitely
recognizably different from
the first two, even though
“xPoKeFaNx”
isn’t
an
English word by any stretch
of the imagination.
Our way of measuring
distinctiveness seems to be
falling apart. Fortunately,
there’s a better approach.
Let’s imagine a language
that has only two valid
sentences, and every tweet
must be one of the two
sentences. They are:
“There’s a horse in
aisle five.”
“My house is full of
traps.”
Twitter would look like
this:
The messages are relatively
long, but there’s not a lot of
information in each one—all
they tell you is whether the
person decided to send the
trap message or the horse
message. It’s effectively a 1 or
a 0. Although there are a lot
of letters, for a reader who
knows the pattern of the
language, each tweet carries
only one bit of information
per sentence.
This example hints at a very
deep idea, which is that
information is fundamentally
tied to the recipient’s
uncertainty
about
the
message’s content and his or
her ability to predict it in
advance.1
Claude
Shannon—who
almost
singlehandedly
invented modern information
theory—had a clever method
for
measuring
the
information content of a
language. He showed groups
of people samples of typical
written English that were cut
off at a random point, then
asked them to guess which
letter came next.
It’s threatening to flood our town
with information!
Based on the rates of
correct guesses—and rigorous
mathematical
analysis
—Shannon determined that
the information content of
typical written English was
1.0 to 1.2 bits per letter. This
means
that
a
good
compression
algorithm
should be able to compress
ASCII English text—which
is 8 bits per letter—to about
⅛th of its original size.
Indeed, if you use a good file
compressor on a .txt ebook,
that’s about what you’ll find.
If a piece of text contains n
bits of information, in a sense
it means that there are 2n
different messages it can
convey. There’s a bit of
mathematical juggling here
(involving, among other
things, the length of the
message and something called
“unicity distance”), but the
bottom line is that it suggests
there are on the order of
about 2140 × 1.1 ≈ 2 × 1046
meaningfully
different
English tweets, rather than
10200 or 10800.
Now, how long would it
take the world to read them
all out?
Reading 2 × 1046 tweets
would take a person nearly
1047 seconds. It’s such a
staggeringly large number of
tweets that it hardly matters
whether it’s one person
reading or a billion—they
won’t be able to make a
meaningful dent in the list in
the lifetime of the Earth.
Instead, let’s think back to
that bird sharpening its beak
on the mountaintop. Suppose
that the bird scrapes off a tiny
bit of rock from the mountain
when it visits every thousand
years, and it carries away
those few dozen dust particles
when it leaves. (A normal
bird would probably deposit
more beak material on the
mountaintop than it would
wear away, but virtually
nothing else about this
scenario is normal either, so
we’ll just go with it.)
Let’s say you read tweets
aloud for 16 hours a day,
every day. And behind you,
every thousand years, the bird
arrives and scrapes off a few
invisible specks of dust from
the top of the hundred-mile
mountain with its beak.
When the mountain is
worn flat to the ground, that’s
the first day of eternity.
The mountain reappears
and the cycle starts again for
another eternal day: 365
eternal days—each one 1032
years long—makes an eternal
year.
A hundred eternal years, in
which the bird grinds away
36,500 mountains, make an
eternal century.
But a century isn’t enough.
Nor a millennium.
Reading all the tweets takes
you ten thousand eternal
years.
That’s enough time to
watch all of human history
unfold, from the invention of
writing to the present, with
each day lasting as long as it
takes for the bird to wear
down a mountain.
While 140 characters may not
seem like a lot, we will never
run out of things to say.
1 It also hints at a very shallow
idea about there being a horse
in aisle five.
LEGO
BRIDGE
Q. How many
Lego bricks
would it take
to build a
bridge
capable of
carrying
traffic from
London to
New York?
Have that
many Lego
bricks been
manufactured?
—Jerry Petersen
A. LET’S START WITH A
less ambitious goal.
Making the connection
There have certainly been
enough Lego1 bricks to
connect
New
York and
London.In LEGO2 units,
New York and London are
700 million studs apart. That
means that if you arranged
bricks like this . . .
. . . it would take 350
million of them to connect
the two cities. The bridge
wouldn’t be able to hold itself
together or carry anything
bigger than a LEGO®3
minifig, but it’s a start.
There have been over 400
billion Lego4 pieces produced
over the years. But how many
of those are bricks that would
help with a bridge, and how
many are little helmet visors
that get lost in the carpet?
Let’s assume we’re building
our bridge out of the most
common LeGo5 piece—the
2x4 brick.
Using data provided by Dan
Boger, Lego6 kit archivist
and
operator
of
the
Peeron.com Lego data site,
I’ve come up with the
following rough estimate: 1
out of every 50 to 100 pieces
is a 2x4 rectangular brick.
This suggests there are about
5–10 billion 2x4 bricks in
existence, which is more than
enough for our one-blockwide bridge.
Supporting cars
Of course, if we want to
support actual traffic, we’ll
need to make the bridge a
little wider.
We probably want to make
the bridge float. The Atlantic
Ocean is deep,[citation needed]
and we want to avoid
building 3-mile-high pylons
out of Lego bricks if we can.
Lego bricks don’t make a
watertight seal when you
connect them together,7 and
the plastic used to make them
is denser than water. That’s
easy enough to solve; if we
put a layer of sealant over the
outer surface, the resulting
block is substantially less
dense than water.
For every cubic meter of
water it displaces, the bridge
can carry 400 kg. A typical
passenger car weighs a little
under 2000 kg, so our bridge
will need a minimum of 10
cubic meters of Lego
supporting each passenger
car.
If we make the bridge a
meter thick and 5 meters
wide, then it should be able
to stay afloat without any
trouble—although it might
ride low in the water—and be
sturdy enough to drive on.
Legos8 are quite strong;
according
to
a
BBC
investigation, you could stack
a quarter of a million 2x2
bricks on top of each other
before the bottom one
collapsed.9
The first problem with this
idea is that there aren’t nearly
enough Lego blocks in the
world to build this kind of
bridge. Our second problem
is the ocean.
Extreme forces
The North Atlantic is a
stormy place. While our
bridge would manage to avoid
the fastest-moving parts of
the Gulf Stream current, it
would still be subjected to
powerful wind and wave
forces.
How strong could we make
our bridge?
Thanks to a researcher at
the University of Southern
Queensland named Tristan
Lostroh, we have some data
on the tensile strength of
certain Lego joints. Their
conclusion, like the BBC’s, is
that
Lego
bricks
are
surprisingly tough.
The optimal design would
use
long,
thin
plates
overlapped with each other:
This design would be pretty
strong—the tensile strength
would be comparable to
concrete—but not nearly
strong enough. The wind,
waves, and current would
push the center of the bridge
sideways,
creating
tremendous tension in the
bridge.
The traditional way to deal
with this situation would be
to anchor the bridge to the
ground so it can’t drift too far
to one side. If we allow
ourselves to use cables in
addition
to
the
Lego
bricks,10
we
could
conceivably
tether
this
massive contraption to the sea
floor.11
But the problems don’t end
there. A 5-meter bridge
might be able to support a
vehicle on a placid pond, but
our bridge needs to be large
enough to stay above water
when waves are breaking over
it. Typical wave heights on
the open ocean could be
several meters, so we need the
deck of our bridge to be
floating at least, say, 4 meters
above the water.
We can make our structure
more buoyant by adding air
sacs and hollows, but we also
need to make it wider
—otherwise it will tip over.
This means we have to add
more anchors, with floats on
those anchors to keep them
from sinking. The floats
create more drag, which puts
more stress on the cables and
pushes
our
structure
downward, requiring more
floats on the structure . . .
Sea floor
If we want to build our bridge
down to the sea floor, we’ll
have a few problems. We
wouldn’t be able to keep the
air sacs open under the
pressure, so the structure
would have to support its own
weight. To handle the
pressure from the ocean
currents, we’d have to make it
wider. In the end, we’d
effectively be building a
causeway.
As a side effect, our bridge
would halt the North Atlantic
Ocean circulation. According
to climate scientists, this is
“probably bad.”12
Furthermore, the bridge
would cross the mid-Atlantic
ridge. The Atlantic sea floor
is spreading outward from a
seam down the middle, at a
rate—in Lego units—of one
stud every 112 days. We
would have to build in
expansion joints, or drive out
to the middle every so often
and add a bunch of bricks.
Cost
Lego bricks are made of ABS
plastic, which costs about a
dollar per kilogram at the
time of this writing. Even our
simplest bridge design, the
one with the kilometer-long
steel tethers,13 would cost
over $5 trillion.
But consider: The total
value of the London real
estate market is $2.1 trillion,
and transatlantic shipping
rates are about $30 per ton.
This means that for less
than the cost of our bridge,
we could buy all the property
in London and ship it, piece
by piece, to New York. Then
we could re-assemble it on a
new island in New York
Harbor, and connect the two
cities with a much simpler
Lego bridge.
We might even have enough left over
to buy that sweet Millennium Falcon
kit.
1 Although enthusiasts will
point out it should be written
“LEGO.”
2 Actually, the LEGO Group®
demands that it be styled
“LEGO®.”
3 On the other hand, writers
have no legal obligation to
include the trademark symbol.
The Wikipedia style guide
mandates that it be written
“Lego.”
4 The Wikipedia style is not
without its critics. The talk
page argument over this issue
featured many pages of heated
arguments, including several
misguided legal threats. They
also debate the italics.
5 OK, nobody styles it this way.
6 Fine.
7 Citation: I made a Lego boat
once and put it in the water and
it sank :(
8 I’m going to get some angry
mail about this.
9 Maybe it was a slow news
day.
10 And sealant.
11 If we wanted to try to use
Lego pieces, we could get kits
that include little nylon ropes.
12 They went on to say, “Wait,
what did you say you were
trying to build?” and “How did
you get in here, anyway?”
13 My favorite Friends episode.
LONGEST
SUNSET
Q. What is
the longest
possible
sunset you
can
experience
while driving,
assuming we
are obeying
the speed
limit and
driving on
paved roads?
—Michael Berg
A. TO
ANSWER
THIS,
WE have to be sure what we
mean by “sunset.”
This is a sunset:
Sunset starts the instant the
Sun touches the horizon, and
ends when it disappears
completely. If the Sun
touches the horizon and then
lifts back up, the sunset is
disqualified.
For a sunset to count, the
Sun has to set behind the
idealized horizon, not just
behind a nearby hill. This is
not a sunset, even though it
seems like one:
The reason it can’t count as
a sunset is that if you could
use arbitrary obstacles, you
could cause a sunset at any
time by hiding behind a rock.
We also have to consider
refraction.
The
Earth’s
atmosphere bends light, so
when the Sun is at the
horizon it appears about one
Sun-width higher than it
would
otherwise.
The
standard practice seems to be
to include the average effect
of this in all calculations,
which I’ve done here.
At the equator in March
and September, sunset is a
hair over two minutes long.
Closer to the poles, in places
like London, it can take
between 200 and 300
seconds. It’s shortest in spring
and fall (when the Sun is over
the equator) and longest in
the summer and winter.
If you stand still at the
South Pole in early March,
the Sun stays in the sky all
day, making a full circle just
above the horizon. Sometime
around March 21, it touches
the horizon for the only
sunset of the year. This sunset
takes 38–40 hours, which
means it makes more than a
full circuit around the horizon
while setting.
But Michael’s question was
very clever. He asked about
the longest sunset you can
experience on a paved road.
There’s a road to the research
station at the South Pole, but
it’s not paved—it’s made of
packed snow. There are no
paved roads anywhere near
either pole.
The closest road to either
pole that really qualifies as
paved is probably the main
road in Longyearbyen, on the
island of Svalbard, Norway.
(The end of the airport
runway in Longyearbyen gets
you slightly closer to the pole,
although driving a car there
might get you in trouble.)
Longyearbyen is actually
closer to the North Pole than
McMurdo
Station
in
Antarctica is to the South
Pole. There are a handful of
military, research, and fishing
stations farther north, but
none of them have much in
the way of roads; just
airstrips, which are usually
gravel and snow.
If you putter around
downtown Longyearbyen,1
the longest sunset you could
experience would be a few
minutes short of an hour. It
doesn’t actually matter if you
drive or not; the town is too
small for your movement to
make a difference.
But if you head over to the
mainland, where the roads are
longer, you can do even
better.
If you start driving from the
tropics and stay on paved
roads, the farthest north you
can get is the tip of European
Route 69 in Norway. There
are a number of roads
crisscrossing
northern
Scandinavia, so that seems
like a good place to start. But
which road should we use?
Intuitively, it seems like we
want to be as far north as
possible. The closer we are to
the pole, the easier it is to
keep up with the Sun.
Unfortunately, it turns out
keeping up with the Sun isn’t
a good strategy. Even in those
high Norwegian latitudes, the
Sun is just too fast. At the tip
of European Route 69—the
farthest you can get from the
equator while driving on
paved roads—you’d still have
to drive at about half the
speed of sound to keep up
with the Sun. (And E69 runs
north-south, not east-west, so
you’d drive into the Barents
Sea anyway.)
Luckily, there’s a better
approach.
If you’re in northern
Norway on a day when the
Sun just barely sets and then
rises again, the terminator
(day-night line) moves across
the land in this pattern:
(Not to be confused with
the Terminator, which moves
across the land in this
pattern:)
I can’t decide which terminator I’d
rather have to run from.
To get a long sunset, the
strategy is simple: Wait for
the date when the terminator
will just barely reach your
position. Sit in your car until
the terminator reaches you,
drive north to stay a little
ahead of it for as long as you
can (depending on the local
road layout), then U-turn and
drive back south fast enough
that you can get past it to the
safety of darkness.2
Surprisingly, this strategy
works about equally well
anywhere inside the Arctic
Circle; so you can get this
lengthy sunset on many roads
across Finland and Norway. I
ran a search for long-sunset
driving paths using PyEphem
and some GPS traces of
Norwegian highways. I found
that over a wide range of
routes and driving speeds, the
longest
sunset
was
consistently about 95 minutes
—an improvement of about
40 minutes over the Svalbard
sit-in-one-place strategy.
But if you are stuck in
Svalbard and want to make
the sunset—or sunrise—last a
little longer, you can always
try
spinning
counterclockwise.3 It’s true
that it will add only an
immeasurably small fraction
of a nanosecond to the
Earth’s clock. But depending
on who you’re with . . .
. . . it might be worth it.
1 Get a picture with the “polar
bear crossing” sign.
2 These instructions also work
for the other kind of
Terminator.
3 xkcd, “Angular Momentum,”
http://xkcd.com/162/.
RANDOM
SNEEZE
CALL
Q. If you call
a random
phone
number and
say “God
bless you,”
what are the
chances that
the person
who answers
just sneezed?
—Mimi
A. IT’S
HARD TO FIND
good numbers on this, but
it’s probably about 1 in
40,000.
Before you pick up the
phone, you should also keep
in mind that there’s roughly a
1 in 1000,000,000 chance
that the person you’re calling
just murdered someone.1 You
may want to be more careful
with your blessings.
However,
given
that
sneezes are far more common
than murders,2 you’re still
much more likely to get
someone who sneezed than to
catch a killer, so this strategy
is not recommended.
Mental note: I’m going to start saying
this when people sneeze.
Compared with the murder
rate, the sneezing rate doesn’t
get much scholarly research.
The most widely cited figure
for average sneeze frequency
comes
from
a
doctor
interviewed by ABC News,
who pegged it at 200 sneezes
per person per year.
One of the few scholarly
sources of data on sneezing is
a study that monitored the
sneezing
of
people
undergoing
an
induced
allergic reaction. To estimate
the average sneezing rate, we
can ignore all the real medical
data they were trying to
gather and just look at their
control group. This group
was given no allergens at all;
they just sat alone in a room
for a total of 176 20-minute
sessions.3
The subjects in the control
group sneezed four times
during those 58 or so hours,4
which—assuming they sneeze
only while awake—translates
to about 400 sneezes per
person per year.
Google Scholar turns up
5980 articles from 2012 that
mention “sneezing.” If half of
these articles are from the
US, and each one has an
average of four authors, then
if you dial the number, there’s
about a 1 in 10,000,000
chance that you’ll get
someone who—just that day
—published an article on
sneezing.
On the other hand, about
60 people are killed by
lightning in the US every
year. That means there’s only
a 1 in 10,000,000,000,000
chance that you’ll call
someone in the 30 seconds
after they’ve been struck and
killed.
Lastly, let’s suppose that on
the day this book was
published, five people who
read it decide to actually try
this experiment. If they call
numbers all day, there’s about
a 1 in 30,000 chance that at
some point during the day,
one of them will get a busy
signal because the person
they’ve called is also calling a
random stranger to say “God
bless you.”
And there’s about a 1 in
10,000,000,000,000 chance
that two of
simultaneously
other.
them will
call
each
At this point, probability
will give up, and they’ll both
be struck by lightning.
1 Based on a rate of 4 per
100,000, which is the average
in the US but on the high end
for industrialized countries.
2 Citation: You are alive.
3 For context, that’s 490
repetitions of the song “Hey
Jude.”
4 Over 58 hours of research,
four sneezes were the most
interesting data points. I
might’ve taken the 490 “Hey
Jude”s.
WEIRD
(AND
WORRYING)
QUESTIONS
FROM
THE
WHAT IF?
INBOX,
#10
Q. What is
the probability
that if I am
stabbed by a
knife in my
torso that it
won’t hit
anything vital
and I’ll live?
—Thomas
Q.
If I were
on a motorbike
and do a jump
off a quarter
pipe ramp,
how fast would
I need to be
moving to
safely deploy
and land using
the parachute?
—Anonymous
Q.
What if
every day,
every human
had a 1 percent
chance of
being turned
into a turkey,
and every
turkey had a 1
percent chance
of being turned
into a human?
—Kenneth
EXPANDING
EARTH
Q. How long
would it take
for people to
notice their
weight gain if
the mean
radius of the
world
expanded by
1cm every
second?
(Assuming
the average
composition
of rock were
maintained.)
—Dennis O’Donnell
A. THE
EARTH IS NOT,
currently, expanding.
People have long suggested
that it might be. Before the
continential drift hypothesis
was confirmed in the 1960s,1
people had noticed that the
continents
fit
together.
Various ideas were put
forward to explain this,
including the idea that the
ocean basins were rifts that
opened in the surface of a
previously smooth Earth as it
expanded. This theory was
never
very
widespread,2
although it still periodically
makes
the
rounds
on
YouTube.
To avoid the problem of
rifts in the ground, let’s
imagine all the matter in the
Earth, from the crust to the
core,
starts
expanding
uniformly. To avoid another
drain-the-oceans
scenario,
we’ll assume the ocean
expands, too.3 All human
structures will stay.
t = 1 second
As
the
Earth
started
expanding, you’d feel a slight
jolt, and might even lose your
balance for a moment. This
would be very brief. Since
you’re
moving
steadily
upward at 1 cm/s, you
woudn’t feel any kind of
ongoing acceleration. For the
rest of the day, you wouldn’t
notice much of anything.
t = 1 day
After the first day, the Earth
would have expanded by 864
meters.
Gravity would take a long
time to increase noticeably. If
you weighed 70 kil-ograms
when the expansion started,
you’d weigh 70.01 at the end
of the first day.
What about our roads and
bridges? Eventually, they
would have to break up,
right?
Not as quickly as you might
think. Here’s a puzzle I once
heard:
Imagine you tied a rope tightly
around the Earth, so it was hugging
the surface all the way around.
Now imagine you wanted to raise the
rope 1 meter off the ground.
How much extra length will you need
to add to the rope?
Though it may seem like
you’d need miles of rope, the
answer is 6.28 meters.
Circumference is proportional
to radius, so if you increase
radius by 1 unit, you increase
circumference by 2π units.
Stretching
a
40,000kilometer line an extra 6.28
meters is pretty negligible.
Even after a day, the extra 5.4
kilometers would be handled
easily
by
virtually
all
structures. Concrete expands
and contracts by more than
that every day.
After the initial jolt, one of
the first effects you’d notice
would be that your GPS
would stop working. The
satellites would stay in
roughly the same orbits, but
the delicate timing that the
GPS system is based on
would be completely ruined
within hours. GPS timing is
incredibly precise; of all the
problems in engineering, it’s
one of the only ones in which
engineers have been forced to
include both special and
general relativity in their
calculations.
Most other clocks would
keep working fine. However,
if you have a very precise
pendulum clock, you might
notice something odd—by
the end of the day, it would
be three seconds ahead of
where it should be.
t = 1 month
After a month, the Earth
would have expanded by 26
kilometers—an increase of
0.4 percent—and its mass
would have increased by 1.2
percent.
Surface
gravity
would have gone up by only
0.4 percent, rather than 1.2
percent, since surface gravity
is proportional to radius.4
You might notice the
difference in weight on a
scale, but it’s not a big deal.
Gravity varies by this much
between
different
cities
already. This is a good thing
to keep in mind if you buy a
digital scale. If your scale has
a precision of more than two
decimal places, you need to
calibrate it with a test weight
—the force of gravity at the
scale factory isn’t necessarily
the same as the force of
gravity at your house.
While you might not notice
the increased gravity just yet,
you’d notice the expansion.
After a month, you’d see a lot
of cracks opening up in long
concrete structures and the
failure of elevated roads and
old bridges. Most buildings
would probably be OK,
although those anchored
firmly into bedrock might
start
to
behave
unpredictably.5
At this point, astronauts on
the ISS would start getting
worried. Not only would the
ground (and atmosphere) be
rising toward them, but the
increased gravity would also
cause their orbit to slowly
shrink. They’d need to
evacuate quickly; they’d have
at most a few months before
the station reentered the
atmosphere and deorbited.
t = 1 year
After a year, gravity would be
5 percent stronger. You’d
probably notice the weight
gain, and you’d definitely
notice the failure of roads,
bridges,
power
lines,
satellites, and undersea cables.
Your pendulum clock would
now be ahead by five days.
What
about
the
atmosphere?
If the atmosphere isn’t
growing like the land and
water are, air pressure would
start dropping. This is due to
a combination of factors. As
gravity increases, then air gets
heavier. But since that air is
spread out over a larger area,
the overall effect would be
decreasing air pressure.
On the other hand, if the
atmosphere is also expanding,
surface air pressure would
rise. After years had passed,
the top of Mount Everest
would no longer be in the
“death zone.” On the other
hand, since you’d be heavier
—and the mountain would be
taller—climbing
more work.
would
be
t = 5 years
After five years, gravity would
be 25 percent stronger. If you
weighed 70 kg when the
expansion started, you’d
weigh 88 kg now.
Most of our infrastructure
would have collapsed. The
cause of the collapse would be
the expanding ground below
them, not the increased
gravity. Surprisingly, most
skyscrapers would hold up
fine under much higher
gravity.6 For most of them,
the limiting factor
weight, but wind.
isn’t
t = 10 years
After 10 years, gravity would
be 50 percent stronger. In the
scenario
where
the
atmosphere isn’t expanding,
the air would become thin
enough to be difficult to
breathe even at sea level. In
the other scenario, we’d be
OK for a little while longer.
t = 40 years
After 40 years, Earth’s surface
gravity would have tripled.7
At
this
point,
even
the
strongest humans would be
able to walk only with great
difficulty. Breathing would be
difficult.
Trees
would
collapse. Crops wouldn’t
stand up under their own
weight.
Virtually
every
mountainside would see
massive landslides as material
sought out a shallower angle
of repose.
Geologic activity would also
accelerate. Most of the
Earth’s heat is provided by
radioactive decay of minerals
in the crust and mantle,8 and
more Earth means more heat.
Since the volume expands
faster than the surface area,
the overall heat flowing out
per square meter will increase.
It’s not actually enough to
substantially warm the planet
—Earth’s surface temperature
is
dominated
by
the
atmosphere and the Sun—but
it would lead to more
volcanoes, more earthquakes,
and faster tectonic movement.
This would be similar to the
situation on Earth billions of
years ago, when we had more
radioactive material and a
hotter mantle.
More active plate tectonics
might be good for life. Plate
tectonics play a key role in
stabilizing
the
Earth’s
climate, and planets smaller
than Earth (like Mars) don’t
have enough internal heat to
sustain long-term geologic
activity. A larger planet would
allow for more geologic
activity, which is why some
scientists
think
that
exoplanets slightly larger than
Earth (“super-Earths”) could
be more friendly to life than
Earth-sized ones.
t = 100 years
After 100 years, we’d be
experiencing over 6 gees of
gravity. Not only would we be
unable to move around to
find food, but our hearts
would be unable to pump
blood to our brains. Only
small insects (and sea
animals) would be physically
able to move around. Perhaps
humans could survive in
specially built controlledpressure domes, moving
around by keeping most of
our bodies submerged in
water.
Breathing in this situation
would be difficult. It’s hard to
suck in air against the weight
of the water, which is why
snorkels can only work when
your lungs are near the
surface.
Outside of low-pressure
domes, the air would become
unbreathable for a different
reason. At somewhere around
6 atmospheres, even ordinary
air becomes toxic. Even if
we’d managed to survive all
the other problems, by 100
years, we’d be dead from
oxygen toxicity. Toxicity
aside, breathing dense air is
difficult simply because it’s
heavy.
Black hole?
When would the Earth
eventually become a black
hole?
It’s hard to answer that,
because the premise of the
question is that the radius is
steadily expanding while the
density stays the same
—whereas in a black hole, the
density increases.
The dynamics of really huge
rocky planets aren’t often
analyzed, since there’s no
obvious way that they could
form; anything that large will
have enough gravity to gather
hydrogen and helium during
planet formation and become
a gas giant.
At some point, our growing
Earth would reach the point
where adding more mass
causes it to contract, rather
than expand. After this point,
it would collapse into
something like a sputtering
white dwarf or neutron star,
and then—if its mass kept
increasing—eventually
become a black hole.
But before it gets that
far . . .
t = 300 years
It’s a shame humans wouldn’t
live this long, because at this
point, something really neat
would happen.
As the Earth grows, the
Moon would, like all our
satellites, gradually spiral
inward.
After
several
centuries, it would be close
enough to the swollen Earth
that the tidal forces between
Earth and the Moon would
be
stronger
than
the
gravitational forces holding
the Moon together.
When the Moon passed
this boundary—called the
Roche
limit—it
would
gradually break apart,9 and
Earth would, for a short time,
have rings.
If you liked it, then you should have
moved a mass inside its Roche limit.
1 The smoking gun that
confirmed the theory of plate
tectonics was the discovery of
sea-floor spreading. The way
sea-floor spreading and
magnetic pole reversal neatly
confirmed each other is one of
my favorite examples of
scientific discovery at work.
2 It turns out it’s kind of dumb.
3 As it turns out, the ocean is
expanding, since it’s getting
warmer. This is (currently) the
main way global warming is
raising the sea level.
4 Mass is proportional to radius
cubed, and gravity is
proportional to mass times
inverse square of radius, so
radius3 / radius2 = radius.
5 Just what you want in a
skyscraper.
6 Although I wouldn’t trust the
elevators.
7 Over decades, the force of
gravity would grow slightly
faster than you’d expect, since
the material in the Earth would
compress under its own weight.
The pressure inside planets is
roughly proportional to the
square of their surface area, so
the Earth’s core would be
squeezed tightly.
http://cseligman.com/text/planet
8 Although some radioactive
elements, like uranium, are
heavy, they get squeezed out of
the lower layers because their
atoms don’t mesh well with the
rock lattices at those depths.
For more, see this chapter:
http://igppweb.ucsd.edu/~guy/sio
and this article: http://worldnuclear.org/info/Nuclear-FuelCycle/UraniumResources/The-CosmicOrigins-ofUranium/#.UlxuGmRDJf4.
9 Sorry, Moon!
WEIGHTLESS
ARROW
Q. Assuming
a zero-gravity
environment
with an
atmosphere
identical to
Earth’s, how
long would it
take the
friction of air
to stop an
arrow fired
from a bow?
Would it
eventually
come to a
standstill and
hover in
midair?
—Mark Estano
A. IT’S
HAPPENED TO
ALL of us. You’re in the belly
of a vast space station and
you’re trying to shoot
someone with a bow and
arrow.
Compared to a normal
physics problem, this scenario
is backward. Usually, you
consider gravity and neglect
air resistance, not the other
way around.1
As you’d expect, air
resistance would slow down
an arrow, and eventually it
would stop . . . after flying
very, very far. Fortunately, for
most of that flight, it
wouldn’t be much of a danger
to anyone.
Let’s go over what would
happen in more detail.
Say you fire the arrow at 85
meters per second. That’s
about twice the speed of a
major-league fastball, and a
little below the 100 m/s speed
of arrows from high-end
compound bows.
The arrow would slow
down quickly. Air resistance
is proportional to speed
squared, which means that
when it’s going fast, the arrow
would experience a lot of
drag.
After ten seconds of flight,
the arrow would have traveled
400 meters, and its speed
would have dropped from 85
m/s to 25 m/s; 25 m/s is
about how fast a normal
person could throw an arrow.
At that speed, the arrow
would be a lot less dangerous.
We know from hunters that
small differences in arrow
speed make big differences in
the size of the animal it can
kill. A 25-gram arrow moving
at 100 m/s could be used to
hunt elk and black bears. At
70 m/s, it might be too slow
to kill a deer. Or, in our case,
a space deer.
Once the arrow leaves that
range,
it’s
no
longer
particularly dangerous . . . but
it’s not even close to stopping.
After five minutes, the
arrow would have flown
about a mile, and it would
have slowed to roughly
walking speed. At that speed,
it would experience very little
drag; it would just cruise
along, slowing down very
gradually.
At this point, it would have
gone much farther than any
Earth arrow can go. Highend bows can shoot an arrow
a distance of a couple
hundred meters over flat
ground, but the world record
for a hand bow-and-arrow
shot is just over a kilometer.
This record was set in 1987
by archer Don Brown. Brown
set his record by firing slender
metal rods from a terrifying
contraption that only vaguely
resembled a traditional bow.
As the minutes stretch into
hours and the arrow slows
down more and more, the
airflow changes.
Air has very little viscosity.
That is, it’s not gooey. That
means things flying through
the air experience drag
because of the momentum of
the air they’re shoving out of
the way—not from cohesion
between the air molecules. It’s
more like pushing your hand
through a bathtub full of
water than a bathtub full of
honey.
After a few hours, the arrow
would be moving so slowly
that it would be barely visible.
At this point, assuming the
air is relatively still, the air
would start acting like honey
instead of water. And the
arrow would, very gradually,
come to a stop.
The exact range would
depend heavily on the precise
design of the arrow. Small
differences in an arrow’s
shape can dramatically change
the nature of the airflow over
it at low speeds. But at
minimum, it would probably
fly several kilometers, and
could conceivably go as far as
5 or 10.
Here’s
the
problem:
Currently, the only sustained
zero-g environment with an
Earth-like atmosphere is the
International Space Station.
And the largest ISS module,
Kibo, is only 10 meters long.
This means that if you
actually
performed
this
experiment, the arrow would
fly no more than 10 meters.
Then, it would either come to
a stop . . . or really ruin
someone’s day.
1 Also, you don’t usually shoot
astronauts with a bow and
arrow — at least not for an
undergraduate degree.
SUNLESS
EARTH
Q. What
would
happen to the
Earth if the
Sun suddenly
switched off?
—Many, many readers
A. THIS
IS PROBABLY
THE single most popular
submission to What If.
Part of why I haven’t
answered it is that it’s been
answered already. A Google
search for “what if the Sun
went out” turns up a lot of
excellent articles thoroughly
analyzing the situation.
However, the rate of
submission of this question
continues to rise, so I’ve
decided to do my best to
answer it.
If the Sun went out . . .
We won’t worry about
exactly how it happens. We’ll
just assume we figured out a
way to fast-forward the Sun
through its evolution so that
it becomes a cold, inert
sphere. What would the
consequences be for us here
on Earth?
Let’s look at a few . . .
Reduced risk of solar flares:
In 1859, a massive solar flare
and geomagnetic storm hit
the Earth. Magnetic storms
induce electric currents in
wires. Unfortunately for us,
by 1859 we had wrapped the
Earth in telegraph wires. The
storm
caused
powerful
currents in those wires,
knocking
out
communications and in some
cases
causing
telegraph
equipment to catch fire.
Since 1859, we’ve wrapped
the Earth in a lot more wires.
If the 1859 storm hit us
today, the Department of
Homeland Security estimates
the economic damage to the
US alone would be several
trillion dollars—more than
every hurricane that has ever
hit the US combined. If the
Sun went out, this threat
would be eliminated.
Improved satellite service:
When a communications
satellite passes in front of the
Sun, the Sun can drown out
the satellite’s radio signal,
causing an interruption in
service. Deactivating the Sun
would solve this problem.
Better astronomy: Without
the
Sun,
ground-based
observatories would be able to
operate around the clock. The
cooler air would create less
atmospheric noise, which
would reduce the load on
adaptive optics systems and
allow for sharper images.
Stable
dust:
Without
sunlight, there would be no
Poynting–Robertson
drag,
which means we would finally
be able to place dust into a
stable orbit around the Sun
without the orbits decaying.
I’m not sure whether anyone
wants to do that, but you
never know.
Reduced
infrastructure
costs: The Department of
Transportation estimates that
it would cost $20 billion per
year over the next 20 years to
repair and maintain all US
bridges. Most US bridges are
over water; without the Sun,
we could save money by
simply driving on a strip of
asphalt laid across the ice.
Cheaper trade: Time zones
make trade more expensive;
it’s harder to do business with
someone if their office hours
don’t overlap with yours. If
the Sun went out, it would
eliminate the need for time
zones, allowing us to switch
to UTC and give a boost to
the global economy.
Safer children: According to
the
North
Dakota
Department of Health, babies
younger than six months
should be kept out of direct
sunlight. Without sunlight,
our children would be safer.
Safer combat pilots: Many
people sneeze when exposed
to bright sunlight. The
reasons for this reflex are
unknown, and it may pose a
danger to fighter pilots during
flight. If the Sun went dark, it
would mitigate this danger to
our pilots.
Safer parsnip: Wild parsnip
is a surprisingly nasty plant.
Its leaves contain chemicals
called furocoumarins, which
can be absorbed by human
skin
without
causing
symptoms . . . at first.
However, when the skin is
then exposed to sunlight
(even days or weeks later), the
furocoumarins cause a nasty
chemical burn. This is called
phytophotodermatitis.
A
darkened Sun would liberate
us from the parsnip threat.
In conclusion, if the Sun
went out, we would see a
variety of benefits across
many areas of our lives.
Are there any
downsides to this
scenario?
We would all freeze and die.
UPDATING A
PRINTED
WIKIPEDIA
Q. If you had
a printed
version of the
whole of (say,
the English)
Wikipedia,
how many
printers
would you
need in order
to keep up
with the
changes
made to the
live version?
—Marein Könings
A. THIS MANY.
If a date took you home and you saw
a row of working printers set up in
his or her living room, what would
you think?
That’s surprisingly few
printers! But before you try to
create a live-updating paper
Wikipedia, let’s look at what
those printers would be
doing . . . and how much
they’d cost.
Printing Wikipedia
People
have
considered
printing
out
Wikipedia
before. One student, Rob
Matthews, printed every
Wikipedia featured article,
creating a book several feet
thick.
Of course, that’s just a small
slice of the best of Wikipedia;
the entire encyclopedia would
be a lot bigger. Wikipedia
user Tompw has set up a tool
that calculates the current size
of the whole English
Wikipedia
in
printed
volumes. It would fill a lot of
bookshelves.
Keeping up with the edits
would be hard.
Keeping up
The
English
Wikipedia
currently
receives
about
125,000 to 150,000 edits each
day, or 90–100 per minute.
We could try to define a
way to measure the “word
count” of the average edit, but
that’s hard bordering on
impossible. Fortunately, we
don’t need to—we can just
estimate that each change is
going to require us to reprint
a page somewhere. Many
edits will actually change
multiple pages—but many
other edits are reverts, which
would let us put back pages
we’ve already printed.1 One
page per edit seems like a
reasonable middle ground.
For a mix of photos, tables,
and text typical of Wikipedia,
a good inkjet printer might
put out 15 pages per minute.
That means you’d need only
about six printers running at
any given time to keep pace
with the edits.
The paper would stack up
quickly.
Using
Rob
Matthews’ book as a starting
point, I did my own back-ofthe-envelope estimate for the
size of the current English
Wikipedia. Based on the
average length of featured
articles vs. all articles, I came
up with an estimate of 300
cubic meters for a printout of
the whole thing in plain text
form.
By comparison, if you were
trying to keep up with the
edits, you’d print out 300
cubic meters every month.
$500,000 per month
Six printers isn’t that many,
but they’d be running all the
time.
And
that
gets
expensive.
The electricity to run them
would be cheap—a few
dollars a day.
The paper would be about 1
cent per sheet, which means
you’ll be spending about a
thousand dollars a day on
paper. You’d need to hire
people to manage the printers
24/7, but that would actually
cost less than the paper.
Even
the
printers
themselves wouldn’t be too
expensive,
despite
the
terrifyingly fast replacement
cycle.
But the ink cartridges
would be a nightmare.
Ink
A study by QualityLogic
found that for a typical inkjet
printer, the real-life cost of
ink ran from 5 cents per page
for
black-and-white
to
around 30 cents per page for
photos. That means you’d be
spending four to five figures
per day on ink cartridges.
You definitely want to
invest in a laser printer.
Otherwise, in just a month or
two, this project could end up
costing you half a million
dollars:
But that’s not even the
worst part.
On January 18, 2012,
Wikipedia blacked out all its
pages to protest proposed
Internet-freedom-limiting
laws. If, someday, Wikipedia
decides to go dark again, and
you want to join the
protest . . .
. . . you’ll have to get a
crate of markers and color
every page solid black
yourself.
I would definitely stick to
digital.
1 The filing system that would
be required for this would be
mind-bending. I’m fighting the
urge to start trying to design it.
FACEBOOK
OF THE
DEAD
Q. When, if
ever, will
Facebook
contain more
profiles of
dead people
than of living
ones?
—Emily Dunham
“Put on your headphones!” “Can’t.
Ears fell off.”
A. EITHER
THE 2060S
OR the 2130s.
There are not a lot of dead
people on Facebook.1 The
main reasons for this is that
Facebook—and its users—are
young. The average Facebook
user has gotten older over the
last few years, but the site is
still used at a much higher
rate by the young than by the
old.
The past
Based on the site’s growth
rate, and the age breakdown
of its users over time,2 there
are probably 10 to 20 million
people who created Facebook
profiles who have since died.
These people are, at the
moment, spread out pretty
evenly
across
the
age
spectrum. Young people have
a much lower death rate than
people in their 60s or 70s, but
they make up a substantial
share of the dead on
Facebook simply because
there have been so many of
them using it.
An elderly Cory Doctorow cosplaying
by wearing what the future thinks he
wore in the past.
The future
About 290,000 US Facebook
users probably died in 2013.
The worldwide total for 2013
is likely several million.3 In
just seven years, this death
rate will double, and in seven
more years it will double
again.
Even if Facebook closes
registration tomorrow, the
number of deaths per year
will continue to grow for
many decades, as the
generation who was in college
between 2000 and 2020
grows old.
The deciding factor in
when
the
dead
will
outnumber the living is
whether Facebook adds new
living users—ideally, young
ones—fast enough to outrun
this tide of death for a while.
Facebook 2100
This brings us to the question
of Facebook’s future.
We don’t have enough
experience
with
social
networks to say with any kind
of certainty how long
Facebook will last. Most
websites have flared up and
then gradually declined in
popularity, so it’s reasonable
to assume Facebook will
follow that pattern.4
In that scenario, where
Facebook starts losing market
share later this decade and
never recovers, Facebook’s
crossover date—the date
when the dead outnumber the
living—will come sometime
around 2065.
But maybe it won’t. Maybe
it will take on a role like the
TCP protocol, where it
becomes
a
piece
of
infrastructure on which other
things are built, and has the
inertia of consensus.
If Facebook is with us for
generations,
then
the
crossover date could be as late
as the mid-2100s.
That
seems
unlikely.
Nothing lasts forever, and
rapid change has been the
norm for anything built on
computer technology. The
ground is littered with the
bones of websites and
technologies that seemed like
permanent institutions ten
years ago.
It’s possible the reality
could be somewhere in
between.5 We’ll just have to
wait and find out.
The fate of our
accounts
Facebook can afford to keep
all our pages and data
indefinitely. Living users will
always generate more data
than dead ones,6 and the
accounts for active users are
the ones that will need to be
easily accessible. Even if
accounts for dead (or inactive)
people make up a majority of
their users, it will probably
never add up to a large part of
its
overall
infrastructure
budget.
More important will be our
decisions. What do we want
for those pages? Unless we
demand
that
Facebook
deletes them, they will
presumably, by default, keep
copies of everything forever.
Even if they don’t, other
data-vacuuming organizations
will.
Right now, next of kin can
convert a dead person’s
Facebook profile into a
memorial page. But there are
a lot of questions surrounding
passwords and access to
private data that we haven’t
yet developed social norms
for. Should accounts remain
accessible? What should be
made private? Should next of
kin have the right to access
email? Should memorial
pages have comments? How
do we handle trolling and
vandalism? Should people be
allowed to interact with dead
user accounts? What lists of
friends should they show up
on?
These are issues that we’re
currently in the process of
sorting out by trial and error.
Death has always been a big,
difficult, and emotionally
charged subject, and every
society finds different ways to
handle it.
The basic pieces that make
up a human life don’t change.
We’ve always eaten, learned,
grown, fallen in love, fought,
and died. In every place,
culture, and technological
landscape, we develop a
different set of behaviors
around these same activites.
Like every group that came
before us, we’re learning how
to play those same games on
our particular playing field.
We’re developing, through
sometimes messy trial and
error, a new set of social
norms for dating, arguing,
learning, and growing on the
Internet. Sooner or later, we’ll
figure out how to mourn.
1 At the time I wrote this,
anyway, which was before the
bloody robot revolution.
2 You can get user counts for
each age group from Facebook’s
create-an-ad tool, although you
may want to try to account for
the fact that Facebook’s age
limits cause some people to lie
about their ages.
3 Note: In some of these
projections, I used US
age/usage data extrapolated to
the Facebook userbase as a
whole, because it’s easier to find
US census and actuarial
numbers than to assemble the
country-by-country for the
whole Facebook-using world.
The US isn’t a perfect model of
the world, but the basic
dynamics — young people’s
Facebook adoption determines
the site’s success or failure while
population growth continues
for a while and then levels off
— will probably hold
approximately true. If we
assume a rapid Facebook
saturation in the developing
world, which currently has a
faster-growing and younger
population, it shifts many of the
landmarks by a handful of
years, but doesn’t change the
overall picture as much as you
might expect.
4 I’m assuming, in these cases,
that no data is ever deleted. So
far, that’s been a reasonable
assumption; if you’ve made a
Facebook profile, that data
probably still exists, and most
people who stop using a service
don’t bother to delete their
profiles. If that behavior
changes, or if Facebook
performs a mass purging of its
archives, the balance could
change rapidly and
unpredictably.
5 Of course, if there’s a sudden
rapid increase in the death rate
of Facebook users — possibly
one that includes humans in
general — the crossover could
happen tomorrow.
6 I hope.
SUNSET ON
THE BRITISH
EMPIRE
Q. When (if
ever) did the
Sun finally set
on the British
Empire?
—Kurt Amundson
A. IT
HASN’T. YET. BUT
only because of a few
dozen people living in an area
smaller than Disney World.
The world’s largest
empire
The British Empire spanned
the globe. This led to the
saying that the Sun never set
on it, since it was always
daytime somewhere in the
Empire.
It’s hard to figure out
exactly when this long
daylight began. The whole
process of claiming a colony
(on land already occupied by
other people) is awfully
arbitrary in the first place.
Essentially, the British built
their empire by sailing around
and sticking flags on random
beaches. This makes it hard
to decide when a particular
spot in a country was
“officially”
Empire.
added
to
the
“What about that shadowy place
over there?” “That’s France. We’ll
get it one of these days.”
The exact day when the
Sun stopped setting on the
Empire
was
probably
sometime in the late 1700s or
early 1800s, when the first
Australian territories were
added.
The
Empire
largely
disintegrated in the early 20th
century, but—surprisingly—
the Sun hasn’t technically
started setting on it again.
Fourteen territories
Britain has 14 overseas
territories,
the
direct
remnants of the British
Empire.
Many newly independent
British colonies joined the
Commonwealth of Nations.
Some of them, like Canada
and Australia, have Queen
Elizabeth as their official
monarch. However, they are
independent
states
that
happen to have the same
queen; they are not part of
any empire.1
The Sun never sets on all
14 British territories at once
(or even 13, if you don’t count
the
British
Antarctic
Territory). However, if the
UK loses one tiny territory, it
will experience its first
Empire-wide sunset in over
two centuries.
Every
night,
around
midnight GMT, the Sun sets
on the Cayman Islands, and
doesn’t rise over the British
Indian Ocean Territory until
after 1:00 A.M. For that hour,
the little Pitcairn Islands in
the South Pacific are the only
British territory in the Sun.
The Pitcairn Islands have a
population of a few dozen
people, the descendants of the
mutineers from the HMS
Bounty. The islands became
notorious in 2004 when a
third of the adult male
population, including the
mayor, were convicted of
child sexual abuse.
As awful as the islands may
be, they remain part of the
British Empire, and unless
they’re kicked out, the twocentury-long British daylight
will continue.
Will it last forever?
Well, maybe.
In April of 2432, the island
will experience its first total
solar eclipse since the
mutineers arrived.
Luckily for the Empire, the
eclipse happens at a time
when the Sun is over the
Cayman Islands in the
Caribbean. Those areas won’t
see a total eclipse; the Sun
will even still be shining in
London.
In fact, no total eclipse for
the next thousand years will
pass over the Pitcairn Islands
at the right time of day to end
the streak. If the UK keeps its
current
territories
and
borders, it can stretch out the
daylight for a long, long time.
But not forever. Eventually
—many millennia in the
future—an eclipse will come
for the island, and the Sun
will finally set on the British
Empire.
1 That they know of.
STIRRING
TEA
Q. I was
absentmindedl
stirring a cup
of hot tea,
when I got to
thinking,
“Aren’t I
actually
adding
kinetic
energy into
this cup?” I
know that
stirring does
help to cool
down the tea,
but what if I
were to stir it
faster? Would
I be able to
boil a cup of
water by
stirring?
—Will Evans
A. NO.
The basic idea makes
sense. Temperature is just
kinetic energy. When you stir
tea, you’re adding kinetic
energy to it, and that energy
goes somewhere. Since the
tea doesn’t do anything
dramatic like rise into the air
or emit light, the energy must
be turning to heat.
Am I making tea wrong?
The reason you don’t notice
the heat is that you’re not
adding very much of it. It
takes a huge amount of
energy to heat water; by
volume, it has a greater heat
capacity than any other
common substance.1
If you want to heat water
from room temperature to
nearly boiling in two minutes,
you’ll need a lot of power:2
Our formula tells us that if
we want to make a cup of hot
water in two minutes, we’ll
need a 700-watt power
source. A typical microwave
uses 700 to 1100 watts, and it
takes about two minutes to
heat a mug of water to make
tea. It’s nice when things
work out!3
Microwaving a cup of water
for two minutes at 700 watts
delivers an awful lot of energy
to the water. When water
falls from the top of Niagara
Falls, it gains kinetic energy,
which is converted to heat at
the bottom. But even after
falling that great distance, the
water heats up by only a
fraction of a degree.4 To boil
a cup of water, you’d have to
drop it from higher than the
top of the atmosphere.
(The British Felix Baumgartner)
How does stirring compare
to microwaving?
Based on figures from
industrial mixer engineering
reports, I estimate that
vigorously stirring a cup of tea
adds heat at a rate of about a
ten-millionth of a watt.
That’s completely negligible.
The physical effect of
stirring is actually a little
complicated.5 Most of the
heat is carried away from
teacups by the air convecting
over them, and so they cool
from the top down. Stirring
brings fresh hot water from
the depths, so it can help this
process. But there are other
things going on—stirring
disturbs the air, and it heats
the walls of the mug. It’s hard
to be sure what’s really going
on without data.
Fortunately, we have the
Internet. Stack Exchange user
drhodes measured the rate of
teacup cooling from stirring
vs. not stirring vs. repeatedly
dipping a spoon into the cup
vs. lifting it. Helpfully,
drhodes posted both highresolution graphs and the raw
data itself, which is more than
you can say for a lot of journal
articles.
The conclusion: It doesn’t
really matter whether you stir,
dip, or do nothing; the tea
cools at about the same rate
(although dipping the spoon
in and out of the tea cooled it
slightly faster).
Which brings us back to the
original question: Could you
boil tea if you just stirred it
hard enough?
No.
The first problem is power.
The amount of power in
question, 700 watts, is about a
horsepower, so if you want to
boil tea in two minutes, you’ll
need at least one horse to stir
it hard enough.
You can reduce the power
requirement by heating the
tea over a longer period of
time, but if you reduce it too
far the tea will be cooling as
fast as you’re heating it.
Even if you could churn the
spoon hard enough—tens of
thousands of stirs per second
—fluid dynamics would get
in the way. At those high
speeds, the tea would cavitate;
a vacuum would form along
the path of the spoon and
stirring
would
ineffective.6
become
And if you stir hard enough
that your tea cavitates, its
surface area will increase very
rapidly, and it will cool to
room temperature in seconds.
No matter how hard you
stir your tea, it’s not going to
get any warmer.
1 Hydrogen and helium have a
higher heat capacity by mass,
but they’re diffuse gasses. The
only other common substance
with a higher heat capacity by
mass is ammonia. All three of
these lose to water when
measured by volume.
2 Note: Pushing almost-boiling
water to boiling takes a large
burst of extra energy on top of
what’s required to heat it to the
boiling point — this is called
the enthalpy of vaporization.
3 If they didn’t, we’d just blame
“inefficiency” or “vortices.”
4
5 In some situations, mixing
liquids can actually help keep
them warm. Hot water rises,
and when a body of water is
large and still enough (like the
ocean), a warm layer forms on
the surface. This warm layer
radiates heat much more
quickly than a cold layer would.
If you disrupt this hot layer by
mixing the water, the rate of
heat loss decreases.
This is why hurricanes tend to
lose strength if they stop
moving forward — their waves
churn up cold water from the
depths, cutting them off from
the thin layer of hot surface
water that was their main
source of energy.
6 Some blenders, which are
enclosed, actually do manage to
warm their contents this way.
But what kind of person makes
tea in a blender?
ALL THE
LIGHTNING
Q. If all the
lightning
strikes
happening in
the world on
any given day
all happened
in the same
place at once,
what would
happen to
that place?
—Trevor Jones
A. THEY
SAY
LIGHTNING
NEVER
strikes in the same place
twice.
“They” are wrong. From an
evolutionary perspective, it’s a
little surprising that this
saying has survived; you’d
think that people who
believed it would have been
gradually filtered out of the
living population.
This is how evolution works, right?
People
often
wonder
whether we could harvest
electrical
power
from
lightning. On the face of it, it
makes sense; after all,
lightning is electricity,1 and
there is indeed a substantial
amount of power in a
lightning strike. The problem
is, it’s hard to get lightning to
strike where you want it.2
A typical lightning strike
delivers enough energy to
power a residential house for
about two days. That means
that even the Empire State
Building, which is struck by
lightning about 100 times a
year, wouldn’t be able to keep
a house running on lightning
power alone.
Even in regions of the
world with a lot of lightning,
such as Florida and the
eastern Congo, the power
delivered to the ground by
sunlight outweighs the power
delivered by lightning by a
factor
of
a
million.
Generating
power
from
lightning is like building a
wind farm whose blades are
turned by a tornado: awesome
impractical.3
Trevor’s lightning
In Trevor’s scenario, all the
lightning in the world hits in
one place. This would make
power generation a lot more
attractive!
By “happened in the same
place,” let’s assume the
lightning bolts all come down
in parallel, right up against
each other. The main channel
of a lightning bolt—the part
that’s carrying current—is
about a centimeter or two in
diameter.
Our
bundle
contains about a million
separate bolts, which means it
will be about 6 meters in
diameter.
Every science writer always
compares everything to the
atomic bomb dropped on
Hiroshima,4 so we may as
well get that out of the way:
The lightning bolt would
deliver about two atomic
bombs’ worth of energy to the
air and ground. From a more
practical standpoint, this is
enough electricity to power a
game console and plasma TV
for several million years. Or,
to put it another way, it could
support the US’s electricity
consumption . . . for five
minutes.
The bolt itself would be
only as narrow as the center
circle of a basketball court,
but it would leave a crater the
size of the entire court.
Within the bolt, the air
would turn to high-energy
plasma. The light and heat
from
the
bolt
would
spontaneously ignite surfaces
for miles around. The
shockwave would flatten trees
and demolish buildings. All
in all, the Hiroshima
comparison is not far off.
Could we protect ourselves?
Lightning rods
The mechanism by which
lightning rods work is
disputed. Some people claim
they actually ward off
lightning strikes by “bleeding”
charge from the ground to
the air, lowering the cloudto-ground voltage potential
and reducing the probability
of a strike. The National Fire
Protection Association does
not currently endorse this
idea.
I’m not sure what the
NFPA would say about
Trevor’s massive lightning
bolt, but a lightning rod
wouldn’t protect you from it.
A copper cable a meter in
diameter could, in theory,
conduct the brief surge of
current from the bolt without
melting. Unfortunately, when
the bolt reached the bottom
end of the rod, the ground
wouldn’t conduct it so well,
and the explosion of molten
rock would demolish your
house all the same.5
Catatumbo lightning
Collecting all the world’s
lightning into one place is
obviously impossible. What
about gathering all the
lightning from just one area?
No place on Earth has
constant lightning, but there’s
an area in Venezuela that
comes close. Near the
southwestern edge of Lake
Maracaibo, there’s a strange
phenomenon:
perpetual
nighttime
thunderstorms.
There are two spots, one over
the lake and one over land to
the
west,
where
thunderstorms form almost
every night. These storms can
generate a flash of lightning
every two seconds, making
Lake Maracaibo the lightning
capital of the world.
If you somehow managed
to channel all the bolts from a
single night of Catatumbo
thunderstorms down through
a single lightning rod, and
used it to charge a massive
capacitor, it would store up
enough power to run a game
console and plasma TV for
roughly a century.6
Of course, if this happened,
the old saying would need
even more revision.
1 Citation: The presentation I
gave to my third-grade class at
Assawompset Elementary
School while wearing a Ben
Franklin costume.
2 And I hear it never strikes in
the same place twice.
3 In case you’re curious, yes, I
did run some numbers on using
passing tornadoes to run wind
turbines, and it’s even less
practical than gathering
lightning. The average location
in the heart of Tornado Alley
has a tornado pass over it only
every 4000 years. Even if you
managed to absorb all the
accumulated energy of the
tornado, it would still result in
less than a watt of average
power output in the long run.
Believe it or not, something like
this idea has actually been
attempted. A company called
AVEtec has proposed building
a “vortex engine” that would
produce artificial tornadoes and
use them to generate power.
4 Niagara Falls has a power
output equal to a Hiroshimasized bomb going off every
eight hours! The atomic bomb
dropped on Nagasaki had an
explosive power equal to 1.3
Hiroshima bombs! For
context, the gentle breeze
blowing across a prairie also
carries roughly the kinetic
energy of a Hiroshima bomb.
5 Your house would already be
catching fire anyway, thanks to
the thermal radiation from
plasma in the air.
6 Since there’s no cellular data
coverage on the southwest
shore of Lake Maracaibo, you’ll
have to buy service through a
satellite provider, which
generally means hundreds of
milliseconds of lag.
LONELIEST
HUMAN
Q. What is
the farthest
one human
being has
ever been
from every
other living
person? Were
they lonely?
—Bryan J McCarter
A. IT’S
HARD TO KNOW
for sure!
The most likely suspects are
the six Apollo command
module pilots who stayed in
lunar orbit during a Moon
landing: Mike Collins, Dick
Gordon, Stu Roosa, Al
Worden, Ken Mattingly, and
Ron Evans.
Each of these astronauts
stayed alone in the command
module while two other
astronauts landed on the
Moon. At the highest point
in their orbit, they were about
3585 kilometers from their
fellow astronauts.
From another point of view,
this was the farthest the rest
of
humanity
has
ever
managed to get from those
jerk astronauts.
You’d think astronauts
would have a lock on this
category, but it’s not so cutand-dried. There are a few
other candidates who come
pretty close!
Polynesians
It’s hard to get 3585
kilometers
from
a
permanently
inhabited
place.1 The Polynesians, who
were the first humans to
spread across the Pacific,
might have managed it, but
this would have required a
lone sailor to travel awfully far
ahead of everyone else. It may
have happened—perhaps by
accident, when someone was
carried far from their group
by a storm—but we’re
unlikely to ever know for
sure.
Once the Pacific was
colonized, it got a lot harder
to find regions of the Earth’s
surface where someone could
achieve
3585-kilometer
isolation. Now that the
Antarctic continent has a
permanent population of
researchers,
it’s
certainly impossible.
almost
Antarctic explorers
During the period of
Antarctic exploration, a few
people have come close to
beating the astronauts, and
it’s possible one of them
actually holds the record. One
person who came very close
was Robert Scott.
Robert Falcon Scott was a
British explorer who met a
tragic end. Scott’s expedition
reached the South Pole in
1911, only to discover that
Norwegian explorer Roald
Amundsen had beaten him
there by several months. The
dejected Scott and his
companions began their trek
back to the coast, but they all
died while crossing the Ross
Ice Shelf.
The
last
surviving
expedition member would
have been, briefly, one of the
most isolated people on
Earth.2
However,
he
(whoever he was) was still
within 3585 kilometers of a
number of humans, including
some other Antarctic explorer
outposts as well as the Māori
on Rakiura (Stewart Island)
in New Zealand.
There are plenty of other
candidates. Pierre François
Péron, a French sailor, says
he was marooned on Île
Amsterdam in the southern
Indian Ocean. If so, he came
close
to
beating
the
astronauts, but he wasn’t
quite far enough from
Mauritius,
southwestern
Australia, or the edge of
Madagascar to qualify.
We’ll probably never know
for sure. It’s possible that
some shipwrecked 18thcentury sailor drifting in a
lifeboat in the Southern
Ocean holds the title of most
isolated human. However,
until some clear piece of
historic evidence pops up, I
think
the
six
Apollo
astronauts have a pretty good
claim.
Which brings us to the
second part of Bryan’s
question: Were they lonely?
Loneliness
After returning to Earth,
Apollo 11 command module
pilot Mike Collins said he did
not feel at all lonely. He
wrote about the experience in
his book Carrying the Fire:
An Astronaut’s Journeys:
Far from feeling lonely or
abandoned, I feel very
much a part of what is
taking place on the lunar
surface . . . I don’t mean to
deny a feeling of solitude.
It is there, reinforced by
the fact that radio contact
with the Earth abruptly
cuts off at the instant I
disappear behind the
moon.
I am alone now, truly
alone, and absolutely
isolated from any known
life. I am it. If a count
were taken, the score
would be three billion plus
two over on the other side
of the moon, and one plus
God knows what on this
side.
Al Worden, the Apollo 15
command module pilot, even
enjoyed the experience.
There’s a thing about
being alone and there’s a
thing about being lonely,
and they’re two different
things. I was alone but I
was not lonely. My
background was as a
fighter pilot in the air
force, then as a test pilot
—and that was mostly in
fighter airplanes—so I was
very used to being by
myself.
I
thoroughly
enjoyed it. I didn’t have to
talk to Dave and Jim any
more . . . On the backside
of the Moon, I didn’t even
have to talk to Houston
and that was the best part
of the flight.
Introverts understand; the
loneliest human in history
was just happy to have a few
minutes of peace and quiet.
1 Because of the curve of the
Earth, you actually have to go
3619 kilometers across the
surface to qualify.
2 Amundsen’s expedition had
left the continent by then.
WEIRD
(AND
WORRYING)
QUESTIONS
FROM
THE
WHAT IF?
INBOX,
#11
Q. What if
everyone in
Great Britain
went to one of
the coasts and
started
paddling?
Could they
move the
island at all?
—Ellen Eubanks
Q.
Are fire
tornadoes
possible?
—Seth Wishman
RAINDROP
Q. What if a
rainstorm
dropped all of
its water in a
single giant
drop?
—Michael McNeill
A. IT’S
MIDSUMMER IN
KANSAS. The air is hot
and heavy. Two old-timers sit
on the porch in rocking
chairs.
On the horizon to the
southwest, ominous-looking
clouds begin to appear. The
towers build as they draw
closer, the tops spreading out
into an anvil shape.
They hear the tinkling of
wind chimes as a gentle
breeze picks up. The sky
begins to darken.
Moisture
Air holds water. If you walled
off a column of air, from the
ground up to the top of the
atmosphere, and then cooled
the column of air down, the
moisture it contained would
condense out as rain. If you
collected the rain in the
bottom of the column, it
would fill it to a depth of
anywhere between zero and a
few dozen centimeters. That
depth is what we call the air’s
total precipitable water
(TPW).
Normally, the TPW is 1 or
2 centimeters.
Satellites measure this water
vapor content for every point
on the globe, producing some
truly beautiful maps.
We’ll imagine our storm
measures 100 kilometers on
each side and has a high
TPW
content
of
6
centimeters. This means the
water in our rainstorm would
have a volume of:
That water would weigh
600 million tons (which
happens to be about the
current weight of our species).
Normally, a portion of this
water would fall, scattered, as
rain—at most, 6 centimeters
of it.
In this storm, all that water
instead condenses into one
giant drop, a sphere of water
over a kilometer in diameter.
We’ll assume it forms a
couple of kilometers above
the surface, since that’s where
most rain condenses.
The drop begins to fall.
For five or six seconds,
nothing is visible. Then, the
base of the cloud begins to
bulge downward. For a
moment, it looks a little like a
funnel cloud is forming. Then
the bulge widens, and at the
ten-second mark, the bottom
of the drop emerges from the
cloud.
The drop is now falling at
90 meters per second (200
mph). The roaring wind
whips up the surface of the
water into spray. The leading
edge of the droplet turns to
foam as air is forced into the
liquid. If it kept falling for
long enough, these forces
would gradually disperse the
entire droplet into rain.
Before that can happen,
about 20 seconds after
formation, the edge of the
droplet hits the ground. The
water is now moving at over
200 m/s (450 mph). Right
under the point of impact, the
air is unable to rush out of the
way fast enough, and the
compression heats it so
quickly that the grass would
catch fire if it had time.
Fortunately for the grass,
this heat lasts only a few
milliseconds because it’s
doused by the arrival of a lot
of cold water. Unfortunately
for the grass, the cold water is
moving at over half the speed
of sound.
If you were floating in the
center of this sphere during
this episode, you wouldn’t
have felt anything unusual up
until now. It’d be pretty dark
in the middle, but if you had
enough time (and lung
capacity) to swim a few
hundred meters out toward
the edge, you’d be able to
make out the dim glow of
daylight.
As the raindrop approached
the ground, the buildup of air
resistance would lead to an
increase in pressure that
would make your ears pop.
But seconds later, when the
water contacted the surface,
you’d be crushed to death
—the
shockwave
would
briefly
create
pressures
exceeding those at the bottom
of the Mariana Trench.
The water plows into the
ground, but the bedrock is
unyielding. The pressure
forces the water sideways,
creating
a
supersonic
omnidirectional jet1 that
destroys everything in its
path.
The wall of water expands
outward
kilometer
by
kilometer, ripping up trees,
houses, and topsoil as it goes.
The house, porch, and oldtimers are obliterated in an
instant. Everything within a
few kilometers is completely
scoured away, leaving a pool
of mud atop bedrock. The
splash continues outward,
demolishing all structures out
to distances of 20 or 30
kilometers. At this distance,
areas shielded by mountains
or ridges are protected, and
the flood begins to flow along
natural valleys and waterways.
The broader region is
largely protected from the
effects of the storm, though
areas hundreds of kilometers
downstream experience flash
flooding in the hours after the
impact.
News trickles out into the
world about the inexplicable
disaster. There is widespread
shock and puzzlement, and
for a while, every new cloud
in the sky causes mass panic.
Fear reigns supreme as the
world fears rain supreme, but
years pass without any signs
of the disaster repeating.
Atmospheric scientists try
for years to piece together
what happened, but no
explanation is forthcoming.
Eventually, they give up, and
the
unexplained
meteorological phenomenon
is simply called a “dubstep
storm,”
because—in
the
words of one researcher—“It
had one hell of a drop.”
1 Just about the coolest triplet
of words I’ve ever seen.
SAT
GUESSING
Q. What if
everyone who
took the SAT
guessed on
every
multiplechoice
question?
How many
perfect scores
would there
be?
—Rob Balder
A. NONE.
The
SAT
is
a
standardized test given to
American
high
school
students. The scoring is such
that
under
certain
circumstances, guessing an
answer can be a good
strategy. But what if you
guessed on everything?
Not all of the SAT is
multiple-choice, so let’s focus
on
the
multiple-choice
questions to keep things
simple.
We’ll
assume
everyone gets the essay
questions and fill-in-thenumber sections correct.
In the 2014 version of the
SAT, there were 44 multiplechoice questions in the math
(quantitative) section, 67 in
the
critical
reading
(qualitative) section, and 47
in the newfangled1 writing
section. Each question has
five options, so a random
guess has a 20 percent chance
of being right.
The probability of getting
all 158 questions right is:
That’s one in 27 quinquatrigintillion.
If all four million 17-year-
olds took the SAT, and they
all guessed randomly, it’s a
virtually certain that there
would be no perfect scores on
any of the three sections.
How certain is it? Well, if
they each used a computer to
take the test a million times
each day, and continued this
every day for five billion years
—until the Sun expanded to a
red giant and the Earth was
charred to a cinder—the
chance of any of them ever
getting a perfect score on just
the math section would be
about 0.0001 percent.
How unlikely is that? Each
year something like 500
Americans are struck by
lightning (based on an
average of 45 lightning deaths
and a 9–10 percent fatality
rate). This suggests that the
odds of any one American
being hit in a given year are
about 1 in 700,000.2
This means that the odds of
acing the SAT by guessing
are worse than the odds of
every living ex-President and
every member of the main
cast of Firefly all being
independently
struck
by
lightning . . . on the same
day.
To everyone taking the
SAT this year, good luck—
but it won’t be enough.
1 I took the SAT a long time
ago, okay?
2 See: xkcd, “Conditional
Risk,” http://xkcd.com/795/.
NEUTRON
BULLET
Q. If a bullet
with the
density of a
neutron star
were fired
from a
handgun
(ignoring the
how) at the
Earth’s
surface,
would the
Earth be
destroyed?
—Charlotte Ainsworth
A. A
BULLET WITH THE
density of a neutron star
would weigh about as much
as the Empire State Building.
Whether we fired it from a
gun or not, the bullet would
fall straight through the
ground, punching through
the crust as if the rock were
wet tissue paper.
We’ll look at two different
questions:
What would the
bullet’s passage do to
the Earth?
If we kept the bullet
here on the surface,
what would it do to
its surroundings?
Could we touch it?
First, a little
background:
What are neutron
bit
of
stars?
A neutron star is what’s left
over after a giant star
collapses under its own
gravity.
Stars exist in a balance.
Their massive gravity is
always trying to make them
collapse inward, but that
squeezing sets off several
different forces that push
them back apart.
In the Sun, the thing
holding off collapse is heat
from nuclear fusion. When a
star runs out of fusion fuel, it
contracts (in a complicated
process involving several
explosions) until the collapse
is stopped by the quantum
laws that keep matter from
overlapping
with
other
matter.1
If the star is heavy enough,
it overcomes that quantum
pressure and collapses further
(with another, more massive
explosion) to become a
neutron star. If the remnant is
even heavier, it becomes a
black hole.2
Neutron stars are some of
the densest objects you can
find (outside of the infinite
density of a black hole).
They’re crushed by their own
immense gravity into a
compact
quantummechanical soup that’s in
some ways similar to an
atomic nucleus the size of a
mountain.
Is our bullet made from
a neutron star?
No. Charlotte asked for a
bullet as dense as a neutron
star, not one made from
actual neutron star material.
That’s good, because you
can’t make a bullet from that
stuff. If you take neutron star
material outside of the
crushing gravity well where
it’s normally found, it will reexpand into superhot normal
matter with an outpouring of
energy more powerful than
any nuclear weapon.
That’s presumably why
Charlotte suggested we make
our bullet out of some
magical, stable material that’s
as dense as a neutron star.
What would the bullet
do to the Earth?
You could imagine firing it
from a gun,3 but it might be
more interesting to simply
drop it. In either case, the
bullet
would
accelerate
downward, punch into the
ground, and burrow toward
the center of the Earth.
This wouldn’t destroy the
Earth, but it would be pretty
strange.
As the bullet got within a
few feet of the ground, the
force of its gravity would yank
up a huge clump of dirt,
which would ripple wildly
around the bullet as it fell,
spraying in all directions. As
it went in, you’d feel the
ground shake, and it would
leave a jumbled, fractured
crater with no entry hole.
The bullet would fall
straight through the Earth’s
crust. On the surface, the
vibration would quickly die
down. But far below, the
bullet would be crushing and
vaporizing the mantle in front
of it as it fell. It would blast
the material out of the way
with powerful shockwaves,
leaving a trail of superhot
plasma behind it. This would
be something never before
seen in the history of the
universe: an underground
shooting star.
Eventually, the bullet would
come to rest, lodged in the
nickel-iron core at the center
of the Earth. The energy
delivered to the Earth would
be massive on a human scale,
but the planet would barely
notice. The bullet’s gravity
would affect only the rock
within a few dozen feet of it;
while it’s heavy enough to fall
through the crust, its gravity
alone wouldn’t be strong
enough to crush the rock very
much.
The hole would close up,
leaving the bullet forever out
of
anyone’s
reach.4
Eventually, the Earth would
be consumed by the aging,
swollen Sun, and the bullet
would reach its final resting
place at the Sun’s core.
The Sun isn’t dense enough
to become a neutron star
itself. After it swallows the
Earth, it will instead go
through some phases of
expansion and collapse, and
will eventually settle down,
leaving behind a small white
dwarf star with the bullet still
lodged
in
the
center.
Someday, far in the future
—when the universe is
thousands of times older than
it is today—that white dwarf
will cool and fade to black.
That answers the question
of what would happen if the
bullet were fired into the
Earth. But what if we could
keep it near the surface?
Set the bullet on a
sturdy pedestal
First, we’d need a magical
infinitely strong pedestal to
put the bullet on, which
would need to sit on a
similarly strong platform large
enough to spread the weight
out. Otherwise, the whole
thing would sink into the
ground.
A base about the size of a
city block would be strong
enough to keep it aboveground for at least a few days,
probably much more. After
all, the Empire State Building
—which weighs as much as
our bullet—rests on a similar
platform, and it’s more than a
few days old[citation needed] and
hasn’t disappeared into the
ground.[citation needed]
The bullet wouldn’t vacuum
up the atmosphere. It would
definitely compress the air
around it and warm it up a
little, but surprisingly, not
really enough to notice.
Can I touch it?
Let’s imagine what would
happen if you tried.
The gravity from this thing
is strong. But it’s not that
strong.
Imagine you’re standing 10
meters away. At this distance,
you feel a very slight tug in
the direction of the pedestal.
Your brain—not accustomed
to nonuniform gravities—
thinks you’re standing on a
gentle slope.
Do not put on roller skates.
This perceived slope gets
steeper as you walk toward
the pedestal, as if the ground
were tipping forward.
When you get within a few
meters, you have a hard time
not sliding forward. However,
if you got a good grip on
something—a handle or a
signpost—you can get pretty
close.
Los Alamos physicists might call this
“tickling the dragon’s tail.”
But I wanna touch it!
To get close enough to touch
it, you would need a very
good grip on something.
Really, you’d need to do this
in a full-body support
harness, or at the very least a
neck brace; if you get within
reach, your head will weigh as
much as a small child, and
your blood won’t know which
way to flow. However, if
you’re a fighter pilot who’s
used to gee forces, you might
be able to pull it off.
From this angle, the blood
is rushing to your head, but
you’d still be able to breathe.
As you stretch out your
arm, the pull gets a lot
stronger; 20 centimeters
(about 8 inches) is the point
of no return—as your
fingertips cross that line, your
arm becomes too heavy to
pull back. (If you do a lot of
one-handed pull-ups, you
might be able to go a little
closer.)
Once you get within a few
inches, the force on your
fingers is overwhelming, and
they’re yanked forward—with
or without you—and your
fingertips actually touch the
bullet (probably dislocating
your fingers and shoulder).
When
your
fingertip
actually comes in contact with
the bullet, the pressure in
your fingertips becomes too
strong, and your blood breaks
through the skin.
In Firefly, River Tam
famously commented that
“the human body can be
drained of blood in 8.6
seconds
given
adequate
vacuuming systems.”
By touching the bullet,
you’ve just created an
adequate vacuuming system.
Your body is restrained by a
harness, and your arm
remains attached to your
body—flesh is surprisingly
strong—but blood pours from
your fingertip much faster
than ordinarily possible.
River’s “8.6 seconds” might
be an underestimate.
Then things get weird.
The blood wraps around
the bullet, forming a growing
dark red sphere whose surface
hums and vibrates with
ripples moving too fast to see.
But wait
There’s a fact that now
becomes becomes important:
You float on blood.
As the blood sphere grows,
the force on your shoulder
weakens . . . because the parts
of your fingertips below the
surface of the blood are
buoyant! Blood is denser than
flesh, and half the weight on
your arm was coming from
the last two knuckles of your
fingers. When the blood is a
few centimeters deep, the
load gets considerably lighter.
If you could wait for the
sphere of blood to get 20
centimeters deep—and if
your shoulder were intact
—you might even be able to
pull your arm away.
Problem: That would take
five times as much blood as
you have in your body.
It looks like you’re not
going to make it.
Let’s rewind.
How to touch a neutron
bullet: salt, water, and
vodka
You can touch the bullet and
survive . . . but you need to
surround it with water.
DO try this at home, and send me
videos.
If you want to be really
clever, you can dangle the end
of the hose in the water and
let the bullet’s gravity do the
siphoning for you.
To touch the bullet, pour
water onto the pedestal until
it’s a meter or 2 deep on the
side of the bullet. It will form
a shape like one of these:
If those boats sink, you’re not
salvaging them.
Now, dip your head and
arm in.
Thanks to the water, you’re
able to wave your hand
around the bullet without any
difficulty! The bullet is
pulling you toward it, but it’s
pulling the water just as hard.
Water (like meat) is virtually
incompressible, even at these
pressures, so nothing critical
gets crushed.5
However, you
may
not
quite be able to touch the
bullet. When your fingers get
a few millimeters away, the
powerful gravity means that
buoyancy plays a gigantic
role. If your hand is slightly
less dense than the water, it
won’t be able to penetrate
that last millimeter. If it’s
slightly more dense, it will be
sucked down.
This is where the vodka and
salt come in. If you find the
bullet tugging on your
fingertips as you reach in, it
means your fingers aren’t
buoyant enough. Mix in some
salt to make the water denser.
If you find your fingertips
sliding on an invisible surface
at the edge of the bullet,
make the water less dense by
adding vodka.
If you got the balance just
right, you could touch the
bullet and live to tell about it.
Maybe.
Alternative plan
Sound too risky to you? No
problem. This whole plan
—the bullet, the water, the
salt, the vodka—doubles as
instructions for making the
most difficult mixed drink in
the history of beverages: the
Neutron Star.
So grab a straw and take a
drink.
. . . and remember: If
someone drops a cherry into
your Neutron Star, and it
sinks to the bottom, don’t try
to fish it out. It’s gone.
1 The Pauli exclusion principle
keeps electrons from getting
too close to each other. This
effect is one of the main reasons
that your laptop doesn’t fall
through your lap.
2 It’s possible there’s a category
of objects heavier than neutron
stars — but not quite heavy
enough to become black holes
— called “strange stars.”
3 A magical, unbreakable gun
that you could hold without
your arm being torn off. Don’t
worry, that part comes later!
4 . . . unless Kyp Durron uses
the Force to drag it back up.
5 When you pull your arm out,
watch for symptoms of
decompression sickness due to
nitrogen bubbles in the blood
vessels in your hand.
WEIRD
(AND
WORRYING)
QUESTIONS
FROM
THE
WHAT IF?
INBOX,
#12
Q. What if I
swallow a tick
that has Lyme
disease? Will
my stomach
acid kill the
tick and the
borreliosis, or
would I get
Lyme disease
from the inside
out?
—Christopher Vogel
Q.
Assuming
a relatively
uniform
resonant
frequency in a
passenger jet,
how many
cats, meowing
at what
resonant
frequency of
said jet, would
be required to
“bring it
down”?
—Brittany
RICHTER 15
Q. What if a
Richter
magnitude 15
earthquake
were to hit
America at,
let’s say, New
York City?
What about a
Richter 20?
25?
—Alec Farid
A. THE
RICHTER
SCALE, WHICH has
technically been replaced by
the “moment magnitude”1
scale, measures the energy
released by an earthquake. It’s
an open-ended scale, but
since we usually hear about
earthquakes with ratings from
3 to 9, a lot of people
probably think of 10 as the
top and 1 as the bottom.
In fact, 10 isn’t the top of
the scale, but it might as well
be.
A
magnitude
9
earthquake
already
measurably alters the rotation
of the Earth; the two
magnitude 9+ earthquakes
this century both altered the
length of the day by a tiny
fraction of a second.
A magnitude 15 earthquake
would involve the release of
almost 1032 joules of energy,
which
is
roughly
the
gravitational binding energy
of the Earth. To put it
another way, the Death Star
caused a magnitude 15
earthquake on Alderaan.
You could in theory have a
more powerful earthquake on
Earth, but in practice all it
would mean is that the
expanding cloud of debris
would be hotter.
The Sun, with its higher
gravitational binding energy,
could have a magnitude 20
quake (although it would
certainly trigger some kind of
a catastrophic nova). The
most powerful quakes in the
known universe, which occur
in the material in a
superheavy neutron star, are
about this magnitude. This is
about the energy release you
would get if you packed the
entire volume of the Earth
with hydrogen bombs and
detonated them all at once.
We spend a lot of time
talking about things that are
large and violent. But what
about the bottom end of the
scale? Is there such a thing as
a magnitude 0 earthquake?
Yes! In fact, the scale goes
all the way down past zero.
Let’s take a look at some lowmagnitude
“earthquakes,”
with a description of what
they would be like if they hit
your house.
Magnitude 0
The Dallas Cowboys running
at full tilt into the side of your
neighbor’s garage
Magnitude -1
A single football player
running into a tree in your
yard
Magnitude -2
A cat falling off a dresser
Magnitude -3
A cat knocking your cell
phone off your nightstand
Magnitude -4
A penny falling off a dog
Magnitude -5
A key press on an IBM
model M keyboard
Magnitude -6
A key press on a lightweight
keyboard
Magnitude -7
A single feather fluttering to
the ground
Magnitude -8
A grain of fine sand falling
onto the pile at the bottom of
a tiny hourglass
. . . and let’s jump all the
way down to
Magnitude -15
A drifting mote of dust
coming to rest on a table
Sometimes it’s nice not to
destroy the
change.
world
for
a
1 Similarly, the F-scale (Fujita
scale) has been replaced by the
EF-scale (“Enhanced Fujita”).
Sometimes, a unit of measure is
made obsolete because it is
terrible — for example, “kips”
(1000 pounds-force), “kcfs”
(thousands of cubic feet per
second), and “degrees Rankine”
(degrees Fahrenheit above
absolute zero). (I have had to
read technical papers written in
each of those units.) Other
times, you get the sense that
scientists just want something
to correct people about.
ACKNOWLED
A bunch of people helped me
make this book you’re looking
at.
Thank you to my editor,
Courtney Young, for being an
xkcd
reader
from
the
beginning and seeing this
book through to the end.
Thank you to the various
terrific people at HMH who
made
everything
work.
Thank you to Seth Fishman
and the Gernert folks for
being patient and tireless.
Thank you to Christina
Gleason for making this book
look like a book, even when it
meant
deciphering
my
scribbled
notes
about
asteroids at three in the
morning. Thank you to the
various experts who helped
me
answer
questions,
including Reuven Lazarus
and
Ellen
McManis
(radiation), Alice Kaanta
(genes),
Derek
Lowe
(chemicals), Nicole Gugliucci
(telescopes), Ian Mackay
(viruses), and Sarah Gillespie
(bullets). Thank you to
davean, who made this all
happen but hates attention
and will probably complain
about being mentioned here.
Thank you to the IRC
crowd for their comments
and corrections, and to Finn,
Ellen, Ada, and Ricky for
sifting through the flood of
submitted questions and
filtering out the ones about
Goku. Thank you to Goku
for apparently being an animé
character
with
infinite
strength, and thus provoking
hundreds
of
What
If
questions, even though I
refused to watch Dragon Ball
Z in order to answer them.
Thank you to my family for
teaching me to answer absurd
questions by spending so
many
years
patiently
answering mine. Thank you
to my father for teaching me
about measurement and my
mother for teaching me about
patterns. And thank you to
my wife, for teaching me how
to be tough, teaching me how
to be brave, and teaching me
about birds.
REFERENCES
Global Windstorm
Merlis, Timothy M., and
Tapio
Schneider,
“Atmospheric dynamics of
Earth-like tidally locked
aquaplanets,” Journal of
Advances in Modeling
Earth Systems 2 (December
2010);
DOI:10.3894/JAMES.2010.2
“What Happens Underwater
During
a
Hurricane?”
http://www.rsmas.miami.edu
happens-underwaterduring-a-hurricane
Spent Fuel Pool
“Behavior of spent nuclear
fuel in water pool storage,”
http://www.osti.gov/energycit
xaMii9/7284014.pdf
“Unplanned
Exposure
During Diving in the Spent
Fuel
Pool,”
http://www.isoenetwork.net/index.php/public
mainmenu-88/isoenews/doc_download/1756ritter2011ppt.html
Laser Pointer
GOOD, “Mapping the
World’s Population by
Latitude,
Longitude,”
http://www.good.is/posts/ma
the-world-s-population-bylatitude-longitude
http://www.wickedlasers.com/
Periodic Wall of the
Elements
Table on page 9 (publication
page 15, pdf page 15) in
http://www.epa.gov/opptintr/
Everybody Jump
Dot Physics, “What
if
everyone
jumped?”
http://scienceblogs.com/dotph
if-everyone-jumped/
Straight Dope, “If everyone
in China jumped off chairs
at once, would the earth be
thrown out of its orbit?”
http://www.straightdope.com
all-chinese-jumped-atonce-would-cataclysmresult
A Mole of Moles
Disover,
“How
many
habitable planets are there
in
the
galaxy?”
http://blogs.discovermagazine
many-habitable-planetsare-there-in-the-galaxy
Hair Dryer
“Determination of Skin Burn
Temperature Limits for
Insulative Coatings Used for
Personnel
Protection,”
http://www.mascoat.com/asse
“The
Nuclear
Potato
Cannon
Part
2,”
http://nfttu.blogspot.com/200
potato-cannon-part-2.html
The Last Human Light
“Wind Turbine Lubrication
and
Maintenance:
Protecting Investments in
Renewable
Energy,”
http://www.renewableenergyw
turbine-lubrication-andmaintenance-protecting-
investments-in-renewableenergy
McComas,
D.J.,
J.P.
Carrico, B. Hautamaki, M.
Intelisano, R. Lebois, M.
Loucks, L. Policastri, M.
Reno, J. Scherrer, N.A.
Schwadron, M. Tapley, and
R. Tyler, “A new class of
long–term stable lunar
resonance orbits: Space
weather applications and the
Interstellar
Boundary
Explorer,” Space Weather,
9,
S11002,
doi:
10.1029/2011SW000704,
2011.
Swift, G.M., et al. “In-flight
annealing of displacement
damage in GaAs LEDs: A
Galileo
story,”
IEEE
Transactions on Nuclear
Science, Vol. 50, Issue 6
(2003).
“Geothermal Binary Plant
Operation and Maintenance
Systems with Svartsengi
Power Plant as a Case
Study,”
http://www.os.is/gogn/unugtp-report/UNU-GTP2002-15.pdf
Machine-Gun Jetpack
“Lecture L14-Variable Mass
Systems:
The
Rocket
Equation”
http://ocw.mit.edu/courses/ae
and-astronautics/16-07-
dynamics-fall-2009/lecturenotes/MIT16_07F09_Lec14.
“[2.4] Attack Flogger in
Service,”
http://www.airvectors.net/avm
Rising Steadily
Otis: “About Elevators,”
http://www.otisworldwide.co
National Weather Service:
“Wind Chill Temperature
Index,”
http://www.nws.noaa.gov/om
chill-brochure.pdf
“Prediction of Survival Time
in Cold Air”—see page 24
for the relevant tables,
http://cradpdf.drdcrddc.gc.ca/PDFS/zba6/p1449
Linda D. Pendleton, “When
Humans Fly High: What
Pilots Should Know About
High-Altitude Physiology,
Hypoxia,
and
Rapid
Decompression.”
http://www.avweb.com/news/
1.html
Short-Answer Section
“Currency in Circulation:
Volume,”
http://www.federalreserve.gov
NOAA, “Subject: C5c, Why
don’t we try to destroy
tropical cyclones by nuking
them?”
http://www.aoml.noaa.gov/hr
NASA,
“Stagnation
Temperature,”
http://www.grc.nasa.gov/WW
Lightning
“Lightning Captured @
7,207
Fps,”
http://www.youtube.com/wat
v=BxQt8ivUGWQ
NOVA, “Lightning: Expert
Q&A,”
http://www.pbs.org/wgbh/no
lightning.html
JGR, “Computation of the
diameter of a lightning
return
stroke”
http://onlinelibrary.wiley.com
Human Computer
“Moore’s Law at 40,”
http://www.ece.ucsb.edu/~str
Little Planet
For another take on The
Little Prince, scroll down to
the last section of this
wonderful piece by Mallory
Ortberg,
http://the-
toast.net/2013/08/02/textsfrom-peter-pan-et-al/
Rugescu, Radu D., and
Daniele Mortari, “Ultra
Long
Orbital
Tethers
Behave
Highly
NonKeplerian and Unstable,”
WSEAS Transactions on
Mathematics, Vol. 7, No. 3,
March 2008, pp. 87-94,
http://www.academia.edu/345
Keplerian_and_Unstable
Steak Drop
“Falling Faster than the
Speed
of
Sound,”
http://blog.wolfram.com/201
faster-than-the-speed-ofsound
“Stagnation
Temperature:
Real
Gas
Effects,”
http://www.grc.nasa.gov/WW
“Predictions of Aerodynamic
Heating on Tactical Missile
Domes,”
http://www.dtic.mil/cgi-
bin/GetTRDoc?
AD=ADA073217
“Calculation of ReentryVehicle
Temperature
History,”
http://www.dtic.mil/dtic/tr/fu
“Back in the Saddle,”
http://www.ejectionsite.com/
“How to Cook PittsburghStyle
Steaks,”
http://www.livestrong.com/ar
how-to-cook-pittsburghstyle-steaks
Hockey Puck
“KHL’s
Alexander
Ryazantsev sets new ‘world
record’ for hardest shot at
114
mph,”
http://sports.yahoo.com/blogs
puck-daddy/khl-alexanderryazantsev-sets-worldrecord-hardest-shot174131642.html
“Superconducting Magnets
for Maglifter Launch Assist
Sleds,”
http://www.psfc.mit.edu/~rad
“Two-Stage
Light
Gas
Guns,”
http://www.nasa.gov/centers/
“Hockey Video: Goalies,
Hits, Goals, and Fights,”
http://www.youtube.com/wat
v=fWj6--Cf9QA
Common Cold
P. Stride, “The St. Kilda
boat cough under the
microscope,” The Journal
—Royal
College
of
Physicians of Edinburgh,
2008; 38:272–9.
L. Kaiser, J. D. Aubert, et
al., “Chronic Rhinoviral
Infection
in
Lung
Transplant
Recipients,”
American
Journal
of
Respiratory and Critical
Care Medicine, Vol. 174;
pp.
1392–1399,
2006,
10.1164/rccm.200604489OC
Oliver, B. G. G., S. Lim, P.
Wark, V. Laza-Stanca, N.
King, J. L. Black, J. K.
Burgess, M. Roth, and S. L.
Johnston,
“Rhinovirus
Exposure Impairs Immune
Responses To Bacterial
Products
In
Human
Alveolar
Macrophages,”
Thorax 63, no. 6 (2008):
519–525.
Glass Half Empty
“Shatter beer bottles: Barehanded
bottle
smash,”
http://www.youtube.com/wat
v=77gWkl0ZUC8
Alien Astronomers
The Hitchhiker’s Guide to
the
Galaxy,
http://www.goodreads.com/b
“A Failure of Serendipity:
The Square Kilometre
Array will struggle to
eavesdrop on Human-like
ETI,”
http://arxiv.org/PS_cache/arx
“Eavesdropping on Radio
Broadcasts from Galactic
Civilizations
with
Upcoming Observatories for
Redshifted
21cm
Radiation,”
http://arxiv.org/pdf/astroph/0610377v2.pdf
“The Earth as a Distant
Planet a Rosetta Stone for
the Search of Earth-Like
Worlds,”
http://www.worldcat.org/title
as-a-distant-planet-arosetta-stone-for-thesearch-of-earth-likeworlds/oclc/643269627
“SETI on the SKA,”
http://www.astrobio.net/exclu
on-the-ska
Gemini
Planet
Imager,
http://planetimager.org/
No More DNA
Enjalbert, Françoise, Sylvie
Rapior, Janine NouguierSoulé, Sophie Guillon, Noël
Amouroux, and Claudine
Cabot,
“Treatment
of
Amatoxin Poisoning: 20Year
Retrospective
Analysis.”
Clinical
Toxicology 40, no. 6 (2002):
715–757.
http://toxicology.ws/LLSAAr
20%20year%20retrospective%
Richard Eshelman, “I nearly
died after eating wild
mushrooms,” The Guardian
(2010),
http://www.theguardian.com/
died-eating-wildmushrooms
“Amatoxin:
A
review,”
http://www.omicsgroup.org/j
7548/2165-7548-2110.php?aid=5258
Interplanetary Cessna
“The Martian Chronicles,”
http://www.xplane.com/adventures/mars.h
“Aerial
Regional-Scale
Environmental Survey of
Mars,”
http://marsairplane.larc.nasa.g
“Panoramic
Views
and
Landscape Mosaics of Titan
Stitched from Huygens Raw
Images,”
http://www.beugungsbild.de/
“New images from Titan,”
http://www.esa.int/Our_Acti
Huygens/New_images_from_
Yoda
Saturday Morning Breakfast
Cereal, http://www.smbccomics.com/index.php?
db=comics&id=2305#comic
Youtube,
“
‘Beethoven
Virus’—Musical
Tesla
Coils,”
http://www.youtube.com/wat
v=uNJjnz-GdlE
“Beast.” The 15Kw 7' tall
DR
(DRSSTC
5),
http://www.goodchildenginee
coils/drsstc-5-10kwmonster
Falling with Helium
De Haven, H., “Mechanical
analysis of survival in falls
from heights of fifty to one
hundred and fifty feet,”
Injury Prevention, 6(1):62-
b-68,
http://injuryprevention.bmj.co
“Armchair Airman Says
Flight
Fulfilled
His
Lifelong Dream,” New
York Times, July 4, 1982,
http://www.nytimes.com/198
airman-says-flight-fulfilledhis-lifelong-dream.html?
pagewanted=all
Jason Martinez, “Falling
Faster than the Speed of
Sound,” Wolfram Blog,
October
24,
2012,
http://blog.wolfram.com/201
faster-than-the-speed-ofsound
Everybody Out
Project Orion: The True
Story of the Atomic
Spaceship,http://www.amazo
Orion-Story-AtomicSpaceship/dp/0805059857
Self-Fertilization
“Sperm Cells Created From
Human Bone Marrow,”
http://www.sciencedaily.com/
Nayernia,
Karim,
Tom
Strachan, Majlinda Lako,
Jae Ho Lee, Xin Zhang,
Alison Murdoch, John
Parrington,
Miodrag
Stojkovic, David Elliott,
Wolfgang Engel, Manyu
Li, Mary Herbert, and Lyle
Armstrong,
“RETRACTION-In Vitro
Derivation Of Human
Sperm From Embryonic
Stem Cells,” Stem Cells and
Development
(2009):
0908w75909069.
“Can sperm really be created
in
a
laboratory?”
http://www.theguardian.com/
laboratory-men
This is discussed more
deeply in F. M. Lancaster’s
monograph Genetic and
Quantitative Aspects of
Genealogy
at
http://www.geneticgenealogy.co.uk/Toc1155701
High Throw
“A Prehistory of Throwing
Things,”
http://ecodevoevo.blogspot.co
of-throwing-things.html
“Chapter 9. Stone tools and
the evolution of hominin
and human cognition,”
http://www.academia.edu/235
_the_evolution_of_hominin_
“The unitary hypothesis: A
common neural circuitry for
novel
manipulations,
language, plan-ahead, and
throwing?”
http://www.williamcalvin.com
“Evolution of the human
hand: The role of throwing
and
clubbing,”
http://www.ncbi.nlm.nih.gov
“Errors in the control of joint
rotations associated with
inaccuracies in overarm
throws,”
http://jn.physiology.org/conte
“Speed of Nerve Impulses,”
http://hypertextbook.com/fac
“Farthest Distance to Throw
a
Golf
Ball,”
http://recordsetter.com/world
record/world-record-forthrowing-golfball/7349#contentsection
Lethal Neutrinos
Karam, P. Andrew. “Gamma
and Neutrino Radiation
Dose from Gamma Ray
Bursts
and
Nearby
Supernovae,”
Health
Physics 82, no. 4 (2002):
491–99.
Speed Bump
“Speed bump-induced spinal
column
injury,”
http://akademikpersonel.duzc
“Speed hump spine fractures:
Injury mechanism and case
series,”
http://www.ncbi.nlm.nih.gov
“The
2nd
American
Conference on Human
Vibration,”
http://www.cdc.gov/niosh/mi
145.pdf
“Speed bump in Dubai +
flying
Gallardo,”
http://www.youtube.com/wat
v=Vg79_mM2CNY
Parker,
Barry
R.,
“Aerodynamic Design,” The
Isaac Newton School of
Driving: Physics and your
car.” Baltimore, MD: Johns
Hopkins University Press,
2003, 155.
The Myth of the 200-mph
“Lift-Off
Speed.”
http://www.buildingspeed.org
myth-of-the-200-mph-liftoff-speed/
“Mercedes CLR-GTR Le
Mans
Flip,”
http://www.youtube.com/wat
v=rQbgSe9S54I
National
Highway
Transportation NHTSA,
Summary of State Speed
Laws, 2007
FedEx Bandwith
“FedEx still faster than the
Internet,”
http://royal.pingdom.com/20
still-faster-than-theinternet
“Cisco Visual Networking
Index:
Forecast
and
Methodology, 2012–2017,”
http://www.cisco.com/en/US
481360_ns827_Networking
_Solutions_White_Paper.htm
“Intel® Solid-State Drive
520
Series,”
http://download.intel.com/ne
“Trinity test press releases
(May
1945),”
http://blog.nuclearsecrecy.com
document-01
“NEC and Corning achieve
petabit
optical
transmission,”
http://optics.org/news/4/1/29
Free Fall
“Super
Mario
Bros.—
Speedrun level 1-1 [370],”
http://www.youtube.com/wat
v=DGQGvAwqpbE
“Sprint
ring
cycle,”
http://www1.sprintpcs.com/su
FOLDER%3C%3Efolder_id
“Glide
data,”
http://www.dropzone.com/cg
bin/forum/gforum.cgi?
post=577711#577711
“Jump. Fly. Land.,” Air &
Space,
http://www.airspacemag.com
today/Jump-Fly-Land.html
Prof. Dr. Herrligkoffer, “The
East Pillar of Nanga
Parbat,” The Alpine Journal
(1984).
The Guestroom, “Dr. Glenn
Singleman and Heather
Swan,”
http://www.abc.net.au/local/a
“Highest
BASE
jump:
Valery
Rozov
breaks
Guinness world record,”
http://www.worldrecordacade
Dean Potter, “Above It All,”
http://www.tonywingsuits.com
Sparta
According to a random
stranger on the Internet,
Andy Lubienski, “The
Longbow,”
http://www.pomian.demon.co
Drain the Oceans
Extrapolated
from
the
maximum pressure tolerable
by icebreaker ship hull
plates:
http://www.iacs.org.uk/docum
“An experimental study of
critical submergence to
avoid free-surface vortices at
vertical
intakes,”
http://www.leg.state.mn.us/d
Drain the Oceans: Part II
Donald Rapp, “Accessible
Water on Mars,” JPL D31343-Rev.7,
http://spaceclimate.net/Mars.
D. L. Santiago et al., “Mars
climate and outflow events,”
http://spacescience.arc.nasa.g
D. L. Santiago et al., “Cloud
formation
and
water
transport on Mars after
major outflow events,” 43rd
Planetary
Science
Conference (2012).
Maggie Fox, “Mars May Not
Have Been Warm or Wet,”
http://rense.com/general32/m
Twitter
The Story of Mankind,
http://books.google.com/book
id=RskHAAAAIAAJ&pg=P
“Counting
Characters,”
https://dev.twitter.com/docs/
characters
“A Mathematical Theory of
Communication,”
http://cm.belllabs.com/cm/ms/what/shanno
Lego Bridge
“How tall can a Lego tower
get?”
http://www.bbc.co.uk/news/m
20578627
“Investigation
Into
the
Strength of Lego Technic
Beams
and
Pin
Connections,”
http://eprints.usq.edu.au/205
“Total value of property in
London soars to £1.35trn,”
http://www.standard.co.uk/bu
news/total-value-ofproperty-in-london-soarsto-135trn-8779991.html
Random Sneeze Call
Cari Nierenberg, “The Perils
of Sneezing, ABC News,”
Dec.
22,
2008.
http://abcnews.go.com/Healt
id=6479792&page=1
Bischoff
Werner
E.,
Michelle L. Wallis, Brian
K. Tucker, Beth A.
Reboussin, Michael A.
Pfaller,
Frederick
G.
Hayden, and Robert J.
Sherertz, “ ‘Gesundheit!’
Sneezing, Common Colds,
Allergies,
and
Staphylococcus
aureus
Dispersion,” J Infect Dis.
(2006), 194 (8): 1119–1126
doi:10.1086/507908
“Annual Rates of Lightning
Fatalities
by
Country”
http://www.vaisala.com/Vaisa
%20papers/Annual_rates_of_
Expanding Earth
“In
conclusion,
no
statistically
significant
present expansion rate is
detected by our study within
the current measurement
uncertainty of 0.2 mm yr
−1.”
Wu, X., X. Collilieux, Z.
Altamimi, B. L. A.
Vermeersen, R. S. Gross,
and I. Fukumori (2011),
“Accuracy
of
the
International
Terrestrial
Reference Frame origin and
Earth expansion, Geophys.”
Res. Lett., 38, L13304,
doi:10.1029/2011GL047450,
http://repository.tudelft.nl/vie
d13e-427c-8c5ff013b737750e/
Lawrence
Grybosky,
“Thermal Expansion and
Contraction,”
http://www.engr.psu.edu/ce/c
Sasselov, Dimitar D., The
life of super-Earths: How
the hunt for alien worlds
and artificial cells will
revolutionize life on our
planet. New York: Basic
Books, 2012.
Franz, R.M. and P. C.
Schutte,
“Barometric
hazards within the context
of deep-level mining,” The
Journal of The South
African Institute of Mining
and Metallurgy
Plummer, H. C., “Note on
the motion about an
attracting centre of slowly
increasing mass,” Monthly
Notices of the Royal
Astronomical Society, Vol.
66,
p.
83,
http://adsabs.harvard.edu/full
Weightless Arrow
“Hunting Arrow Selection
Guide:
Chapter
5,”
http://www.huntersfriend.com
“USA Archery Records,
2009,”
http://www.usaarcheryrecords
“Air flow around the point of
an
arrow,”
http://pip.sagepub.com/conte
STS-124: KIBO, NASA,
http://www.nasa.gov/pdf/228
Sunless Earth
“The 1859 Solar–Terrestrial
Disturbance
and
the
Current Limits of Extreme
Space Weather Activity,”
http://www.leif.org/research/
%2Extreme%20Space%20We
“The extreme magnetic
storm of 1–2 September
1859,”
http://trsnew.jpl.nasa.gov/dspace/bitstr
1310.pdf
“Geomagnetic
Storms,”
http://www.oecd.org/governa
“Normalized
Hurricane
Damage in the United
States:
1900–2005,”
http://sciencepolicy.colorado.
2476-2008.02.pdf
“A Satellite System for
Avoiding Serial Sun-Transit
Outages and Eclipses,”
http://www3.alcatellucent.com/bstj/vol491970/articles/bstj49-81943.pdf
“Impacts of Federal-Aid
Highway
Investments
Modeled
by
NBIAS,”
http://www.fhwa.dot.gov/pol
“Time zones matter: The
impact of distance and time
zones on services trade,”
http://eeecon.uibk.ac.at/wope
14.pdf
“Baby
Fact
Sheet,”
http://www.ndhealth.gov/fam
“The photic sneeze reflex as a
risk factor to combat pilots,”
http://www.ncbi.nlm.nih.gov
“Burned by wild parsnip,”
http://dnr.wi.gov/wnrmag/htm
Updating a Printed
Wikipedia
BrandNew: “Wikipedia as a
Printed
Book,”
http://www.brandnew.uk.com
as-a-printed-book/
ToolServer:
Edit
rate,
http://toolserver.org/~emijrp/
QualityLogic: Cost of Ink
Per Page Analysis, June
2012,
http://www.qualitylogic.com/
Cost-of-Ink-Per-PageAnalysis
_US_1-Jun2012.pdf
Sunset on the British
Empire
“Eddie Izzard-Do you have a
flag?”
http://www.youtube.com/wat
v=uEx5G-GOS1k
“This Sceptred Isle: Empire.
A 90 part history of the
British
Empire,”
http://www.bbc.co.uk/radio4/
“A Guide to the British
Overseas
Territories,”
http://www.telegraph.co.uk/n
files/londonwikileaks/8305236/AGUIDE-TO-THEBRITISH-OVERSEASTERRITORIES.html
“Trouble
in
Paradise,”
http://www.vanityfair.com/cu
“Long History of Child
Abuse
Haunts
Island
‘Paradise,’”
http://www.npr.org/template
storyId=103569364
“JavaScript Solar Eclipse
Explorer,”
http://eclipse.gsfc.nasa.gov/JS
index.html
Stirring Tea
“Brawn
Mixer,
Inc.,
Principles of Fluid Mixing
(2003),”
http://www.craneengineering
“Cooling a cup of coffee with
help
of
a
spoon,”
http://physics.stackexchange.c
a-cup-of-coffee-with-helpof-a-spoon/5510#5510
All the Lightning
“Introduction to Lightning
Safety,” National Weather
Service, Wilmington, Ohio,
http://www.erh.noaa.gov/iln/
Bürgesser Rodrigo E., Maria
G. Nicora, and Eldo E.
Ávila, “Characterization of
the lightning activity of
Relámpago del Catatumbo,’’
Journal of Atmospheric and
Solar-Terrestrial
Physics
(2011),http://wwlln.net/publi
Loneliest Human
BBC Future interview with
Al Wolden (April 2, 2013),
http://www.bbc.com/future/s
the-loneliest-humanbeing/1
Raindrop
“SSMI/SSMIS/TMIderived Total Precipitable
Water-North
Atlantic,”
http://tropic.ssec.wisc.edu/rea
time/mimictpw/natl/main.html
“Structure
of
Florida
Thunderstorms
Using
High-Altitude
Aircraft
Radiometer and Radar
Observations,” Journal of
Applied
Meteorology,
http://rsd.gsfc.nasa.gov/912/e
SAT Guessing
Cooper, Mary Ann, MD.,
“Disability, Not Death Is
the Main Problem with
Lightning
Injury,”
http://www.uic.edu/labs/light
National
Oceanic
and
Atmospheric
Administration (NOAA),
“2008 Lightning Fatalities,”
http://www.nws.noaa.gov/om
Neutron Bullet
“Influence of Small Arms
Bullet Construction on
Terminal
Ballistics,”
http://hsrlab.gatech.edu/AUT
McCall, Benjamin, “Q & A:
Neutron Star Densities,”
University
of
Illinois,
http://van.physics.illinois.edu
id=16748
COLOPHON
The body of this text was set
Adobe Caslon Pro,
a Caslon variant designed by Carol
Twombly
in 1990 based on Caslon’s
specimen pages.
The section headings and question
titles
were set in Univers, a realist sans
serif
designed by Adrian Frutiger in
1954.
The questions were set in Glypha,
a square serif typeface designed
by Adrian Frutiger in 1977.
ABOUT THE
AUTHOR
RANDALL MUNROE, a former
NASA roboticist, is the creator of
the webcomic xkcd and the author
of xkcd: volume 0. The
International Astronomical Union
recently named an asteroid after
him; asteroid 4942 Munroe is big
enough to cause a mass extinction
if it ever hits a planet like Earth.
He lives in Cambridge,
Massachusetts.