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I've found this phrase appears more than twice. Ted-ed at 1:15

So, to use matrices, we need to learn how they work. It turns out, you can treat matrices just like regular numbers. You can add them, subtract them, even multiply them. You can't divide them, but that's a rabbit hole of its own. Adding matrices is pretty simple. All you have to do is add the corresponding entries in the order they come.

What does rabbit hole mean? How to use it? Could you please give me some examples?

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  • The idiomatic expression rabbit hole is used only once in the video, as far as I could tell.
    – Mari-Lou A
    Jan 21, 2017 at 12:15
  • @Mari-LouA The other one is keep in my brain subconsciously. If I find it out I will tell you.
    – Rain
    Jan 21, 2017 at 12:20
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    Probably a reference to the novel Alice in Wonderland. Discovering how deep the rabbit hole goes means finding out that something is much more strange / amazing than what initially seems.
    – mathreadler
    Jan 21, 2017 at 15:28
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    Besides coming from Alice in wonderland, the phrase is also used in the movie "The Matrix". Based on the topic (and on several of the graphics in the video), I'm sure it was used at least in part because it was a memorable phrase from the movie.
    – BowlOfRed
    Jan 22, 2017 at 9:30
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    @BowlOfRed: The Matrix used it as a reference to Alice in Wonderland. Seriously, without Alice in Wonderland that line in the Matrix does not even make sense!!
    – slebetman
    Jan 22, 2017 at 12:32

4 Answers 4

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Rabbit hole commonly refers to either an actual rabbit burrow where rabbits live, or, as an idiomatic phrase used in your Ted-Ed example, the hole Alice went down following the white rabbit in Alice in Wonderland. It metaphorically describes something unknown, possibly fantastical, that will lead to much more complexity than it initially appeared.

In the video he is using rabbit hole to humorously state that the reason for no matrix division is beyond what he can cover in a 4'40" long video. He is giving a top level description of mathematical matrices to an audience that is unlikely to be familiar with the concept. You can add, subtract, and multiply matrices, but you cannot divide them.

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  • 8
    Just to emphasize the word "possibly" in Rich's answer -- the expression is frequently used when there is absolutely no element of the fantastical. We use it quite frequently to warn fellow programmers that the problem they are attempting to solve "is a rabbit hole they don't want to go down", meaning that although in many cases there may even be an initial approach which seems straightforward, the problem likely goes "deeper" than it appears and will consume much more time than might first be expected. See also: can of worms.
    – A C
    Jan 21, 2017 at 22:43
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    Some great examples are on the TV Tropes website for "Down the Rabbit Hole" ...but I warn you when going to that site, as it is very likely to lead you down a rabbit hole ....
    – BruceWayne
    Jan 22, 2017 at 5:22
  • It is, perhaps, worth noting that due to the history of Alice in Wonderland (which was written by a mathematician as a satire on certain mathematical controversies that were current at the time of publication) the phrase is particularly prevalent when describe mathematical ideas.
    – Periata Breatta
    Jan 22, 2017 at 6:41
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    It's worth noting that StackExchange, TVTropes, and other sites often invite you to go down the rabbit hole, by following links to seemingly-related articles and questions, and following seemingly-related links in those, until... it's four hours later and you forgot what you were originally trying to accomplish. Remember what happened to Alice; you get wrapped up in a whole other world which is larger and more immersive than you were first led to expect.
    – flith
    Jan 23, 2017 at 6:52
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The idiomatic expression, a "rabbit hole" is a reference to Lewis Carroll's "Alice in Wonderland". Its modern meaning is a detour from your work efforts that will require a great deal of time and analysis, while producing no useful result. It is a dead end or a fool's errand.

A June 4, 2015 article in the New Yorker magazine recounts the evolution of the phrase over time.

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    I think comparison of matrix division with "dead end" or "fool's errand" is very incorrect. Trying to divide matrices will certainly have useful result.
    – Egor Skriptunoff
    Jan 22, 2017 at 12:33
  • @EgorSkriptunoff The drive to prove people wrong can also give useful results. We are maybe not having technical issues but managemental ones.
    – mathreadler
    Jan 23, 2017 at 8:41
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A rabbit warren is an artificial enclosure for raising rabbits.

Rabbit Warrens.

The rabbit was also introduced into England, probably from Iberia, by the Normans for their fur and meat. Originally rather delicate creatures in order to thrive they had to be sheltered from the elements, protected from predators and fed regularly. To facilitate this artificial warrens were built consisting of low flat topped mounds, 10 to 20 metres long, 5 to 10 metres wide and up to a metre high sometimes surrounded by a shallow ditch. Such mounds are often called pillow mounds [...] Warrens sometimes of considerable size existed on Dartmoor and around Thetford into the early twentieth century. Such large establishments boasted extensive banks to enclose the warrens and other features including vermin traps and pitfalls for catching the rabbits.

Source: The Archaeology Of Hunting.

The word warren also refers to a colony of wild rabbits or other rodents with many holes, often interconnected.

rabbit warren illustration

Source:

Thus a rabbit warren can be a system of interconnected rabbit holes and tunnels, or a figurative term for something complicated.

Possibly the "rabbit hole" in:

You can't divide them, but that's a rabbit hole of its own.

means a rabbit warren, used figuratively to mean something complicated.

Thus it is possible that in this case "rabbit hole" = "rabbit warren" = something complicated.

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A rabbit hole is a metaphor for something that can trip you up (i.e. cause problems), just as a real hole to a rabbit's burrow can do.

rabbit hole

bizarre or difficult state or situation —usually used in the phrase down the rabbit hole

  • shoreline residents are finding themselves helplessly falling down a rabbit hole in their [Sisyphean] efforts to halt beach erosion

Merriam-Webster

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    It's not a reference to being tripped, but a reference to Alice in Wonderland.
    – anon
    Jan 21, 2017 at 20:06

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