You may already be familiar with the mythical Library of Babel, but if you're not then allow me the honor of introducing it to you! The Library of Babel is a short story/thought experiment written by the Argentine author Jorge Luis Borges. Imagine there's a library that contains every book of 410 pages that could ever be written using the letters of the Latin alphabet. Each book has 410 pages, each has 40 lines, and each line is around 80 characters. Most of the books in the library are just full of gibberish: random letters that make no sense in any human language. But, due to the scale of it, somewhere in the library you'll find a page that is written in a perfectly understandable human language.

The genius of the Library of Babel is that there are a limited number of combinations of letters you can fit into a book, which means that the total number of books it contains is finite (though incomprehensibly large). The implication is that you can actually find anything (in any language) that could ever be written at some location in the library. The library is not infinite, so if you had enough time you could find anything you wanted.

Think about it.

Somewhere there's a book (or sequence of books) that perfectly narrates your life from the moment you were born till you breathe out your last breath. Books that talk about your inner demons, about all the decisions you've ever agonized over, and whether they were correct or not. Books that narrate your entire family history, some as a drama, some as a comedy, and some as if they were written by a pirate. Books that are actually a perfect index of the lives of those you love, or even an index of the library itself. More than that, in the library you'll find all plays, stories, novels, and scientific papers humanity has ever produced and those it will produce. You can even get more meta and find a book that contains a program that generates the whole library! Books meticulously describing the whole of creation, from the astronomically large to the quantum. Entire volumes describing a leaf as it falls on a crisp, golden Sunday afternoon.

So, so, so many books. And yet, there's only a limited set of them.

The question arises then, "How can a finite set of books perfectly describe the universe and yet the universe be infinite?" Of course, this assumes that the universe is indeed infinite, which is something we don't really know, but I'll choose to run with it for this post.

Recently, I stumbled on this excellent website called https://libraryofbabel.info/. The idea is that it allows you to explore a digital version of the Library of Babel.

(As an aside, I really doubt that this site has the full library, as it would be astronomical in size. I imagine that what they do is dynamically generate pages as users "search" the library by creating pages on the fly that contain whatever the user searched for. Still, it's a very nice idea and an excellent art piece!)

Now, I think it would be useful to have an idea of just how large this library is. Rather than talking about books and pages, let's simplify it a bit and do as was done in libraryofbabel.info: every book is actually a document of 1,312,000 characters. Let's assume we work with whitespace, comma, period, and all 26 lowercase letters from the Latin alphabet (a total of 29 possible characters). That means that the total possible number of documents is:

$29^{1312000} \approx 10^{1918666}$

That's a truly mind-boggling, mind-numbing number! Compare that to the estimated number of atoms in the visible universe, $10^{82}$, which is almost laughable by comparison. Here, we're talking about numbers so large that our feeble human minds just can't wrap themselves around them.

And yet, a colossal number is not the same as true infinity. It can't, by definition, define everything there is to define in a truly infinite universe. The library is vast, but at the same time it's limited because it's only composed of discrete items. Reality is continuous, analog, infinite.

It can seem like a paradox, but really it isn't if you think about it. We often fall into the trap of thinking that language can describe everything that exists, but the truth is that many things just can't be represented with words. You can spend thousands of words describing the chirping of birds at sunrise or the sounds of waves crashing on the shore, but no matter how hard you try or how much detail you go into, you'll never be able to truly have the reader live the experience of listening to those birds or experience the crashing of the waves1. You won't even be able to transmit effectively what you were thinking or feeling at that moment, nor even your pure perception.

The truth is that words are no more than a shadow of what we see around us. The real magic comes when both the reader and the writer have lived similar experiences, so if I make shadows on the wall with my hands, then you will know what I mean, even though I might not be able to place you inside my thoughts and feelings2.

One might even argue that often a looser representation of something actually gives a better impression of the thing itself. For instance, I find this to be very true for haikus. If you read something like Bashō's travelogue "The Narrow Road to the Deep North," you kind of get the impression that he's using haikus as if they were photographs that share a certain impression, accompanied by actual prose detailing the journey. Some examples:

Breaking the silence
Of an ancient pond
A frog jumped into water -
A deep resonance

or

Roses at the roadside
Perishing one after another
In the mouth of a horse

or

A butterfly
Poised on a tender orchid,
How sweetly the incense
Burns on its wings

or

With a hat on my head
And straw sandals on my feet,
I met on the road
The end of the year

Again, this only works if you've ever found yourself in a similar situation, and from there you can sort of get what he means. Our shared humanness is the real medium through which Bashō manages to transmit what he means with these loose descriptions.

...

Anyway.

Language is "good enough". It can even be a beautiful thing in its own right, but it can't describe most (none?) of the things out there. It occupies its own, very reduced slice of existence. It is, unsurprisingly, just a symbolic representation. And yet we often think that what we say and think is what really is.

We often insist on making words the center of how we see the world. We think in words, relate in words; even what I'm doing here is making sense in words. But perhaps a better way to experience life would be to really go out there and touch the grass without making concepts about it? It also makes you wonder why humans so often tend to fight so much about the words we choose to describe the exact same thing, often making them more important than the thing itself.

It reminds me of the famous Zen parable:

Don't confuse the pointing finger for the moon.

Postscript:

  • An idea I didn't end up including in the post above but I still think is worth mentioning is that one, in theory, could have a function that is able to both tell you exactly where a book in the library is as well as generate that book. I think there's an interesting parallel between this and LLMs acting as "views" into this vast space.
  • I've been reading a lot of One Piece lately, picking it up after a year-long break. Currently in chapter 434. It's so good! Truly excellent fiction. This is probably the main reason why I've been slacking with keeping my blog updated.
  • Next week I'm going on a long vacation with my family. Not sure if/how this is going to impact my writing here :)

Footnotes

  1. And these words I'm writing here might even resonate with you right now, and call back memories of walks on the shore or in the park. But what's happening there is that it only works because the words are evoking something in our shared experience rather than because they're describing it perfectly. Imagine I instead try to poetically describe the majestic mating calls of the striped Shantigan tiger, you would have absolutely no clue about what I mean, no matter how hard I try. In this way we can see that words work more like "pointers" than actual "describers". ↩

  2. This is basically a parallel to Plato's Allegory of the cave. The difference being that we're going one step further and saying that even the people outside the cave are just communicating each with each other using shadows, and somehow it works but it's never perfect. In that respect they're the same as the ones chained inside the cave. ↩