This is a loose English version of my Facebook post.
This thought experiment is based on Daniel Dennett’s Library of Mendel (originally from Fechner), although he used it to illustrate something completely different.
Imagine a library that has all the possible books ever written. Suppose each book is 500 pages with 40 lines each, with 50 spaces for each line. Each page will then consist of 2000 characters per page (including spaces). Say there are 100 possible characters (including space and punctuation marks), which should cover upper and lower cases of English and European variations of the alphabet.
Somewhere in the library, there is a book consisting of nothing but blank pages, and another book consisting of nothing but obscenities. It is a large, but finite, library.
Within this library you can find every book ever published, and their translations in all languages, including long-lost ancient ones. If the book you are looking for is longer than 500 pages, it can be found in the library, properly split and numbered into different volumes.
Fascinatingly enough, here you can find your biography that is 100% accurate, not only for your past, but also perfectly predict everything in the future, to the day you die. In fact, you can find it written in regular English, ebonics, limericks, or with obscenities scattered throughout.
You can also find the correct value of pi (3.14159265358979…), up to infinite precision, volume after volume. You can find it spelled out as well, like three point one four one five nine two six five and so on. Paradoxically, pi itself is infinite, however you can find it in this large but finite library.
In this library, you can find anything you want to know about the universe, from Mozart to your innermost thoughts.
Everything I have written so far is technically true. It is also completely misleading and deceptive.
- Choice of words. The use of “library” and “books” primes you to think of them as what you commonly encounter. In fact, the vast majority of “books” contain nothing but gibberish. The chance of you finding a volume that contains English words is astronomically small. Among these volumes, the chance of you finding a volume that contains grammatically correct sentences is also astronomically small. Among these volumes, the chances of you finding a volume that makes sense is again, astronomically small. Among these volumes, the chances of you finding a volume that is correct, is again, astronomically small. This is very different from the concept of “book” or “library” that you are used to, where every volume is meaningful and deliberately written to convey a thought. An analogy would be me pointing to a bunch of numbers and proclaiming, “within these numbers you can find the winning combination of the next 100 lottos”. The difference being that the odds are better finding the lotto numbers.
- The example of pi is also completely misleading. You need to know pi to the precision you want in order to find the volumes, not the other way around. Yes, pi is infinite, and the volumes are technically finite, so how does that work? It works because sooner or later, you will reuse the volumes. Specifically, a volume will be reused when a 1,000,000 digit sequence repeats and aligns. Sounds crazy, but it is a mathematical certainty.
- Using “your biography” induces you to be emotionally invested. It uses your narcissism against yourself. After all, who doesn’t want to know their own future? The problem is, even though such a biography exists, you wouldn’t know which one is correct, even if you could find it.
To break away from this nonsense, we need to adjust the parameters and see what happens. In Dennett’s terms, it is “turn the knobs on the intuition pump”. What happens when we reduce the number of pages from 500 to just one page? Well, the library becomes much smaller, and you are simply retrieving pages instead of volumes. What happens when we reduce it further, to just one line of 50 spaces? What happens when we reduce it to just one character?
One character? That’s easy. It’s just the original 100 character set. Everything is simply built from this character set.
In fact, we can further reduce it to 0 and 1, if we encode into ASCII or Unicode.
This thought experiment shows how framing can mislead one into thinking a certain way, how cherry picking special cases can paint a rosy picture, how the brain is not equipped to deal with large numbers (scope insensitivity), how easy it is to see meaning in randomness, and how getting emotionally involved can cloud one’s judgment. Politicians use these dirty tricks, as do weight loss commercials.
Sharpening one’s thinking tools, along with some understanding of psychology, can come in super handy. Especially when you need to deceive others effectively.