Answer by Jim Stone:
You enter a library, . . .
. . . take a book off the shelf, and notice that it’s filled with seemingly random strings of characters.
You take another book off the shelf. Same thing.
You examine a few more books and notice that all the books are quite similar.
Each book has exactly 500 pages. Each page has exactly 40 lines. And each line has exactly 50 character slots.
You examine a few more books and estimate that there are roughly 100 potential characters (including a blank spaces) that can go into each character slot.
Then you notice a sign that says “START HERE.” You go there, pick the first book off the shelf, and see that every page is blank.
You pick up the next book. It has a single letter ‘A’ in the first character slot, and all the other pages are blank.
You pick up the third book. It has a single letter ‘B’ in the first character slot. And, again, all the other pages are blank.
Then you look out across the library, and the shelves go on and on as far as the eye can see.
Your best guess is that each book in this library is a unique combination of characters, and that, collectively, the books in the library cover all the combinations that can be formed in books of this nature.
You do some quick math and calculate that there must be 100^(500*40*50) books — or 100^1,000,000 (one-hundred to the millionth power) books.
A vast number indeed.
Then you begin to wonder what books might be out there.
There must be:
- A copy of “Hamlet,” — TAKE THAT, infinite monkeys!
- A copy of “Hamlet” with one typo.
- A copy of “Hamlet” with a different typo.
- A copy of “Hamlet” with two typos.
- A book containing all the best Quora answers that can fit in 500 pages — including some answers that haven’t been written yet.
- An accurate 500-page biography of your life (from your birth until your death).
- An extremely elegant proof of the Riemann Hypothesis (or is it a counterexample?)
- A book containing a cure for cancer.
Wow! Just wow!
This is exciting.
Those books are out there somewhere. You just know it.
You have a cure for cancer almost at your fingertips!
Then the reality of the situation hits you, and you realize that the odds of finding any book you might want to find are very, very, . . . in fact vanishingly, . . . slim..
The numbers are just too big.
And there you sit with mixed emotions — torn between absolute wonder at what books must sit in this library, and abject depression because you’ll never find them.
This is basically Jorge Luis Borges’s “Library of Babel” thought experiment.
It never fails to blow my mind.