this post was submitted on 08 Dec 2024
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It's a great article IMO, worth the read.
But :
This is such a stupid analogy, the chances for said monkeys to just match a single page any full page accidentally is so slim, it's practically zero.
To just type a simple word like "stupid" which is a 6 letter word, and there are 25⁶ combinations of letters to write it, which is 244140625 combinations for that single simple word!
A page has about 2000 letters = 7,58607870346737857223e+2795 combinations. And that's disregarding punctuation and capital letters and special charecters and numbers.
A million monkeys times a million years times 365 days times 24 hours times 60 minutes times 60 seconds times 10 random typos per second is only 315360000000000000000 or 3.15e+20 combinations assuming none are repaeated. That's only 21 digits, making it 2775 digits short of creating a single page even once.
I'm so sick of seeing this analogy, because it is missing the point by an insane margin. It is extremely misleading, and completely misrepresenting getting something very complex right by chance.
To generate a work of Shakespeare by chance is impossible in the lifespan of this universe. The mathematical likelihood is so staggeringly low that it's considered impossible by AFAIK any scientific and mathematical standard.
The quote is misquoting the analogy. It is an infinite number of monkeys.
The point of the analogy is about randomness and infinity. Any page of gibberish is equally as likely as a word perfect page of Shakespeare given equal weighting to the entry if characters. There are factors introduced with the behaviours of monkeys and placement of keys, but I don't think that is the point of the analogy.
Yeah, it always seems that every time someone questions the wisdom or validity of this analogy seems not to understand it.
It's either the misunderstanding that the constraints of the hypothetical are finite (a million vs. infinity).
Or the insistence that any sufficiently infinitesimal chance is "practically zero", when literally any likelihood multiplied by infinity is going to guarantee an occurrence.
You can actually expand the infinite monkey theory to say that an infinite number of monkeys using typewriters for an infinite amount of time would write every single book ever written in any language the keyboard is capable of typing, as well as every possible book that could ever even theoretically exist, an infinite number of times, and still be correct.
Any infinite set of random (or even semi-random) characters will contain every possible set of characters that could ever exist, of any length. The works of Shakespeare are also encoded into Pi, we just haven't calculated enough digits to discover one yet (and very likely never will).