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 actual analog isn't a million monkeys. you only need one monkey. but it's for an infinite amount of time. the probability isn't practically zero, it's one. that's how infinity works. not only will it happen, but it will happen again, infinitely many times.
Infinite monkeys and infinite time is equally stupid, because obviously you can't have either, for the simple reason that the universe is finite.
And apart from that, it's stupid because if you use an infinite random, EVERYTHING is contained in it!
I'm sorry it just annoys the hell out of me, because it's a thought experiment, and it's stupid to use this as an analogy or example to describe anything in the real world.
You wouldn't need infinite time if you had infinite monkeys.
An infinite number of them would produce it on the very first try!
Then the fun part is finding which monkey has the result...
Obviously, but as I wrote BOTH are impossible, so it's irrelevant. I just didn't think I'd have to explain WHY infinite monkeys is impossible, while some might think the universe is infinite also in time, which it is not.
I also already wrote that if you have an infinite string everything is contained in it.
But even with infinite moneys it's not instant, because technically each monkey needs to finish a page.
But I understand what you mean, and that's exactly why the theorem is so stupid IMO. You could also have 1 monkey infinite time.
But both are still impossible.
When I say it's stupid, I don't mean as a thought experiment which is the purpose of it. The stupid part is when people think they can use it as an analogy or example to describe something
It's a theorem. It's theoretical. This is like complaining about the 20 watermelon example being unrealistic: that's not what it is about.
It's OK it exist, it's a thought that is curious enough. I'd even go so far and say it can have an educational function for children.
I just don't get why some people seem to think it's relevant in so many situations where clearly it's not.
That's not true. Something can be infinite and still not contain every possibility. This is a common misconceptoin.
For instance, consider an infinite series of numbers created by adding an additional "1" to the end of the previous number.
So we can start with 1. The next term is 11, followed by 111, then 1111, etc. The series is infinite since we can keep the pattern going forever.
However at no point will you ever see a "2" in the sequence. The infinite series does not contain every possible digit.
why do you keep changing the parameters? yeah, if you exclude the possibility of something happening it won't happen. duh?
that's not what's happening in the infinite monkey theorem. it's random key presses. that means every character has an equal chance of being pressed.
no one said the monkey would eventually start painting. or even type arabic words. it has a typewriter, presumably an English one. so the results will include every possible string of characters ever.
it's not a common misconception, you just don't know what the theorem says at all.
That's just not true. One monkey could spend eternity pressing "a". It does't matter that he does it infinitely. He will never type a sentence.
If the keystrokes are random that is just as likely as any other output.
Being infinite does not guarantee every possible outcome.
Any possibility, no matter how small, becomes a certainty when dealing with infinity. You seem to fundamentally misunderstand this.
no. you don't understand infinity, and you don't understand probability.
if every keystroke is just as likely as any other keystroke, then each of them will be pressed an infinite number of times. that's what just as likely means. that's how random works.
if the monkey could press a for an eternity, then by definition it's not as likely as any other keystroke. you're again changing the parameters to a monkey whose probability of pressing a is 1 and every other key is 0. that's what you're saying means.
for a monkey that presses the keys randomly, which means the probability of each key is equal, every string of characters will be typed. you can find the letter a typed a million times consecutively, and a billion times and a quadrillion times. not only will you find any number of consecutive keystrokes of every letter, but you will find it repeated an infinite number of times throughout.
being infinite does guarantee every possible outcome. what you're ruling out from infinity is literally impossible by definition.
That's exactly my point. Infinity can be constrained. It can be infinite yet also limited. If we can exclude something from infinity then we have shown that an infinite set does NOT necessarily include everything.
this has nothing to do with the matter
Anything with a nonzero probability will happen infinitely many times. The complete works of Shakespeare consist of 5,132,954 characters, 78 distinct ones. 1/(78^5132954 ) is an incomprehensibly tiny number, millions of zeroes after the decimal, but it is not zero. So the probability of it happening after infinitely many trials is 1. lim(1-(1-P)^n ) as n approaches infinity is 1 for any nonzero P.
An outcome that you'd never see would be a character that isn't on the keyboard.
This is actually a way dumber argument than you think you’ve made.
The original statement was that if something is infinite it must contain all possibilities. I showed one of many examples that do not, therefore the statement is not true. It's a common misconception.
Please use your big boy words to reply instead of calling something "dumb" for not understanding.
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).
It was a big YouTube science video subject last week... Suddenly everyone has a real educated opinion on the matter with statistics and everything.
In the meantime weasel programs are very effective, and a better, if less known metaphor.
Sadly the monkeys thought experiment is a much more well known example.
Irrelevant nerd thought, back in the early nineties, my game development company was Monkey Mindworks based on a joke our (one) programmer made about his method of typing gibberish into the editor and then clearing the parts that didn't resemble C# code.
That's how they made that ET game back in the day
C# didn't exist in the early 90s, perhaps you're thinking of another language?
Obligatory: 95% of paint splatters are valid perl programs
It may have been C+ or merely C with OOP features. I was writing the enemy-AI code (not to be confused with actual learning systems) in visual basic (and made some sweet pathfinding algorithms at the time), but took it too seriously and ended up breaking my brain.
We had a publisher and it was going to be awesome and then Windows 95 came out and broke all our code.
I hear you. My fucking dog keeps barking up stupid Mexican novellas and Korean pop. C'mon Rosco! Go get me the stick buddy! The stick! No! C'mon! The cat didn't kill your father and then betray you for the chicken!!! Nobody likes your little dance that you do either, you do it because you sick in the brain for the Korean Ladies! Get otta here!
Don't look for statistical precision in analogies. That's why it's called an analogy, not a calculation.
You are missing a piece of the analogy.
After each key press the size of the letters change, so some become more likely to be hit than others.
How the size of the keys vary is the secret being sought, and this training requires many, many more monkeys than just producing Shakespeare.
AI data analyst here. The above is an excellent extension of the analogy.
Now, imagine another monkey controlling how the size of the keys vary. There might even be another monkey controlling that one.
The analogy doesn't seem to break until we start talking about the assumptions humans make for efficiency.