What kind of "study" would this even be? I thought the point of the infinite monkey thing was to talk about regular distributions and eventualities of every possible string showing up. I don't think anyone claimed that any relatively-long string would show up in any reasonable amount of time necessarily, but it's kind of a bizarre assertion to make.
It's sort of like stating the runtime efficiency of a Bogosort; the runtime efficiency is unbounded. Theoretically any list could be sorted on the first run, but it could also just keep sorting in an unbounded fashion for forever, though given enough time (which could be tens of trillions of years or longer), it will eventually be sorted if we assume regular distribution of random numbers.
I think it is even worse: infinite instances of bogosort are 100% guarantueed to finish instantly, because we are running in parallel here and the ones that are unbounded don't matter at all when at least one of then gets it right. And given the fact that there is a non-zero chance of bogosort getting it right first try, means it there are infinite bogosort instances getting it right first try.
This is also true for the infinite typing monkeys: one of them is getting it right by chance, unless that chance is 0 (and it isn't).
The theorem is called "infinite monkey theorem". That means infinite amount of time. A googol years is not infinite, it's infinite times smaller than that. In an infinite amount of time they will write Shakespeare works (if they type randomly enough and not with some bias like never typing certain combinations of letters)
Also, at least the article could have said what the actual probability is then? Are we talking 1e-500, 1e-1000000, 1 / googolplex, or what?
EDIT: of the above examples 1e-1000000 is the closest I think (in order of magnitude of exponent), based on something like 30^5000000 divided through some amount of years assuming ~5 characters per word. So perhaps "If every atom in the universe was a universe in itself" won't get us there, but recursively repeat that process a million times and we do get there
Reverse Gellman effect: you witness pedants in your own domain surgically tear down a harmless puff piece and immediately know this must be happening 24/7 in every other domain where fun is modestly attempted
Yes, but the theorem is meant to explain what can happen in the universe over long time scales.
The point is that there isn't enough time in the universe for all the random stuff to happen that scientists pin on random chance. The theorem was memorable, but a cop out.
> Yes, but the theorem is meant to explain what can happen in the universe over long time scales.
I never understood it that way. I always interpreted it as a fun way to explain the mathematical truth that no matter how low a probability is, as long as it is technically above 0, the event it describes WILL eventually occur given enough time/trials/etc.
I can't see anybody ever interpreting it as a statement about the real, actual, universe. Just like I don't think anybody truly believes that flipping a real coin with non-identical sides (such as every currency coin I've ever used) must have EXACTLY 50% probability of landing on either side. Surely people can separate the mathematical ideal/concept from constraints of physical reality.
I don't think I've ever heard anyone use the infinite monkey example outside of theoretical mathematics; I'm sure someone has, but when I've heard it, it was to describe regular distribution of random.
I think it's a very bizarre thing for these mathematicians to act like they discovered something that I don't think anyone really disputed.
Perhaps not in our observable universe, but in the space of all possible physics that could take place and / or beyond the observable universe if it actually is infinitely big there, perhaps it can? (as in, anything can happen, there will be copies of the Earth with subtle differences somewhere there, Boltzmann brains appearing purely out of quantum fluctuations, etc...)
"Infinite monkeys" would produce Shakespeare and every other book, document, and all future possible book and document in the amount of time equal to the number of letters in the book and the typing rate of a monkey. It wouldn't take an infinite amount of time. :)
Yes, I always imagined this being just a silly exercise in pulling out a finite outcome from infinity. It’s not meant to be provable or disprovable, just hard to comprehend because we cannot think in infinite terms.
Yeah, I might be naive, since they're professional mathematicians and I'm not, but their conclusion feels like saying that they "tested" the concept of infinity and found that it's simply unreachable. To me, the infinite monkey theorem is an abstract idea and not something that needs to be "tested", though it's certainly fun to run the numbers.
They didn't "test" the concept of infinity. They said that the results of the infinite monkey theorem are well known, and they wanted to see what happens in the finite case.
Not the point of the article, but this got me curious...
> Shakespeare’s canon includes 884,647 words – none of them banana.
If this article (1) is accurate, Shakespeare never even knew what a banana is, and he never tried it, since he died ~2 decades before they came to England:
> England got its first glimpse of the banana when herbalist, botanist and merchant Thomas Johnson displayed a bunch in his shop in Holborn, in the City of London, on April 10, 1633.
> Here, we consider the Finite Monkeys Theorem and look at the probability of a given string being typed by one of a finite number of monkeys within a finite time allocation consistent with estimates for the lifespan of our universe
I thought the saying was “infinite monkeys..” and in that case you would get the full works of Shakespeare immediately. With an infinite amount of time and one monkey you’d get the full works of Shakespeare in every language supported by the typewriter any number of times in a row you wished. In fact, you’d get anything you wanted as long as the probability was > 0
Edit: after walking my dogs, isn’t the probability of the full works of Shakespeare never being typed out also > 0? (I can’t believe I’m actually spending calories on this..)
I'm picturing scientists in another universe clenching their butts as the monkey goes to type the last letter of Hamlet..... and misses 't' for 'r' and the whole observation hall erupts with loud groans
Sounds to me that the more interesting question would be graphing out the relationship of time and the amount of monkeys needed for one to write Shakespeare.
Kind of embarrassing to even be in this thread spending time here but would it not also be probable, however unlikely, to never get the full works of Shakespeare?
The reporting on this paper is crazy. In the highlights section of the paper’s page on the journal’s website it says “The long-established result of the Infinite Monkeys Theorem is correct, but misleading.” but the Guardian article says “Australian mathematicians call into question the ‘infinite monkey theorem’ in new research on old adage”, which I read as contradictory to what’s in the paper.
Readit News
It's sort of like stating the runtime efficiency of a Bogosort; the runtime efficiency is unbounded. Theoretically any list could be sorted on the first run, but it could also just keep sorting in an unbounded fashion for forever, though given enough time (which could be tens of trillions of years or longer), it will eventually be sorted if we assume regular distribution of random numbers.
ETA:
Ok, I read through the actual paper, and it's clearly meant more as a joke, which I don't think was made clear in this article: https://www.sciencedirect.com/science/article/pii/S277318632...
This is also true for the infinite typing monkeys: one of them is getting it right by chance, unless that chance is 0 (and it isn't).
Also, at least the article could have said what the actual probability is then? Are we talking 1e-500, 1e-1000000, 1 / googolplex, or what?
EDIT: of the above examples 1e-1000000 is the closest I think (in order of magnitude of exponent), based on something like 30^5000000 divided through some amount of years assuming ~5 characters per word. So perhaps "If every atom in the universe was a universe in itself" won't get us there, but recursively repeat that process a million times and we do get there
The point is that there isn't enough time in the universe for all the random stuff to happen that scientists pin on random chance. The theorem was memorable, but a cop out.
I never understood it that way. I always interpreted it as a fun way to explain the mathematical truth that no matter how low a probability is, as long as it is technically above 0, the event it describes WILL eventually occur given enough time/trials/etc.
I can't see anybody ever interpreting it as a statement about the real, actual, universe. Just like I don't think anybody truly believes that flipping a real coin with non-identical sides (such as every currency coin I've ever used) must have EXACTLY 50% probability of landing on either side. Surely people can separate the mathematical ideal/concept from constraints of physical reality.
I think it's a very bizarre thing for these mathematicians to act like they discovered something that I don't think anyone really disputed.
Relatedly, I wrote an essay that covers this a few years back: https://medium.com/@beadey.teigh/typewriters-29309c8e3b71
> Shakespeare’s canon includes 884,647 words – none of them banana.
If this article (1) is accurate, Shakespeare never even knew what a banana is, and he never tried it, since he died ~2 decades before they came to England:
> England got its first glimpse of the banana when herbalist, botanist and merchant Thomas Johnson displayed a bunch in his shop in Holborn, in the City of London, on April 10, 1633.
(1) https://theconversation.com/the-day-bananas-made-their-briti...
Or in other other words: random generation is highly unlikely to produce something valuable.
Or in other other other words: the amount of useful information in "the library of babel" is miniscule compared to noise.
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> working out that even if all the chimpanzees in the world were given the entire lifespan of the universe, they would “almost certainly” never
Who assumed the original adage had the constraint of the universe’s lifetime.
> Here, we consider the Finite Monkeys Theorem and look at the probability of a given string being typed by one of a finite number of monkeys within a finite time allocation consistent with estimates for the lifespan of our universe
But point taken, the article is sensationalizing.
Edit: after walking my dogs, isn’t the probability of the full works of Shakespeare never being typed out also > 0? (I can’t believe I’m actually spending calories on this..)
No
If either were truly infinite not only would this be possible, it would be mandatory and would occur infinite times.
it's all there regardless