Infinite Monkey Theory

Is this possible? Say there are infinite monkeys with infinite typewriters for infinite time. Would one of them eventually produce Hamlet by Shakespeare?

Other urls found in this thread:

en.wikipedia.org/wiki/The_Library_of_Babel
libraryofbabel.info/
en.m.wikipedia.org/wiki/Infinite_monkey_theorem
twitter.com/SFWRedditGifs

Infinite monkey + infinite time + LaTeX = secrets of the universe.

If you had an infinite amount of monkeys you wouldn't need infinite time lol

Infinite means all the possible outcomes, so yeah, I believe so.

If infinite anything existed in the real universe, the whole universe would collapse into a black hole. (Either at the speed of light, or at infinite speed, I'm not sure which.)

In a mathematical hypothetical, it could happen, but it would be wildly harder to find the right monkey then to just reinvent the works of Shakespeare yourself.

No because eventually they'll shit all over the typewriters because they're fucking monke- wait Jamie could you pull up that article about how monkeys think? I was reading earlier that a tenth of a monkeys average time is spent thinking about shit, when they're going to shit, how their going to shit. It's really fascinating. Have you seen that video of the monkey throwing shit at itself in a mirror?

en.wikipedia.org/wiki/The_Library_of_Babel

Almost certainly, yes. Infinity is pretty big.

You also dont need infinite monkeys. Just one will do.

>okay man but I just don't think you're grasping the capacity of a chimp's mind
>like they're smart but man not that smart
>yes yes I know what you mean by infinity, I just don't see it happening
>i mean eventually one of those chimps is gonna get halfway there and then fuck it up by pounding on the keys
>its just not possible

no.

assuming these are immortal monkeys, their brains have finite limitations on what they can produce.

Essentially what you're saying is that monkeys aren't proper random string generators, which I would assume is true.

>If infinite anything existed in the real universe, the whole universe would collapse into a black hole
What?

with infinity monkeys, one of them would type out Hamlet in the minimum amount of time that Hamlet can be typed.

infinite yes

but you'd need unspeakable numbers of monkeys to achieve that in finite bounds, probably orders of magnitudes more monkeys than there are atoms in the universe

Yes, but then you dont need infinite time.

The real question is, if the monkeys were to type pseudorandom strings instead of actually random ones, would they still be able to do it?

No, it's not. The monkey can kept typing "x".

But if it were infinite he would eventually do something else.

Would he really? You would have to prove that monkey's brains can generate fully random strings.

Speaking of "infinite monkeys" are useless, because there can be no such thing. What you can say though, is that the probability gets arbitrarely close to 1 as the amount of monkeys increase.

Okay let's say you just have 1 monkey for infinite time.

It can already be done with the library of babel.

>literally

>library of babel.
Is that just a poetic way of saying "the set of all possible character combinations of size (410 * 3200)"?

I wonder what the longest piece of coherent writing found in the books is.
Spooky stuff.

SQRT(2) = 1.414214.... non-repeating non-terminating sequence of digits.

So no, an infinite number of monkeys and infinite time is not sufficient to ensure the production of Hamlet via random key strokes.

B4 someone says "but there is an infinite number of moneys AND typewriters, so...." The combination is still countable and can be correlated isomorphically with the natural numbers.

All writing of some length is found in the library of babel. It uses some kind of strange algorithm that eventually produces every letter combination up to a number of letters, then it has a reverse algorithm to look up its seed that generates it.

The library of babel can produce any unique page, but it cannot produce pages longer than its standard length (because that would require a bigger algorythm)

No they'd all die of dehydration long before that point.

With probability 1, yes. But it's worth noting that they will also almost certainly produce every book that isn't Hamlet, including a version of Hamlet where Wildberger is instructed by the ghost of Brouwer to kill the non-constructivist King of Denmark so it's not that meaningful a result...

The number of digits in sqrt(2) is countable though, so as long as there are at least uncountably many monkeys it should be fine.

>SQRT(2) = 1.414214.... non-repeating non-terminating sequence of digits.
>So no, an infinite number of monkeys and infinite time is not sufficient to ensure the production of Hamlet via random key strokes.
Hamlet is a finite number of symbols, so... that makes no sense.

What if I give you an uncountable number of 1s? Can you make a 2?

Okay, Karl. Consider a SINGLE, never mind an infinite number of chimps. The probability of the chimp typing the complete works of either Hamlet or Shakespeare in some interval of time is (assumed nonzero) p. Assume independence, as the chimp isn't really learning, nor is it doing any worse outside of reason lol.

Then prob of success on the first try would be [math]p[/math], success on the second would be [math](1-p)p[/math], success on the third gives [math](1-p)^2p[/math] and so on. Thus we have,

[math]\sum_{x=0}^{\infty} p(1-p)^x=p+(1-p)p+(1-p)^2p+...=p/(1-(1-p))=p/p=1
[/math]

You would think that the infinite amount of time would allow this to be true. But because they are all monkeys, this is not completely random. So eventually they would all type the same nonsense with the same patterns due to genetic makeup.

>What if I give you an uncountable number of 1s?
no need, 2 is enough

What is even this?

>harry potter is produced before hamleg

enjoy user
libraryofbabel.info/

It is obvious that the probability it will happen eventually is 100%, the key word being eventually, implying that this is a statement about the long term average probability. It is possible that the monkey types the wrong letter forever, as there is no constraint against this.

>It is possible that the monkey types the wrong letter forever
the odds of this are far less than the quantum fluctuations of the typewriter and the monkey's paw aligning in such a way that they pass through each other. Don't think constraints really matter given infinite values.

Technically, 1 monkey, 1 typewriter (assuming infinite life and durability etc) and unlimited time would not only produce hamlet, Mr. Monkey would produce it an infinite number of times.

Its not a matter of odds. You and many others in this thread are misunderstanding the basic nature of probability. There is nothing that stops Hamlet from NOT being produced in an infinite amount of time, so it will not necessarily happen. This is the only applicable logic to this scenario, because one cannot observe what happens after an infinite time anyways. Thats why theres so many tangents about limits in this thread.

If there were infinite monkeys they would produce it instantly

You're forgetting that most people here grossly misinterpret concepts even as mind-numbingly simple as the law of large numbers

This is mostly a paradox only in the sense that there is no well defined way of what infinite is in this scenario, or rather there is no good way of changing the language into something mathematical and objective.

so you can't post a paragraph from a book and get a full page?

yes there is, stupid

1. take probability equation
2. limit at infinity

nobel prize, please

Huh, Im still not sure how exactly it works but its pretty neat

Holy kek

What does it do?

Probability is just a model, this question is a shit test for people who don't know what probability actually means.

Guys, imagine you have access to an unlimited library. In this library, each book is 1000 pages long that consists random permutation of English alphabet and all Math symbols.
Now, since the library consists of that many books, there must be
>A book that contains the cure to cancers
>A book that contains the solution to Reimann hypothesis
>A book that proves P = NP or not
>A book that contains Hamlet by Shakespeare
>A book that contains Hamlet by Shakespeare with typos
You know, the point is someday out computer can be powerful enough to generate all of these. The problem is how to find our answers in all of the possibility. Would brute force them faster than waiting for a genius in the field to come up with these books?

They randomly assort dictionary words and put a bunch of trash in the mix, then generate the "books" over time so that each one has at least one sensible string. Just as it says on the homepage, its impossible for them to store all combinations of 3200 characters, so they dont do that. They just give the illusion of it by exploiting how limited language is.

I'm afraid you've got your head somewhere in the cosmos. Protons would decay before useful strings to big questions would come out of a random generator, this monkey shit is a thought expertiment and IS NOT PHYSICAL which people still do not seem to understand.

Its an algorithm that makes every single combination of 1,312,000 characters. So its everything that can ever be said in said amount of characters

while talking about what monkeys may write in infinite time is something of a philosophical debate, what monkeys can write in finite time is not. the chance of something remotely useful coming out of a computer randomly even with theoretical limits on speed is virtually nonexistant in the time to the end of the universe

Oh really? Bastards.

Ahh thats kind of a letdown for some reason. Awesome concept though

How can you search it? Like how did the navy seal 300+ kills pasta show up there?

I just searched dont know how this shit works desu fampai

You do realize that the number of permutations for a book with 1000 pages are finite?
I didn't say that the computer has to be random everytime it generate a book.
It does not generate the same books twice.
That is why it is possible (it still needs a fucking powerful computer).

There are theoretical limits on computation speeds and what you are suggesting will never be practical.

>The only limit is our mind user
Is what I was going to say but yeah. It won't even be possible to create such a computer even if the universe dies.
If you have a grasp of all permutations then you are basically a god yourself though.

Yeah, and eventually one of the monkeys will type out how all numbers added together equals -1/12.

This is funny. Mind if I post it somewhere else?

Lol no. Race conditions.

are you serious senpai?

Redundant stupid fucking question. Seriously, not even faggot monkies use typewriters anymore. Why not just ask
> given infinite assholes spouting diarrhea on an infinite sheet of velvet, might those assholes thusly produce a quality represention of OP?

Answer: Yes. Yes the will.

The wrong viewpoint- it's not whether or not it's possible. The bottle neck is in the interpretation, not the generation.
Infinite books requires infinite interpretations of the book. The limit isn't the what, it's the who.
The appropriate response to this bullshit is "sure, but can the retarded user reading the cure for cancer actually recognize what it is".

this is like saying that pi contains all sequences ever
it's just not true

If people are monkeys, yes.
If monkeys generated random keystrokes, the answer would also be yes, but probably in a very fucking long time (think how long it takes a computer to brute force one 8 character password).
The problem is, monkeys do not generate random keystrokes. They tend to push the buttons they like the most. See en.m.wikipedia.org/wiki/Infinite_monkey_theorem

you'd just have to sift through an infinite amount of data

you'd need infinitely many monkeys to do this. im beginning to think its monkeys all the way down

It does contain all finite sequences though

that is assuming the distribution of the digits is truly random.

In an infinite universe ALL possible outcomes have to happen at least once. And that regards to absolutely everything, not just monkeys.

Lots of blatantly wrong retards in this thread but these guys are less obvious.

Given that LaTeX input is a finite alphabet then at most one can produce a countable number of sentences. So a monkey typing over an infinite amount of time would at most produce a countable number statements. You wouldn't even have a fact for each real number, not even close.

Let me rephrase the question.

Do pi has inside all the numerical constants in the universe?

No, because monkeys are not random enough and the thought experiment is incorrectly structured. Appending "infinite" to any portion of this thought experiment won't help the outcome. Monkeys are not machines.

This is the correct answer.

There's literally no way modern technology can store and search the library properly. We don't even have enough digital storage space in existence to do it. It could be done in the future if storage was increased and properly compressed and we had fully integrated quantum computing to search it.

If that ever happens, you bet your ass that tard and religious types will pour over it trying to make up and validate pretty much every ass itch they've ever felt. There's even a chance you could predict the future with it, but which future you predict may be a problem.

No, it eventually repeats.

This is the same...
Infinite time = infinite possibilities
Infinite possibilites = include all possibilities, so hamlet

Linda
Borges wrote a very nice short story about it

That would make it rational mate.

How do you think Shakespeare did it?

Yes

Pi is not proved to be normal.

"We've heard that a million monkeys at a million keyboards could produce
the complete works of Shakespeare; now, thanks to the Internet,
we know that it is not true."
– Robert Wilensky, UC Berkeley (1996)

>a million
No it's actually infinite ya dumb ass

Yes, in exactly an infinite amount of time, but who has that long to wait?

Oh pls, show me the formula that approaches zero as monkeys go to infinite.

They wouldn't produce it instantly but they would produce it in the minimum time possible.

I think we can assume that not all monkeys are alike, and that all monkeys have different ways of "randomly" typing. So each monkey would have a different probabliity of hitting each key (also a different probability for not hitting anything), and this would lead to an issue of certain keys not getting pushed often enough by every monkey to ever produce anything resembling human literature. If we were to actually run an experiment, we might find that most monkeys only type with one finger and rarely move that finger away from a few keys, and when it uses more fingers, it is only to smash a bunch of keys at the same time.

I'm pretty sure the only answer to this question is t = infinite.

Which is infinite, so basically never as far as humans are concerned.

Infinity is a large number. Chances scale up to 100%. So saying a monkey is most likely to only hit 1 or 2 keys doesn't even matter, over either an infinite amount of time or an infinite amount of monkies they'd end up typing of shakespear or blahblah simply just because the other letters to the alphabet happen to be next to the 2 keys the monkey is pressing and he'a bound to accidently hit of them at any given point so yea.. Shakespear. I win.

If you had an infinite amount of monkeys and an infinite amount of typewriters, they would produce Hamlet in a short amount of time (how ever long it takes a monkey to type from start the finish - a day maybe?)

Or, you could have a single monkey on a single type writer for an infinite amount of time, and he would also create hamlet eventually.

Do you understand the meaning of the word "theorem"?

pretty sure you have a strange misunderstanding of some basic concepts user.

>It could be done in the future if storage was increased and properly compressed and we had fully integrated quantum computing to search it.

no it couldn't, it's more information than there are atoms in the visible universe.

I dont think you grasp the concept of infinite. It would eventually happen. Look if a monkey sat down at a typewriter for a infinite amount of time and never stopped using the keys. He would type a complete sentence by accident right? Given enough time that monkey will make two sentences by accident that perfectly coincide. And finally. Eventually Shakespeare's hamlet

you show me the function for amount of monkeys typing -> time until shakespeare and i'll show you the formula that approaches zero as monkeys go to infinite

This is the reason Java is such a popular language, only that the output isn't Shakespeare but running code.

you mean Haramblet
>amirite?