Infinite Monkey Theory

>>8612799
Infinite monkey + infinite time + LaTeX = secrets of the universe.

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

>>8612799
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.

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>>8612799
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?

https://en.wikipedia.org/wiki/The_Library_of_Babel

>>8612799
Almost certainly, yes. Infinity is pretty big.

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

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>>8612830
>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

>>8612799
no.

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

>>8612849
Essentially what you're saying is that monkeys aren't proper random string generators, which I would assume is true.

>>8612825
>If infinite anything existed in the real universe, the whole universe would collapse into a black hole
What?

>>8612837

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

>>8612858
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?

>>8612824
No, it's not. The monkey can kept typing "x".

>>8612866
But if it were infinite he would eventually do something else.

>>8612870
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.

>>8612883
Okay let's say you just have 1 monkey for infinite time.

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It can already be done with the library of babel.

>literally

>>8612958
>library of babel.
Is that just a poetic way of saying "the set of all possible character combinations of size (410 * 3200)"?

>>8612958
I wonder what the longest piece of coherent writing found in the books is.
Spooky stuff.

>>8612799

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.

>>8612983
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)

>>8612799
No they'd all die of dehydration long before that point.

>>8612799
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...

>>8612987
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.

>>8612987
>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.

>>8613028
What if I give you an uncountable number of 1s? Can you make a 2?

>>8612799
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]

>>8612799
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.

>>8613032
>What if I give you an uncountable number of 1s?
no need, 2 is enough

>>8612958
What is even this?

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>>8613024
>harry potter is produced before hamleg

>>8613073
enjoy anon
https://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.

>>8613094
>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.

>>8613114
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.

>>8612799

If there were infinite monkeys they would produce it instantly

>>8613138
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.

>>8612992
>>8612983
>>8612958
so you can't post a paragraph from a book and get a full page?

>>8613182

yes there is, stupid

1. take probability equation
2. limit at infinity

nobel prize, please

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>>8612983
Huh, Im still not sure how exactly it works but its pretty neat

>>8613199
Holy kek

>>8613199
What does it do?

>>8613189
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?

>>8613199
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.

>>8613205
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.

>>8613202
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

>>8613205
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

>>8613213
Oh really? Bastards.

>>8613213
Ahh thats kind of a letdown for some reason. Awesome concept though

>>8613220
How can you search it? Like how did the navy seal 300+ kills pasta show up there?

>>8613230
I just searched dont know how this shit works desu fampai

>>8613223
>>8613216
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).

>>8613238
There are theoretical limits on computation speeds and what you are suggesting will never be practical.

>>8613239
>The only limit is our mind anon
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.

>>8613259
This is funny. Mind if I post it somewhere else?

>>8613173
Lol no. Race conditions.

>>8613230
are you serious senpai?

>>8612799
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.

>>8613216
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 anon reading the cure for cancer actually recognize what it is".

>>8612799
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 https://en.m.wikipedia.org/wiki/Infinite_monkey_theorem

>>8612817
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

>>8613379
It does contain all finite sequences though

>>8613420
that is assuming the distribution of the digits is truly random.

>>8612799
In an infinite universe ALL possible outcomes have to happen at least once. And that regards to absolutely everything, not just monkeys.

>>8612817
>>8613220
>>8613930
>>8613410
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.

>>8612799

Let me rephrase the question.

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

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>>8612799
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.

>>8612831
This is the correct answer.

>>8613224
>>8613225
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 >>>/x/ 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.

>>8613951
No, it eventually repeats.

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>>8612900
This is the same...
Infinite time = infinite possibilities
Infinite possibilites = include all possibilities, so hamlet

>>8612966
Linda
Borges wrote a very nice short story about it

>>8613963
That would make it rational mate.

>>8612799
How do you think Shakespeare did it?

>>8613350
Yes

>>8613420
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)

>>8614301
>a million
No it's actually infinite ya dumb ass

>>8612799
Yes, in exactly an infinite amount of time, but who has that long to wait?

>>8613173
Oh pls, show me the formula that approaches zero as monkeys go to infinite.

>>8614496
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.

>>8614506
Which is infinite, so basically never as far as humans are concerned.

>>8612881
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.

>>8612799
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.

>>8612799
Do you understand the meaning of the word "theorem"?

>>8613138
pretty sure you have a strange misunderstanding of some basic concepts anon.

>>8613962
>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.

>>8612844
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

>>8614496

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

>>8612799
This is the reason Java is such a popular language, only that the output isn't Shakespeare but running code.

>>8612799
you mean Haramblet
>amirite?

>>8615121
It might happen right away

>>8613949

there is no limit to the length of what they write. even if they have a finite alphabet they can write infinitely long papers. idi0t

Maybe.

It could be that in infinite time one of the infinite monkeys happen to write it by chance.

But infinite time + infinite monkeys doesnt mean it will happen for sure.

For example if all monkeys press just "x" and infinite amount of times nothing happens.

>>8612831
Fucking this. Also, in the same note, https://en.wikipedia.org/wiki/The_Immortal_(short_story)

>>8614446
tell it to Wilensky, ya dumb ass

>>8614950
>Infinity is a large number.
It's not a number at all.

>>8612821
Sharp, like it.

>>8612883
>Speaking of "infinite monkeys" are useless, because there can be no such thing
Aww, sweet. Poor child. Lurk more. Or learn math.

>>8616340
Lrn2physics fgt pls

>>8612799
Of course. It's infinity. Not only could they write all his stupid stories, they could mindlessly churn out "better" stories.