/sci/ - Science & Math

>>9660518
http://libraryofbabel.info/
You killed a thread for a google search.

>>9660518
Statistics tells you right off the bat that just because something has a X probability you have no way of saying it WILL happen, so the theorem is flawed and the person who created it didn't understand the most basic principles of statistics.

>>9660524
what’s this links relevance? I have obviously already searched and read about it, hence the wiki link. I’m looking for a solid sci discussion, and don’t care that I killed off what was probably either a picture some guys foot and a request for medical advice, a stale climate change thread, Elon Musk general masturbation, Neil Tyson/Bill Nye twitter bait, IQ / race boasting and roasting, or the greentext ‘how to spot a brainlet’ thread

>>9660526
I’ve never before heard of this, can ya sauce me, m8? Seems to be the intuitive counter argument that I’m seeking, wonder why I’ve never heard it

Why is this theorem popular if stats 101 shuts it down?

>>9660535
The other anon already told you.

A probabilistic function f(x, y) that utilizes time = x, and monkey count = y, and outputs the probability of creating Z, where Z is any wanted output, approaches 1 as x, y approach infinity, however since there is never and end to this function you can not say definitively that you will get Z with infinite x, y.

Brainlets will say that because the limit of the function is 1, given the parameters it will certainly occur, but this is not the case in actual statistics.

>>9660518
>so given enough time and monkeys they will all eventually be produced

Not given enough time - given infinite time. In a definite timespan it is very improbable.

Say you have 40 keys on a keyboard and a novel consisting of a million signs. What a randomly generating mechanism, like a monkey, has to do is simply get a 1/40 chance a million times in a row to get your results. So there is only a single possible world in a billions of billions worlds where they would type of your desired novel. To put it mathematically, the chance of a monkey writing your desired novel (1/40)^1000000, which is non-zero. Obviously this is not possible in the actual world but only because there are no actual infinities.

>I think the monkeys would always, forever, only pound out jiberish like “haiendid dkdicnsnwdjdidicjdnsiwuebd dndnd”.

There is a couple of worlds where they happen to generate coherent sentences, and only one world in which they type out your desired novel fully.

>>9660535
Go to the link I posted, click "Search" then type in whatever you want. The point is that this is a randomly generated string of text that can be used to derive any known textual information from. In the same way that all of our credit card numbers are hidden in pi. The randomly generated text is mostly useless but it is an interesting application of enough monkeys at enough typewriters sort of thinking.

This is the same sort of reason why life itself was able to develop, there were a lot of mistrials but eventually a monkey typed out the right chemicals and a stable form of "life" was made.

>>9660526
If something has a probability X and given an infinite number of trials it eventually will happen. Now it might not happen in any conceivable time frame, but as long as the infinity is non-terminating it will eventually have a trial that works out.

>>9660538
Because the people who come up with these kinds of thought experiments are faggots.

>>9660546
thanks, I've just only previously heard it asserted with a dizzying amount of authority and confidence in the fact that it 'will' happen, I didn't know the consensus among non-brainlets is that it not happening over an infinite amount of time is also not incorrect. I thought it was a logical/mathematical/statistical gray area, but I suppose it's not, and is instead completely formalized.

>>9660553
>not given enough time - given infinite
as was (or so I thought) implied. after it has happened, it is 'enough'.

>>9660554
I started to explore now that I'm off mobile, pretty cool site anon. not something I'd frequent of course, but a nice bookmark. thanks

>>9660560
no

>>9660518
It's true under this assumption:
>If the keys are pressed randomly and independently, it means that each key has an equal chance of being pressed.
Which might not be actually true for monkeys on typewriters.

>>9660518
Using a Poisson distribution, unless λ for each monkey = 0 or approaches 0 as the number of monkeys approaches infinity, such an event will eventually happen, no matter how improbable it is per monkey per unit of time.

>>9660572
but as >>9660571 points out that's based on certain assumptions about the probability of particular actions

assuming all states are equally probable works fine for toy models in quantum mechanics, but not necessarily for something as complicated as monkeys writing manuscripts.

>>9660575
If we are going to worry about such things then we need to worry about where we are going to house these monkeys and how we are going to feed them. Even if there isn't an equal probability for each key it doesn't affect the end result.

>>9660572
>>9660571
>>9660575
yes, I'm ok with monkeys being random character generators. But >>9660572, you go in direct opposition to what others have said. You state it WILL happen, how can you be so certain?

certainly there's a chance that given an infinite amount of time it won't happen, sort of reminiscent of a halting problem, in my opinion

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

What if the monkey is just wrapping his hands clunkily instead of typing with fingers on the keyboard? Then certain character strings are likely to favored and disfavored, and the monkey may never produce a certain Shakespearean sentence because the character string on the qwerty keyboard would be disfavored by the arrangement of the monkey's fingertips. Perhaps.

>>9660575
>assuming all states are equally probable works fine for toy models in quantum mechanics
Nothing about what I just described assumes that all states must be equally probably. The point I am trying to make is that the probability of a monkey typing the works of Shakespeare in a given unit of time is some amount, probably something extremely tiny but > 0%. For such an event to never happen, there are 2 possibilities. A, the monkeys typing the works of Shakespeare is literally impossible, not just astronomically, or B, this astronomically small probability must get smaller and smaller with each additional monkey-hour, and approach 0 as the number of monkey-hours approaches infinity.

>>9660584
>You state it WILL happen, how can you be so certain?
I'm not. I covered this here: >>9660590
>certainly there's a chance that given an infinite amount of time it won't happen, sort of reminiscent of a halting problem, in my opinion
And for it to not happen after an infinite amount of time, it must have one of the two probability states mentioned previously. Either λ = 0, or approaches 0 as monkey-hours approaches infinity.

>>9660590
*equally probable

OP has a severe case of brainlets
the theory isnt really about monkeys; think of it like this:
If a computer randomly generated letters and numbers for an infinite amount of time, then it would over infinite time write out every single letter combination possible in every order possible
therefore over an infinite amount of time the computer would have generated shakespeares play.
>is every one on here 13 or dumb

>>9660524
>tfw OP's question as well as your response were already in there before you even posted them
http://libraryofbabel.info/book.cgi

>>9660518
That is what happened when you consider we're just evolved monkeys

>>9660619
Unironically this

>>9660619
Ha. That's a neat solution to this.

>>9660518
Monkeys are not random. They tend to peck the same key over and over.

>>9660518
What are you doing on 4chan, Karl Pilkington?

>>9660605
Computer generated random numbers are pseudorandom. A series of numbers generated by a computer may seem random, but they are predetermined by the method and seed used for generating them.

Therefore a given random number generating sequence has one and only one corresponding series of letters and numbers. Therefore there is one and only one sequence for a given number-to-letter cipher that will produce one of Shakespeare's plays.

>>9660660
s'alright, 'innit?

>>9660599
no, you say it will happen, correct? you give two explicit scenarios:

>A, the monkeys typing the works of Shakespeare is literally impossible, not just astronomically, or B, this astronomically small probability must get smaller and smaller with each additional monkey-hour, and approach 0 as the number of monkey-hours approaches infini

We can rule out A, since a monkey is physically capable of it. Otherwise, if you have some other definition of impossible, this is just a round a bout statement. I also don't understand B, because the more time that is allowed, the higher the odds are of it happening, so the probability should increase, if anything


In addition to that, I can quote (you) here saying it WILL happen: "such an event will eventually happen, no matter how improbable it is per monkey per unit of time."

>>9660605
no shit it's not about monkeys retard, you clearly either haven't even read the thread (like a dumbo) or you have shit reading comprehension (in which case you're even more retarded). FURTHERMORE, you black hole of a brainlet, the whole point of it is that there IS a possibility a monkey could type it, it's just more unlikely (presumably) that a monkey would type shakespear before a random number generator, SO, even if it we are literally talking about infinite monkeys, the problem is exactly the same: since there is a possibility, it *should* happen.

feel dumb? you should

>>9660658
regardless, there's still a possibility, that's the whole point...

>>9660619
>we evolved from monkeys
Back to >>>/x/

>>9660864
>I also don't understand B, because the more time that is allowed, the higher the odds are of it happening, so the probability should increase, if anything
See pic related. The probability will increase, but it will not necessarily converge at 100%.
>In addition to that, I can quote (you) here saying it WILL happen: "such an event will eventually happen, no matter how improbable it is per monkey per unit of time."
Only if lambda is constant, or if there is a limit to how small it can get.

>>9660611
really makes you think

>>9660921
goddammit anon stop contradicting yourself, you said it will decrease as time goes on:
>>9660590
> A, the monkeys typing the works of Shakespeare is literally impossible, not just astronomically, or B, this astronomically small probability must get smaller and smaller with each additional monkey-hour, and approach 0 as the number of monkey-hours approaches infinity.
>B, this astronomically small probability must get smaller and smaller with each additional monkey-hour, and approach 0 as the number of monkey-hours approaches infinity
>small probability must get smaller and smaller with each additional monkey-hour, and approach 0

are you trying to fuck with me?
.

>>9660963
What is it exactly that you don't understand? Literally nothing that I said is contradictory.

>>9660518
I feel like this theorem would be less confusing for brainlets if we took the monkeys out entirely. Just imagine a random letter generator. Now run it for an infinite amount of time. The works of Shakespeare will appear somewhere in the output. It's not difficult to understand.

>>9660584
>sort of reminiscent of a halting problem, in my opinion
You know how I know you're an undergrad who doesn't know what they're talking about?

>>9660518
If your thesis begins with untestable logical impossibilities like infinite time, monkeys, and typewriters, then of course unprovable logical impossibilities like you describe will results.

>>9660560
u

>>9660518
The math which applies to statistical mechanics can not be used on these scales.

>>9660518
It wouldn't necessarily happen. The monkey could just spam the letter "a" for eternity. Just because it is possible does not mean that it is either probable or necessary.

>>9661011
because this clearly isn't a halting problem? HENCE the word strictly subjective word reminiscent, faggot. get some reading comp before messin with the dad

>>9661031
this statement is not always true, a lot of math is founded upon similar conditions (infinity, and so, naturally, some impossibilities - but these are not illogical in any way). further, the monkeys or typewriters don't make a fucking difference brainlet

>retard

the monkeys would die of old age before they wrote 3 intelligible pages

>>9661225
>the
there's an infinite amount of monkeys as well, but I agree with it not necessarily being true, and personally don't think it would ever happen.

>>9660518
the monkey idea is retarded because monkeys are not "random creatures".
just imagine a computer which is constantly generating random latters from a to z. now, all of shakespeares works have a combined symbol count of
884,421 times 8 average length letters per word= 7.075.368 letters.
Considering the alphabet has 26 different symbols, typing a string of 5 symbols in the correct order has a probability of 0.038 (≈1/26) to the power of five.
mind you, an average computer can generate 10^15 characters per year.
now, the probability of writing all of shakespeares works in a certain order would be 0.038^7.075.368
a computer can type out all of shakespeares works (if it hits this probability) in about 8 seconds. so every eight seconds we get a random batch that could be shakespeare. now, if we increase the amount of computers to a few billion, we get 3*3 billion. which is still astronomically small for the pribability. this is however if they only run for three seconds. if they run for a whole year, the number increases to 9.4*10^16.
if we let them run for a million years,
we only get to ^22.
So basically, to get one fucking match of all of shakespeares works we need a near infinite amouny of computers running a near infinite amount of time.

>>9661258
god what is UP with these BRAINLETS not understanding that it doesn't matter that the monkeys aren't random? the chance still exist, therefore it's still possible, the odds are just smaller. All the same logic leads to the same conclusions.

Additionally, computer 'random number generators' are notorious for not being truly random, faggot

And your calculations are unfounded and useless

>>9661264
Not only did the monkeys produce nothing but five total pages largely consisting of the letter S, the lead male began by bashing the keyboard with a stone, and the monkeys continued by urinating and defecating on it. Mike Phillips, director of the university's Institute of Digital Arts and Technology (i-DAT), said that the artist-funded project was primarily performance art, and they had learned "an awful lot" from it. He concluded that monkeys "are not random generators.

>>9661237
No, its not founded upon having an infinite number of things, its founded upon the use of infinity as a large limit to determine convergence.

>further, the monkeys or typewriters don't make a fucking difference brainlet
Being able to acquire an infinite amount of them makes a big difference in the ability to test this thesis, since you didn't seem to understand that my use of infinite applied not only to time, but also to the monkeys and typewriters.

"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)

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

>>9660518
It's the same idea that by pressing 1 or 0 randomly infinitely, at some point you will have encoded Shakespeare's plays using the bytes for ascii codes.

Another similar idea is that since pi is irrational, eventually there will exist a point where shakespeare's plays are encoded in the digits of pi

>>9661359
>randomly infinitely
figuratively literally
Lrn2adverb fgt pls

>infinite

>>9660518
Given a text of length N and any probability X in (0,1), there exists a length L such that the probability of the text occurring somewhere in the random key presses of length L is greater than X.

As you require X to be closer to 1, L will get bigger.

Another way to think of it is that there are 2^N bit strings of length N.
Imagine a keyboard with 2^N keys (one key for each bit string of length N).
After M random key presses, the probability of a specific key not being pressed is (1-2^-N)^M.
The probability that a specific key is pressed at least once is 1-(1-2^-N)^M.
Let X=1-(1-2^-N)^M.
1-X=(1-2^-N)^M
M=log(1-X)/log(1-2^-N)
Let X = 0.5 and treat the problem like a coin toss.

Thinking ONLY gibberish will be produced is as brainlet as thinking you will never get heads in an infinite coin flip.

>>9660518
Thought experiments are retarded and always gimped. For instance, monkeys wouldn't type every combination possible, they'd just end up in a chaotic random loops with minor permutations. Because monkeys are too similar to each other mentally they will all end up with pretty much the same incoherent crap typed out.

This isn't the Library of Babel after all. The monkey business is based on he monkeys not repeating loops. It hinges specifically on that and nothing else. This is just another example of why all math is lies.

> or do I have a severe case of the brainlets?

Not at all. Math simply doesn't work in the real world. It is a fantasy concept.

>>9661359
>Another similar idea is that since pi is irrational, eventually there will exist a point where shakespeare's plays are encoded in the digits of pi
Irrationality doesn't imply that. No one knows if pi contains all possible permutations of digits

>>9661651
>I can't comprehend infinity
Classic

>>9661659
>No one knows
Isn't it just inherently unknowable? No matter how many digits you calculate, you can never know if a pattern will be revealed at the next digit?

>>9660518
>>9660526
>>9660560
>>9660588
>>9661240

Its less about statistics and more about probability in the infinite sense. Its difficult to grasp because humans can't really conceptualize what infinite monkeys, typewriters, and time would look like but to be accurate, they would not only type out any and all Shakespeare works, but they would be completed in every keystroke that's ever done by them forever because somewhere in that 25 million character subset of infinite, its being completed (and there are infinite subsets of 25 million in an infinite set.)

I used 25 million as a large exaggeration but you get the point.

>>9660518
>I think the monkeys would always, forever, only pound out jiberish like “haiendid dkdicnsnwdjdidicjdnsiwuebd dndnd”
That's because you don't truely understand randomness or infinity or both.

>>9661666
No true at all. We know for example that all base ten digits are equally represented in pi, a property which is not generally true for irrationals.

If its infinite monkeys infinite typewriters and infinite time then they will eventually type out every combination possible.

WHAT DO YOU NOT UNDERSTAND ABOUT THE CONCEPT OF INFINITY?

>>9661276
>No, its not founded upon having an infinite number of things,
What are you trying to say here? The monkeys on typewriters IS very clearly founded upon an infinite number of monkeys on type writers and units of time. And many, many more maths rely on infinities.

>Being able to acquire an infinite amount of them makes a big difference in the ability to test this thesis, since you didn't seem to understand that my use of infinite applied not only to time, but also to the monkeys and typewriters.
You completely dodged the point. No SHIT they are infinite (I have no idea why you seem to think I didn't understand this, as it's been explicitly stated repeatedly), but it ultimately doesn't matter that it's MONKEYS not a random number generator - that was the point skirted.

>>9661796
They won't though, not necessarily at least. Do you fail to understand there's also the possibility they will type jibberish until the end of time?

>>9661771
shit points faggot, I understand them fine.

>>9661651
thanks anon you get it, the others here are very proudly displaying their ignorance

>>9661268
you RETARD. LISTEN UP: The monkey has a POSSIBILITY of typing Shakespear. It is PHYSICALLY ABLE to, therefore there is a chance, no matter how small. The hypothesis is that given enough monkeys and time (an infinite amount of each, to be more precise), that because there is a small probability, it WILL happen.

I however don't think it would happen, and I don't think it would happen with a real random character generator either (unless they only output unique permutations, in which case, by process of elimination, it eventually would).

>>9662419
Need more monkeys than ever been seen for a longer period of time that has since happened.

Even one 300 word page of approximately 1500 characters will be impossible given the current understanding of the universe even if they typed non-stop plugged into a matrix where they can type 5 quadrillion peta-words per a billionth of a femtosecond squared.

>>9662491
>Need more monkeys than ever been seen for a longer period of time that has since happened.
Yeah.. That's why we call the amount infinite.

>>9660518
You lack understanding about the power of infinity.

>>9662419
You are baiting right?

>>9660518
It wouldn't matter anyway unless you had enough people to read all the content the monkeys produce.

"If a monkey randomly types a Shakespear play in a room and nobody is there to read it, does it ever randomly type a Shakespear play?"

>>9662419
>Do you fail to understand there's also the possibility they will type jibberish until the end of time?
no, the chance of that is 0, eventually theyll do it

>>9662399
>And many, many more maths rely on infinities.
No, they rely on unbounded limits, not an infinite number of things.

>it ultimately doesn't matter that it's MONKEYS not a random number generator
You can't expect to form a coherent thesis that relies on acquiring an infinite amount of random number generators either.

>>9663328
This is not necassarily true.

>>9664037
Infinities are unbounded limits, and these lead directly to an infinite number of things, thus.. (I assume you can take it from here).

>coherent thesis
Many would beg to differ, though I personally agree with you. Do you think there is also a possibility that given an infinite amount of RNG (random number generators) that they could indefinitely not produce Shakespear?

>>9660518
You will love "The Lego Box Racing Car" Theorem then. It goes like this.

"Given sufficient attempted shakes of a box filled with legos, each shake lasting around 10 seconds each with consistant intensity, will cause the chaotic system to eventually yield reckogniseable shapes, up to and including a tiny fully formed race car."

The object of this is to form parallels between the formation of complex molecules and the formation of our universe through such chaotic means as an explosion in a vacuum. AKA The Big Bang.

>>9660518
In a analog range the sections of a curve can be split infinitely. Since the chimp operates analog bases this means its errors can be infinite with infinite attempts leaving a false possibility.

>>9664847
In this system, there is a 100% chance the monkeys will produce an infinitely long sequence of nothing but the letter "a". However, this doesn't mean only the letter "a" will be produced. There will also be an infinitely long sequence of nothing but the letter "b" (and an infinite amount of said sequence). An infinite amount of monkeys will produce nothing but gibberish for an infinite period of time. However, there will still be an infinite amount of monkeys that do produce meaningful sentences, and an infinite amount of monkeys will do so without a single typo. An infinite amount of typewriters will break before they can produce even a single letter, but there will still be an infinite amount of typewriters that will work. An infinite amount of monkeys will die from heart attacks as soon as they start typing, but there will still be an infinite amount of monkeys to do the typing.

you stupid motherfucker

>>9664946
See I think this is bullshit too, despite understanding it.


>>9665309
Your just restating the hypothesis, the point is that I don’t believe any of it.

>>9665315
Tell me why

>>9660518
Shut up brainlet.

>>9665598
>Thinking your and you're are interchangeable.
No wonder you can't accept the theorem, I can barely believe you're capable of tying your shoes.

>>9665309
>In this system, there is a 100% chance the monkeys will produce an infinitely long sequence of nothing but the letter "a".
Wrong. The chance of that occurring is almost zero.

>>9660518
Infinite time + non zero probability = it will happen

Why is so hard to understand?

>>9667308
Couldn’t it also not happen for an infinite amount of time? I mean honestly, I don’t see how you could deny that’s a possibility.

>>9667315
You confuse infinity with very long time, is not, its literally infinite

>>9667308
It will almost certainly happen you mean.

>>9667300
so by saying the chance is "almost zero" you're agreeing that it's 100% chance that it would.

>>9667315
>Couldn’t it also not happen for an infinite amount of time?
You are correct! The only way to ensure that a shakespeare play would be written is to have certain restrictions on the experiment. You'd have to say that the monkey plays are finite in length, and that no monkey novel repeats. This would force every combination to exist given infinite time, and one of those combinations would be a shakespeare play.

But if the monkey typings are not given any boundaries, then they could type for an infinite amount of time and never re-produce a play. Some infinites are bigger than others.

>>9660518
Might help to think of it in another way...

If you had a truly random number generator, rolling 0-9, and had it generating strings of numbers for an infinite amount of time (keep in mind it doesn't matter how quickly it generates them, since it has infinite time), would it eventually generate a string of numbers that consecutively contained every single social security number in the US? Every number in the 1987 New York White Pages? etc. etc.

Monkeys and Shakespeare just adds a emotional judgement connotation that might make the simple fact harder to see. ...and I suppose, as monkeys aren't truly random, might even add a flaw to the analogy. It maybe monkeys are prone to hitting a certain set of keys, and never hit certain combinations, thus yes, you'd never get Shakespeare's plays, regardless of time... But the idea is if you generate truly random strings of letters, similar to the example above, eventually you'll get Shakespeare's plays.

Mind, don't ask how you make anything "truly random".

>>9660524
rarely do you see a thread so completely and utterly finished in the first post

>>9667329
this. if something doesn't happen over an infinite time period, it never happens. that means its chance of happening is exactly 0 %.

>>9660524
But where's the P = NP proof?

[math]S E R I O U S - Q U E S T I O N[/math]
Building upon the monkey theorem, given an added supposition that the universe is infinite, is it reasonable to conclude that all probable events at a given moment are simultaneously and continuously occurring an infinite number of times?

>>9668897
>simultaneously
Yes.
>continuously
No.
>infinite number of times
Yes.

>>9662491
Ya but tree(3) monkeys for tree(3) years is probably enough even if they only type one character per year. Afterall, the difference between a plank second and a year is only a handful of orders of magnitude and basically 0 compared to tree(3).

>>9668897
Problem is the matter in the universe is finite, only has a limited time to interact, and a limited time to remain energetic, so no. Even if the matter in the universe were somehow infinite, it'd still be no, since space is expanding, eventually each chunk of matter effectively becomes its own universe, unable to interact with any other. For instance, in so many trillion years, from our perspective, the entire universe is going to consist of a single large galaxy made up of a merging of this galactic cluster. We will no longer be able to see nor interact with any other galaxy, thus there's a finite amount of matter to work with, which is all running down and falling into holes, as most stars don't recycle.

But I suppose, if you had infinite matter, you'd at least get every combination possible repeated an infinite number of times, and all at the same time, but if we had infinite matter, the CMB would look very different, and we probably wouldn't be able to observe it.

It only works in a fictional scenario of infinite time, immortal monkeys, and indestructible typewriters. Generally, anything with the term "infinite" in it is a thought experiment with only indirect applications in reality.

>>9662419
>They won't though, not necessarily at least. Do you fail to understand there's also the possibility they will type jibberish until the end of time?
>end of time
>infinite
You clearly do not understand the proposal.

If you have infinite time, not only will they do it, they will do it an infinite number of times - even if the type one letter every 100 trillion years.

That's assuming they are truly random, and immortal, etc.

>>9660524
You do know that this website doesn't actually contain all of those words, all it is just a map from a address to words. ie just a compression algorithm

>>9660526
You are correct for a finite domain. OP is talking about an infinite amount of time

>>9660526
>you have no way of saying it WILL happen
with finitely many trials. With infinitely many trials you do

>>9668791
Thank you, this I cannot deny. But others still assert that I’m simply not understanding ‘infinity’, but I dont think they’re even trying to understand my point.

>>9667329
>you confuse infinite
No, I don’t.. I believe the monkeys are much more likely to produce identical copies of jibberish for all eternity than they are Shakespear’s plays.

>>9667308
Demonstrably wrong as agreed upon by the mathematical and logical community, hence the term ‘almost surely’.

>>9660518
>I think the monkeys would always, forever, only pound out jiberish like “haiendid dkdicnsnwdjdidicjdnsiwuebd dndnd”.
if there is no time limit anything with a probability of happening will happen "given enough time", no matter how little the chance is. I guess there is a chance that it could go on forever and ever and ever and some more without happening but I assume it's really small
it could work with a single immortal monkey too, you'd just have to wait a lot most likely. or maybe you're lucky and it happens within a day

so it boils down to is time infinite or not?
I feel like these things are pointless to discuss, it's kinda fun to think about for a few seconds though

>>9669290
The chance of producing "aa aa aa aaa aa aa" is the exact same as the chance of producing "to be or not to be".

>>9668827
It doesn’t matter if the monkeys aren’t too truly random. The fact they aren’t truly random only amplifies the strength of the assertion and makes the primary theme the Obvious focal point: if there IS a chance, as in the probability over an infinite period of time is nonzero, then it WILL happen. Since it is possible for monkeys to do this (supposedly, going beyond that and debating if it’s possible does break the example), then, given infinite monkeys and time it WILL happen.

It’s harder to imagine monkeys doing it than RNGs, but to me this strengthens the expiriment. However, I don’t think that given infinite RNGs and time that they will certainly eventually produce all SSNs (or any other list of n length), I think they can go on infinitely without producing them too.

Actually this brings up a somewhat coherent counter arguement by flipping the hypothesis on itself: since each monkey has a distinct chance of not typing Shakespear, why is not possible that given infinite monkeys and time that each will NOT type Shakespear? Sort of like inducting from 1 monkey to n+1 monkeys.

>>9669182
>>9669182
End of time was a poor choice of words, but I can assure do understand the hypothesis completely, I just don’t believe it. And you’re not nexassarily right either, hence the existence of the term ‘almost surely’

>>9669251
Then induct on the domain size.... lol tard

>>9669253
This is what I’m disagreeing with obviously

>>9669298
It’s quite literally not, using empirical evidence you can statistically disprove this.

>>9669298
This is true only for a truly random number generator, which we are not talking about here, retard. We are talking about monkeys, which coincidentally favored hitting repeated ‘a’s

>>9669302
Well, no, it has to be truly random, or at least fairly random. If the monkeys only ever swipe up and down the keyboard rows, there's no possibility that the combination will ever occur.

But yeah, so long as it's random enough that the possibility exists, it's a certainty, given *infinite* time.

>>9669309
>I just don’t believe it
Well, okay, but why?

>>9669737
Do we agree that a physical, real life monkey has a nonzero possibility chance of typing Shakespear given infinite time and mortality (and whatever else I may be forgetting, beyond human knowledge of language and typing ability)? Because if the chance is nonzero, then my point still stands.

>>9669740
Well, why can’t it just not happen? This is what I believe. And apparently so do others, hence the term ‘almost surely’, which indicates the chance of it happening - given infinite time, monkeys and typewriters - is less than 100%. If we can’t say it will certainly happen, there’s a chance it won’t.

In a similar respect, though I don’t know where I stand on this, given infinite pennies, penny flippers and time, I don’t know if I believe that it’s possible that at least one (possibly an infinite amount) of the penny flippers will get heads an infinite amount of times. I feel there has to be some sort of regression to the mean, in which case one will always get tails eventually, and likewise a monkey will always make an error before typing Shakespear verbatim.

>>9669854
Please excuse this excess of typos, many of which are not misspellings or grammatical errors but poorly structured and non sensical sentences that I forgot to edit. I hope you get the big ideas.

>>9660675

Some doofus just released a real rng using quantum bits

>>9669854
>Because if the chance is nonzero
That's the "if" here. Again, if all your monkeys do is swipe rows, and never do anything else, then ya get nothing but "asdfghjkl" forever. (Ow, my finger.) So the scenario requires a certain degree of randomness from your monkeys.

>>9669854
>Well, why can’t it just not happen?
Well, no, not if you have infinite time. It will, eventually, inevitably, happen. Provided the string of characters is random, they'll similarly type out the Bible and everything else that mankind has ever written, and ever will write, and do it all an infinite number of times. There's no chance of an endless totally random string of characters not containing all of those. (In addition to an never ending string of garbage, of course.)

The fact that it's an *infinite* random string removes any almost surely. It's an absolute certainty.

>>9669871
Even QM is pseudorandom, just fundamentally unpredictable from our perspective. More than random enough, given infinite time though.

100% probability does not mean that something will happen if infinites are involved, you stupid brainlets.

>>9670047
If there is any probability something will happen within a period of time, there is a 100% probability that it will happen with infinite time, and if it's something that can be repeated, it will happen an infinite number of times.

>>9670089
A 100% probability that something will happen with infinite time does not mean that it will happen even once.

>>9670117
I coulda come up with a counterexample for that, but now you're just trolling.

Suffice to say, if you have an infinitely long string of truly random characters, it will contain everything ever written and infinite number of times. Well, provided it's written in the alphabet so used (though I suppose it'd also contain translations of all other written works, and speech).

>>9670122
>I coulda come up with a counterexample for that, but now you're just trolling.
Typical brainlet, thinks that an instance of 'a and b is true' disproves 'a does not imply b'.
>Suffice to say, if you have an infinitely long string of truly random characters, it will contain everything ever written and infinite number of times. Well, provided it's written in the alphabet so used (though I suppose it'd also contain translations of all other written works, and speech).
Not the same.

>>9670128
How is it not the same?

If you have an immortal set of monkeys producing truly random letters for an infinite time, what's the inevitable result?

An infinitely long string of truly random characters.

So, if you admit that you would find all the written works that ever were or ever will be an infinite number of times in such a string... Does not that mean that the monkeys in this scenario, who produce the same sort of string, will inevitably do the job?

What is it with brainlets and the infinite monkeys thing?
My dad is a fucking brainlet and he is always getting angry about the monkeys on typewriters. It just seems to really confuse him. He once posted a letter to fucking Cambridge University with a list of questions about it including:

1. Why are they using typewriters and not keyboards?
2. Isn't there also a certainty that the building is of infinite size, and therefore there are infinite fire hazards, so the building will burn down and destroy the monkeys work?
3. In the Universe with infinite monkeys would there also be infinite Shakespeares, meaning that the monkeys would have to type the works of Shakespeare the original then type the works of ALL the other Infinite shakespeares, which is impossible?
4. Do they know how to touch type?

They never responded but it was very embarrassing as I studied at the University and had connections there.
I tried answering his brainlet tier inqueries but he had no interest.

>>9670329
Top kek

>>9660584
The halting problem is about deterministic machines, not stochastic ones, and it has nothing do with (in)finite monkeys on typewriters

>>9670329
Sounds like your dad would fit right in here