/lit/ - Literature

[Anonymous No.17294349]

So what is the answer to the monkey typewriter question?

[Anonymous No.17294371]

Well so far the media is mostly in the hands of monkeys and they haven't written anything coherent so if it is true it's an asymptotic thing.

[Anonymous No.17294405]

>>17294349
If there’s an infinite amount of time and an infinite amount of possibilities they will write literally anything and everything else before they could possibly get to writing Shakespeare

[Anonymous No.17294413]

>>17294349
>So what is the answer to the monkey typewriter question?
Space and time aren't unlimited, so there can't be an infinite amount of Monkeys, but thats not a real answer since Monkey Typewriter isnt a problem that needs to be solved

[Anonymous No.17294416]

>>17294349
An infinite number of monkeys on and infinite number of typewriters with an infinite amount of time would write the word "nigger" an infinite number of times.

[Anonymous No.17294417]

Serious question: what does it matter what a theoretical bunch of monkeys would or would not do with an infinite amount of time? Aren't there real problems to solve which are more important?

[Anonymous No.17294423]

[Anonymous No.17294427]

>>17294416
Based. Embrace monke.

[Anonymous No.17294429]

The answer is right here.

[Anonymous No.17294436]

>>17294416
you just described 4channel retard

[Anonymous No.17294488]

>>17294436

[Anonymous No.17295658]

>>17294417
Aren't there more important things you should be doing instead of posting on an imageboard?

[Anonymous No.17295760]

>>17294436
And?

[Anonymous No.17295772]

>>17294371
Good post

[Anonymous No.17295780]

>>17294436

[Anonymous No.17295868]

>>17294349
All of the monkeys could literally spend eternity punching the "A" key.
Shakespeare remains unwritten, Theory refuted.

[Anonymous No.17295906]

>>17294349
if the number of monkeys was infinite then Shakespeare would be written instantly (as well as every thing else)

[Anonymous No.17295937]

>>17295868
Retard

[Anonymous No.17296719]

>>17295937
He's actually right, even if it's really unintuitive. Imagine that you're flipping a coin an infinite amount of times and you record each flip as a "0" for tails and a "1" for heads. An example of the output being something like: 101000010110111001010110100011... and so on unto infinity. That is to say, the outcome of this infinite coin flipping experiment would be an infinite set comprised of zeros and ones. Now imagine the (inclusive) number line of real numbers from zero to one, in binary form. The reals are uncountable, and are informally depicted below:

[00000000...00000000]
[00000000...00000001]
[00000000...00000011]
...
[11111111...11111100]
[11111111...11111110]
[11111111...11111111]

So this infinite amount of sets represents the infinite amount of outcomes we could get from our infinite coin flipping experiment. Rather than actually flipping coins, we can instead throw a random dart (with infinitesimally small tip and other impossible properties) at the above described [0,1] binary number line, and get a result. The resultant set will not necessarily contain an infinite amount of zeros and ones. In fact, it may contain no zeros or no ones. Example results are shown below:

[01010101...01010101]
[10000000...00000000]
[11111111...11111111]
[01110110...00001110]
And so on...

Now rather than the two sided coin, let's imagine a 30 sided die: with 26 sides for letters, one side for comma symbol, one side for colon symbol, and one side for period symbol. You write a story by rolling the die, and then jotting down the symbol that comes up, then rolling the die again, jotting down the resultant symbol, and so on and so forth. As you can see, this experimental set up is equivalent to the infinite typing monkey(s) with perfectly random keystrokes. And like the coin flipping experiment described above, the resultant set will not (and cannot) contain every possible set. You might get: [AAAAAAAA...AAAAAAAA]

[Anonymous No.17296740]

>>17296719
Whenever this discussion comes up my mathlet brain seems to find that it hinges on the definition of the word 'random'

[Anonymous No.17296766]

>>17296740
Rather the definition of infinity, whether infinite coin flips necessitates at least one head, and one tail

[Anonymous No.17296793]

>>17296766
>hether infinite coin flips necessitates at least one head, and one tail
Doesn't this depend on what 'randomness' function is determining the outcome of each flip?

[Anonymous No.17296842]

>>17294349
we can't assume that infinite time equals infinite results because there is just as much chance as the same sequence of events being repeated infinitely as there is the off-chance of apes writing Hamlet.

[Anonymous No.17296871]

>>17296719
But wouldn’t you also be throwing an infinite number of darts? Each monkey produces a single sequence yes but if you also have an infinite amount of producers?

[Anonymous No.17296924]

>>17296871
Not sure how it would effect the overall probability that any one dart would land on a set that contained Shakespeare's writings, but there remains a chance that each dart lands on AAAAAAAA... or BBBBBBBB... or ABABABAB... or some other gibberish.

[Anonymous No.17296951]

>>17296924
I just have a hard seeing the how if you pick an infinite amount of sequences from an infinite amount of generators none of them would contain Shakespeare. That being said I’m ass at math especially of the theoretical kind.

[Anonymous No.17296957]

>>17296924
>there remains a chance
>infinite darts
Is that really how that works?

[Anonymous No.17296967]

>>17294413
>Space and time aren't unlimited
Wrong and wrong

[Anonymous No.17296993]

>>17296951
there's such a thing in math that a probability being so low that it is virtually counted as 0. it stands to reason that the results with the highest probability of occurring will extend infinitely.

[Anonymous No.17297001]

The observer effect.

[Anonymous No.17297085]

>>17296951
Alright consider what factors play into the most common results into occurring (in this case the monkeys lacking the necessary faculties to formulate elaborate strings of words and prose), now consider what kind of insane flux or outlier would cause it to shift so drastically towards a very specific direction (i.e. Monkeys writing Shakespeare). Yet in this scenario, no real change within the monkeys occur, they simply keep typing for the rest of time until they happen upon it.

[Anonymous No.17297322]

>>17296719
No, he's not

The chance of the monkey not writing the complete works of shakespeare is 0%

[Anonymous No.17297326]

>>17297322
>The chance of the monkey not writing the complete works of shakespeare is 0%
Source: Your asshole.

[Anonymous No.17297370]

anything is possible given the infinite, even reincarnation

[Anonymous No.17297462]

If you flip a coin an infinite amount of times, is there a possibility it will be heads every time?

[Anonymous No.17297593]

>>17296993
Refer back to the coin flipping example. The probability that a given set contains at least one heads is 100%, but the set which contains no heads, i.e. [00000000...00000000], still exists. The probability that this set is achieved is zero, but it is still possible for the set to be achieved.

P(set contains no heads) =
P(set contains all tails) =
lim x->inf (1/(2^x)) = 0, where x is the number of coin flips in a set

The probability of not getting a head is zero, but there still exists a chance, an infinitesimally small chance, of getting no heads and all tails in a set.

Now apply this same line of thinking to the infinite immortal monkeys. Instead of heads and tails, lets use yes (represented by "Y") and no (represented by "N"). When a given monkey succeeds in reproducing Shakespeare, we'll mark down "Y". And when a given monkey doesn't succeed in reproducing Shakespeare, we'll mark down "N". The resultant sets from all of the immortal, random monkeys will be of the form:

[NNNNNNNN...NNNNNNNN]
[NNNNNNNN...NNNNNNNY]
[NNNNNNNN...NNNNNNYY]
...
[YYYYYYYY...YYYYYYNN]
[YYYYYYYY...YYYYYYYN]
[YYYYYYYY...YYYYYYYY]

The set [NNNNNNNN...NNNNNNNN] exists, therefore it is possible that all of the immortal, random monkeys never reproduce Shakespeare's work.

But you might say:
>that's false, it is impossible for a given monkey to not reproduce Shakespeare's work, therefore the only possible outcome for all the monkeys is [YYYYYYYY...YYYYYYYY] and it is therefore necessarily impossible that Shakespeares work is not reproduced.

To this I say, refer back to the 30 sided die example above, and you'll see that it is always possible (and perhaps overwhelmingly likely, I don't know the math) that a given monkey does not reproduce Shakespeare's work.

[Anonymous No.17297668]

>>17294349
A monkey randomly using a typewriter would be unable to reach certain letter sequences as it would require intent and understanding of what is being written. They are not creating random text, they are physically interacting with a typewriter which has a very specific layout and functionality - not to mention dexterity limitations of a monkey.

Actual point was random text generation, monkey produced text is not random.

[Anonymous No.17298176]

>>17297326
It's basic statistics retard

[Anonymous No.17298192]

>>17297326
The monkey types infinitely. There are a finite number of letters and punctuation marks, but infinite text. Everything that has ever been written is there, but also everything that could ever be written. Your own doofus comment is in the monkey's cage somewhere.

A better treatment of this question is in Borges's short story "The Library of Babel."

[Anonymous No.17298223]

>>17296719
Your explanation is wrong. It's more akin to the infinite decimal expansion of pi, which does in fact contain every other integer sequence somewhere along it. The monkey-typewriter test is about randomness, not probability.

[Anonymous No.17298239]

Uhh mathbros...?

[Anonymous No.17298706]

>>17298223
>the infinite decimal expansion of pi, which does in fact contain every other integer sequence somewhere along it.
proofs?

[Anonymous No.17299012]

>>17296719
did you actually write all of this to explain that it's possible for the monkeys to just press the A key?

[Anonymous No.17299026]

>>17298192
>There are a finite number of letters and punctuation war, but infinite text. Everything that has ever been written is there
That's not true. First, the infinite text could have repetitions -- there's nothing prohibiting that. Second, even with infinite text, that doesn't imply all possibly strings will be in there. For instance, the monkeys could just type using A and B alternating in the pattern ABABBABBBABBBBAB...B and so on. The pattern never repeats (number of Bs always growing) and nothing of value is ever written.
>A better treatment of this question is in Borges's...
If Borges has as bad of an understanding of math as you do, I'd rather not read it, thanks.

[Anonymous No.17299031]

>>17298223
this is conjectured but not proven

[Anonymous No.17299064]

>>17299026
Infinite repetitions occur almost never. All strings that ends in an infinite repetitions can be mapped to the rationals, the strings that don't can be mapped to the reals.

[Anonymous No.17299072]

>>17299064
it doesn't have to be infinite repetitions, it can just be a set of select sequences that are used. You seem very confused about math. Irrationals don't inherently contain every possible sequence.

[Anonymous No.17299094]

>>17299072
Those also happen almost never. In fact, every sequence that doesn't contain Shakespeare (or any other finite sequence) occurs almost never, assuming all keys have a nonzero probability and are independent of the last. I promise you I'm not confused, whether or not you choose to believe me.

[Anonymous No.17299105]

>>17299094
>assuming all keys have a nonzero probability and are independent of the last
based retard, this is the exact thing that's in dispute. You can't just assume that.

[Anonymous No.17299128]

>>17299105
The premise is that the monkey's typing randomly, why are you assuming otherwise?

[Anonymous No.17299146]

>>17299128
the premise is that the monkey is banging on the keyboard without knowing what it's doing. Random is not part of the premise

[Anonymous No.17299153]

>>17299128
for instance, maybe the monkeys only ever type in 10 word sentences

[Anonymous No.17299288]

Georg Cantor proved that there are infinite infinities. For example, the set of natural numbers is infinite, but so is the set of even natural numbers, which happens to be a subset of the latter, half of it to be exact. And so on for primes etc.

Then of course, there are infinite sets that are larger than even the infinite set of the naturals ℕ.

For example there are infinitely more real numbers than naturals. Consider Cantor's diagonalization proof.

suppose you have a two sets of numbers, one a natural and one a real, that are paired one to one

1 ----> 0.1874...
2 ----> 0.1875...
3 ----> 0.1877...
4 ----> 0.1878...
Now suppose for every value in this paired set, you increment the value +1 in the the place that its natural number corresponds to. For example:

1 ----> 0.2876...
2 ----> 0.1977...
3 ----> 0.1888...
4 ----> 0.1879...

The number you would get is .2989... which is never mapped to a natural.

Suppose now an analogy where each natural number is a monkey, and each real number decimal expansion, which can be infinite in its own right, is them typing on the keyboard. The problem breaks down because we are no longer dealing with real numbers but the finite alphabet of 26 letters. If you try again to map it...

1 ----> ABCD
2 ----> BCDE
3 ----> CDEF
4 ----> DEFG

And so on, you would still have the same property of the cantor diagonalization. This becomes evident if you substitute each letter of the alphabet for its ordinality, e.g. A is 1, B is 2, etc. And you substituted each one for the next in line as in the first example. Three would in other words be combinations of letters that the monkeys don't type.
If that is the case, it is at least possible that the set of letters comprising the complete work of shakespeare is not typed by any of the monkeys, but it would be included in the diagonal product of the they compose. Because This larger infinity compensates for the limitations of any smaller infinity

QED

Screen cap this, I solved it.

[Anonymous No.17299293]

>>17297322
ANY specific outcome has a 0% chance of occurring when the outcome has infinitely many steps, yet one will occur. It's the same as saying that you're 100% likely to get Shakespeare, that's true but it's still possible not to and there are infinitely many outcomes that don't have it.

[Anonymous No.17299304]

>infinity
>random
spooks

[Anonymous No.17299308]

>>17299288
Why are you assuming that monkeys typing corresponds to mathematical processes at all?

[Anonymous No.17299337]

>>17294349
It's not true that monkeys typing forever would eventually reproduce shakespeare, just like it's not true that the series of integers forever will eventually produce a repeat.
Just because there is an infinite series does not imply anything whatsoever about loops.
This error got Nietzsche too, btw.

[Anonymous No.17299382]

>>17299337
>This error got Nietzsche too, btw.
This in reference to his attempt at justifying eternal return, yes? I always thought it was so bizarre that he even tried to justify something that is only really needed as a way of thinking about or viewing life. Was it in Will to Power that this comes up, because that could explain it since he may have just written it down in his notes with no intention to ever do anything with the idea.

[Anonymous No.17299410]

>>17298223
Brainlet, that conjecture hinges on the fact that pi is irrational, which means it not only doesn't terminate but it also doesn't end with a repeating sequence. There's nothing inherent to an infinite group of monkeys that prevents them from all typing the same repeating sequence.

[Anonymous No.17299440]

>>17294349
>>17294371
>>17294405
>>17294413
>>17294416
>>17294417
>>17294423
>>17294427
>>17294429
>>17294436
>>17294488
>>17295658
>>17295760
>>17295772
>>17295780
>>17295868
>>17295906
>>17295937
>>17295937
>>17296719
>>17296740
>>17296766
>>17296793
>>17296842
>>17296871
>>17296924
>>17296951
>>17296957
>>17296967
>>17296993
>>17297001
>>17297085
>>17297322
>>17297326
>>17297462
>>17297593
>>17297668
>>17298176
>>17298192
>>17298223
>>17298239
>>17298706
>>17299012
>>17299026
>>17299031
>>17299064
>>17299072
>>17299094
>>17299105
>>17299128
>>17299146
>>17299153
>>17299288
>>17299293
>>17299304
>>17299308
>>17299337
>>17299382
>>17299410

Everyone in this thread is literally as retarded as a monkey and you niggers have been talking about it for what seems like eternity. So yeah, i haven't seen any Shakespeare yet in this thread

[Anonymous No.17299445]

>>17299410
does it not also hinge on pi's digits having a normal distribution? I don't know the conjecture but I doesn't seem right that being irrational would be enough to claim that

[Anonymous No.17299922]

>>17298176
statistics also says any of us should just randomly blow up at any moment but it doesn't so shove your "statistics" up your fat nigger ass.

[Anonymous No.17300541]

>>17294349
I've written about this before in my first book, which was named after the whole monkey typewriter thing. Most of the book isn't great, but I'm still glad I finished it.
Here's a section from the monkey business chapter that explains what I think of the typewriter silliness:
>Let’s ignore whether one monkey in this scenario could or could not write such a large amount and focus on why I’m even bringing this up in the first place. Usually I go over the first part in my head, debating whether it’s true. Imagine a room that spans infinitely (ha ha it’s very hard) with all these monkeys bashing away on the typewriters. Shakespeare isn’t what pops into my mind. What I think of is what constitutes art and the nature of infinite possibilities. Let’s pretend that each monkey wouldn’t know about the existence of any other monkey taking up the same space to make everything simpler. This cuts out chimp on chimp timelines, as silly as that sounds. We have all of these chimps, all of these typewriters and it’s implied some form of paper for these apes to produce the complete works of Shakespeare. They are now able to be in a state of either writing or not writing. Even with this simplified infinity of all simian possibilities, why should you care about whether one creates art that you could already read? A monkey writing all of Shakespeare is impressive, at least in reality, but in infinity, there’s plenty more absurd existences that surpass a copy and paste job. I’ll start simple with my theoretical possibilities and I’ll ramp them up over time, but before that, I’ll add some clarifications on each monkey’s condition.