/sci/ - Science & Math

>>7168852
I agree with you, apparently its true . To mathematicians type people we would sound ignorant, but I just don't think it would happen

>>7168852
"It will almost surely happen" =/= "it will happen"

The probability of picking an irrational number from the unit interval is 1 too (uniform distro), doesn't mean you will pick an irrational number.

>>7168852

Because typing a shakespeare play by accident has a probability that is not zero. It's not IMPOSSIBLE.

So, let that probability be x, where x is very very very very small but still greater than 0.

The probability that a given monkey will NOT type a shakepeare play is then 1-x.

The probability that N monkeys will not type a shakespeare play is (1-x)^N.

As N gets larger, (1-x)^N gets smaller. In fact, you can make (1-x)^N as close to zero as you want, just by making N larger and larger. And if N is infinite, then (1-x)^N (which you will remember, is the probability that none of them type out a shakespeare play) becomes zero.

>>7168858
>"It will almost surely happen" =/= "it will happen"

Mathematically true, but practically false. Something with P=1 will happen.

>>7168852
there are only (number of characters in a shakespeare play) factorial permutations to go through

this is very large but it's not infinite

in fact, if it truly were an "infinite monkeys in an infinite universe" situation, it would happen instantly, or at least after enough time has passed to type out each character.

>>7168865
>Something with P=1 will happen.
Wrong, you will always get something with P=0 because each number has probability 0.

>>7168869
whoops my calculation is wrong but you get the idea

>>7168871

Right, but that's not describing a physical situation. That's what I meant by "mathematically true, but practically false."

>>7168861
>The probability that N monkeys will not type a shakespeare play is (1-x)^N.

how does the probability increase with more monkeys? Thats just like saying two people flipping a coin is more likely to gain heads twice than one person flipping twice, not the case when the probability is 50% each flip regardless of the number of people, it doesnt change.

>>7168884
or decrease, inverse that

Lets Zeno-ify the infinite monkeys a bit.

You have one monkey that hits a key on a type writer at a 1 second interval, but that interval halves every time it hits a key. The monkey will stop once he has typed out a Shakespeare play.

In less than two seconds, he will have created a Shakespeare play. Thanks wikipedia.

Nothing is truly random. Things do appear random though, because to actually calculate all of the variables to make an accurate prediction is far beyond human ability.


Also, stupid question. Impossible to test

>>7168888
>>7168884
So i guess just substitute N for the number of attempts is what you're saying.

On paper it might work but surely on an infinite time span the monkey could just continuously write out anything other than shakespeare regardless of number of attempts throughout time

>>7168899
I have seen the future before though, which wouldn't be possible if things weren't random. I wouldn't be able to collapse the future wavefunction.

>>7168900
no actually the number of attempts wouldn't change probability either, seeing as the monkey has no knowledge to block past attempts and could just smash the same combination of keys again in the future. Fuck knows

>>7168900
>but surely on an infinite time span the monkey could just continuously write out anything other than shakespeare regardless of number of attempts throughout time

The probability of that is zero.

>>7168852
infinity is a hard concept to grasp for our limited brains.

take a random generator randomly generating numbers and letters, in infinite time you'll have, among lots of crap, a readable shakespeare play.

Infinity is a very strange concept with very strange consequences, OP. There is a good reason for infinity not having any physical meaning. By analogy to the infinite monkey conjecture, pi contains infinite information. A portion of it's digits will be an exact transcript of everything everyone who has ever lived will have ever done or will do. Food for thought.

>>7168910
How though when it could just carry on writing lots of crap throught the infinite timespan never reaching anything shakespear like?

>>7168907
Can you explain how adding more monkeys would make it less likely that they didn't type shakespeare than one doing it repeatedly ? i.e N in the equation

>>7168919
because the chance for it is not 0 which mens that in an infinite time period it will happen.

in infinite time the random generator will write you shakespear, the bible, das kapital, harry potter and every other book which has ever existed, could have existed or will exist.

>>7168916
just had a braingasm, thanks

>>7168923
or how repeated attempts makes it any less likely that a monkey didn't type a shakespeare play? that equation seems flawed, why would this lower the probability? It would make sense if the previous attempt was then placed on a blacklist and the monkey couldnt do that combination again, but it could

>>7168926
>because the chance for it is not 0 which means that in an infinite time period it will happen.

I cant grasp this please explain it, why does it mean it will happen? why couldnt it just carry on not happening forever?

>>7168941
>why couldnt it just carry on not happening forever?

It can in the sense that it is "possible," but it won't in the sense that the probability of it is zero.

In the same way and for the same reason, if you a flip a coin infinite times, the probability of you NEVER getting tails is zero.

>>7168954
>It can in the sense that it is "possible," but it won't in the sense that the probability of it is zero.
Whaaat.
Ah fuck this i'm too tired, will look it up tomorrow. Peace out nigga, have a gif

>>7168941
day 1. no Shakespeare play.
day 2. no shakespeare play.
day 57. same
day 834. same
day (largest number you can think of.) same
day (largest number you can think of to the power of the the largest number you can think of.) still no play
day (so large it makes the previous days look like 0.001 compared to the total volume of the visible universe in Planck units.
day (so large it does the same to the sum of the previous days.)
repeat ad infinium.

the numbers we're talking about are so indescribably large that it will happen. assuming the type writer cannot be destroyed and the monkeys respawn/cannot die, it will happen. look into trying to understand infinity. it's really hard to wrap your head around how big it is.

you dumb, op?

>>7168916
>>7168933

Not true. Are at least, we're not sure yet.
http://www.goodmath.org/blog/2014/05/22/infinite-and-non-repeating-does-not-mean-unstructured/

See Kittel & Kroemer problem 2.4

>>7168852
Isnt this the same as the number Pi containing everyones phonenumber?

>>7168884
you are mixing your outcomes together. the monkeys work independently, in your example its like the monkeys are working on the same typewriter.

>>7168852
it already has happened, we have a copy of those plays written by a "monkey" named will.

>>7168916
>>7168916
Did you think we wouldn't notice your pi troll if you threw in some good information at the beginning of your post?

>>7168852

If this is true, won't all of my physical brain matter be reformed once more and therefore my conscious as well, transporting me to a new life immediately after my death in this one?

>>7168883
That's a meaningless distinction in the context of this thread.

>>7168855
The point is that time is experienced in bounded intervals, and the law of large numbers only applies to a probability distribution in the limit.

>>7169058
>That's a meaningless distinction in the context of this thread.

Not at all. Monkeys and typewriters are a physical situation. "Choosing a real number at random" is not.

>>7168852
You can derive it with a little thought.

Probability of a string of k digits to appear in a string of N≥k digits in base b is
<span class="math"> 1 - \displaystyle \left( \frac{b^k -1}{b^k} \right )^{N-k+1}[/spoiler].
The limit of this as N approaches infinity is 1, regardless of b and k.

If there were infinite monkeys wouldn't every work of art ever be created instantly?

>>7169107
Yes.

>>7169107
no, because monkeys don't think like us.

>>7169154
Leave /sci/ forever

>>7169107
But wait, if there were already infinite monkeys then there wouldn't be space for anything else.

>>7169157
I've been here longer than you've been in this world.

The concept you are looking for OP
http://en.wikipedia.org/wiki/Almost_surely

The infinite monkeys would have typed the play as fast as the monkeys are capable of typing that amount of material. There are infinite of them, after all, thus it is certain that the play will have been typed as soon as the time it takes to type it has passed, and it will have been typed infinite times. Do you people not understand infinity?

>>7169879
I'm not even sure why this is still being discussed, honestly.

>monkeys are gay and retarded, which means they type randomly
>which means no pattern
>which means over an infinite amount of time, they will repeat all patterns
>then assfuck each other cause there gay

>>7169923
Bitch please. *their

monkey taps away on the same key into infinity ... fails to even write a Tom clAncy novel

infinity doesn't imply unlimited variation

What is the chance one monkey can type a Shakespeare play? ZERO

Just because you have an infinite amount of monkeys doesn't mean the chance is now suddenly 100%.

"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)

>>7168852
Consider a type writer with only 5 keys: A, C, H, N and 4. If a monkey starts hitting random keys he will eventually write “4CHAN”. Probably within a few minutes.

Now consider a normal type writer and give the monkey years and years and eons of time to hit random keys. Eventually he will write a Shakespeare play.

It’s just basis probability.

>>7170214
*basic*

why do you assume the keystrokes would be random? what does random even mean in this context?

>>7168852
http://en.wikipedia.org/wiki/Almost_surely

>>7168852

Think of it in basic probability. The odds of typing any given character is 1 in (number of total available characters), the odds of typing two successive characters is 1 in (number of total available characters)^2. The odds of typing out a Shakespeare play randomly is 1 in (number of total characters)^(number of characters in the Shakespeare play)

Given a process of typing out random successive characters, and infinite time you'll surely eventually type it out, despite how unimaginably small the odds are.

>>7170385
>why do you assume the keystrokes would be random? what does random even mean in this context?

The only necessary assumption is that the probability that a monkey will type the first letter correctly is not zero.

>>7170090
>infinity doesn't imply unlimited variation

It DOES imply all possible outcomes. Are you saying it is physically impossible to type out a play?

>>7170090
But the premise is, that the monkeys tap random keys. Sure, if I throw 6 sided dice an infinite amount of times, I'll never get a 7, but that's not what we're talking about.

>>7170477
(Not that anon, but...)
Though there is infinite time, there are also infinite variations on what each monkey could type.

If the universe is infinite, then there are infinite planets. Does that mean then that there is a planet out there entirely full of Mandarin-speaking, hopping Danny DeVito's?

Well, we know that nature has created at least one Danny DeVito, and it's reasonable to assume he can hop, and that he is capable of learning Mandarin, so why wouldn't randomness and infinity allow for an entire planet full of them if there are an infinite number of planets? Because it's a horribly flawed premise.

The premise for the infinite monkeys illustration seems equally flawed, as it doesn't take into account reality.

>>7169081
Yep, infinitely many monkeys and typewriters is a real thing. God I fucking hate amateur mathematicians.

>>7168971
If all it takes is that the chance for the outcome to occur has to be greater than zero, plus infinite time, then you could say this scenario could also happen:
>Could infinite number of single-celled organisms with typewriters write out a Shakespeare play, given infinite time?

The answer is also yes, because there is a chance some of those organisms could evolve into larger creatures that could eventually grow limbs that would allow them to operate a typewriter.

However, the question seems more palatable when posed as a random text generator and infinite time, rather than infinite monkeys/infinite time.

>>7170549

I can't tell if you're trolling or retarded.

>>7170535
>The premise for the infinite monkeys illustration seems equally flawed, as it doesn't take into account reality.
The premise includes the assumption that they type randomly. Obviously if they all only hit a single key then none of them will write shakespeare

>>7170535
>If the universe is infinite, then there are infinite planets. Does that mean then that there is a planet out there entirely full of Mandarin-speaking, hopping Danny DeVito's?

If there is a way that could occur, then yes. If there isn't, then no.

Certainly there is a way a monkey could type a play - he just has to push some buttons.

>>7170612
>he just has to push some buttons.

But no one has ever seen a monkey randomly type a play, there's no evidence for it being possible.

>>7168852
>"Whatever can happen will happen"
keyword CAN. We don't know what all the possibilities are so we really can't say that the monkeys will produce Shakespeare or not.

>>7170620
Arguing like that, you could say that nothing that hasn't actually ever happened is absolutely possible to happen.

The probability of picking a specific random number on the real line is 0.

If I pick an infinite amount of real number, the probability of picking a specific real number is still 0.

Checkmate monkeys

>>7168858
>The probability of picking an irrational number from the unit interval is 1 too (uniform distro), doesn't mean you will pick an irrational number.
Yes it does, if you pick randomly. If you throw a dart (an imaginary dart with an infinitely sharp point, etc...) at a number line on a wall, the chances that you will hit exactly 0.5 or 0.123 or any rational number are exactly zero.

infinity means if something is possible it will eventually happens whatever it is.

>>7170639
no

1/x will never reach 0, ever.

>>7170640
that's because it's impossible in the first place, mate

>>7168852
Look at the digits of pi. Your phone number is in there. You social security number is in there. Your phone number multiplied by your social security number is in there. Every Shakespeare play compressed into a .ZIP file is in there.

>>7170651
Pop sci please, that's not true

>>7170651
*maybe

>>7170654
It's probably true.

>>7170654
It's trivially provable. Find your phone number in pi. Find your social security number. You won't even need special software to do it. Your 9-digit SS number will probably be found in the first 10^9 digits (1 billion). Your phone 10-digit number will probably be found in the first 10^10 digits (10 billion). And so on.

>>7170654
Why isn't it true?

>>7170663
lol no

>>7170668
lol yes. It's almost certain that pi is normal.

>>7170668
What's he wrong about?

>>7170620
>But no one has ever seen a monkey randomly type a play

But they have seen a monkey push a button, and that's all that is necessary.

>>7170671
In the trivially provable part.

>>7170654
>>7170668
Yeah I know what your implying, that maybe pi isn't normal. But it is. And even if it weren't, the choose some other irrational number that is. OP's question wasn't about pi. It was about randomness eventually producing a string of text. So pick your favorite random number generator and go away.

>>7168910
with space characters as well, including tabs and indentations. eventually it will write out.

>>7169180
>he doesn't know /sci/ has only been around for about 5 yeads

>>7170632
None of Shakespeare's plays are infinitely long, nor are there infinite keys on a keyboard.

Checkmate, faggot.

>>7169030
*ape

>>7170854
chimps can do uncountably infinite things other than hit keys on a keyboard.
or they can just wait

If "whatever can happen will happen" is true, and "monkeys never type a play" is a possibility of things that can happen, it follows that in an infitine timespan monkeys will never type the play. I can tell this is wrong, but can anyone explain why? Or if this type of situation has a name in philosophy

>>7170870
>chimps can do uncountably infinite things other than hit keys on a keyboard.

Even if that were true you would still be wrong, as long as the probability that a monkey hits a key on the keyboard is greater than zero.

>>7170875
>I can tell this is wrong, but can anyone explain why?

Sure. "Anything" means any finite event. "Monkeys never type a play" describes an infinite stretch of time.

>>7169046
No because it can't happen.
>>>/b/

>>7170893
Gotcha. Gracias

>>7170884
> Even if that were true you would still be wrong, as long as the probability that a monkey hits a key on the keyboard is greater than zero.
but it's not.
It happens almost never because there's infinite things to do and only finite things that are typing.
http://en.wikipedia.org/wiki/Almost_surely

Niggers... It already happened.
>ancient aliens wondered if monkeys can write some shitty play
>lel, probability is not null.
>lets watch these apes.
>wth Neanderthal, igniting fire wont help you write a play, lel.
>omg who the hell is this Shakespeare. Wtf is he writing.
>fucking lost the bet. The probability was never the null.

You see my point, my dear friend?

>>7170913
what's the probability of choosing a number in the interval (0, 1/2) if you have to choose a number in the interval (0, 1)? is it 0 because there are infinitely many numbers outside the interval (0,1/2)?

>>7170940
more like what's the probability of choosing 1,2,3,4, or 5 in the interval of (0, 10)

Have they read shakespeare?

>>7168861
More lke 1/(number of letters in Romeo & Juliette)^26 =! 0

>>7168852
The biggest problem with this theorem is that human brains are not too good at grasping the concept of infinity.

>>7170608
Just admit that you're a complete fucking idiot and move on.

>>7168852


I often think about those monkeys. Sitting there there in an infinite Universe, banging away randomly on their typewritters.

I think about the number of times they would get all the way through "Hamlet" and then, right on the last word, make a fuck up.

I am sure it would be very frustrating to ayone waiting to watch it happen.

>>7168852
Imagine the fucking concept of infinity. Given infinite time how could it not happen?

>>7168899

"stupid question.Impossible to test"

AH HAHAHAHAHAHHA! Oh my aching sides!

Ya dont say? Impossible to test! Really? Is that a fact?

HAHAHAHAHAHAHHAHAHHAHAHAHAHA!

Oh dear! Fuck me! I havent laughed this much in a long time.

"Impossible to test."

HAHAHAHAHAHAHHAHAHAHAHAHa!

Oh my God! ! You Sir, are a gold mine!

I read this whole thread and no one brought up Dawkin's Weasel program

>>7171119

Actual last line of Hamlet:

Let four captains
Bear Hamlet, like a soldier, to the stage,
For he was likely, had he been put on, 53 340
To have prov’d most royally; and, for his passage, 54
The soldiers’ music and the rites of war
Speak loudly for him.
Take up the bodies. Such a sight as this 344
Becomes the field, but here shows much amiss.
Go, bid the soldiers shoot. Exeunt marching, [bearing off the dead bodies;] after which a peal of ordnance are shot off.

Now for our monkey filled Infinite Universe.

{Insert an insane amount of time}

One monkey finally gets to the last bit, having written Hamlet perfectly up until this point....

Go, bid the soldiers shoot. Exeunt marching, [bearing off the dead bodies;] after which a peal of ordnance are shot orf.

DAMMIT! DAMMIT! DAMMIT! DAMMIT! DAMMIIT!

>>7171130
>responding seriously to bait

a random letter generator spits out a letter ever second for infinity

it is possible to imagine that this machine will generate a pattern of recurring letters (the literary equivelent of a repeating decimal)

This chances of this happening are incomprehensibly small. but still >0.

This being the case, the likelihood of the machine spelling out a shakespear play are <100%

>>7171130
>>>/b/

isn't it the same with irrational numbers like Pi?

meaning that every possible sequence of numbers is possible (as the sequence of Pi is infinitely long)

>>7172033
>>7172033
No, not necessarily

>>7171254
false, the probability of recurring sequence "till the end" is 0.

>>7168852
They would actually write an infinite number of Shakespeare plays...

>>7168919

It's probability. It's incredibly unlikely, but with an infinite amount of time it WILL eventually and inevitably happen.

Your statement is something akin to this:

"How can a die ever land on a 6? It'll just keep landing on the other numbers for the rest of time."

The only difference is the size of the probabilities.

Assumptions:
- The probability of hitting any key is uniform
- The probability of hitting any key is independent of previous key hits
- The average word is 5 characters long (can't find a character count, only a word count) - 5 is 10fastfinger's average which includes spaces between words
- We ignore that we might have to hold shift and hit a key (such as in capitalisation - not sure if this exists on typewriters)
- Our typewriter has 49 keys

The probability of our monkey typing our Romeo and Juliet, beginning at some arbitrary key-stroke, is:

(1/49)^4422105

As we have 4422105 characters to account for.

Maple won't give me an output for this as it is 1/x where x is some integer to large to display.

Further, we can infer that for our number of characters typed n, we have (n-4422105) + 1 possible chances of Romeo and Juliet being produced. Let's say our monkey hits, on average, 1 key per second. Well to get to the first attempt takes our monkey 4422105 seconds (51.18 days). From then on, it's one additional permutation per letter.

We get:

(((1/(49^4422105))*((((49^4422105)-1)/(49^4422105))^(n-1))) =0.5

If you solve for n (and then round up to the next n), then add 4422104, this is the expected number of random keystrokes you would need to make before getting Romeo and Juliet. I'm having a friend calculate this number through Maple as his computer is far faster than mine, though it might not solve within in any reasonable amount of time.

>>7172460

I found another way to work out the number which is much faster and Maple is saying that the number is too big to display. Maple is also refusing to save it to a text file. Any help?

>>7168852
not if that "whatever" has a 0% chance of happening in the first place

>>7173160
As I understand it, the premise is, that there's a chance >0 that a monkey presses a button on a typewriter. That's sufficient.

>>7168858
So what you're saying is that 0.9999999... =/= 1 ?

>>7170385
because people say "monkeys at type writers" but they don't actually mean that.

A monkey would never spend so long investigating a type writer by tapping the keys because there is no reward for it doing so.

What they actually mean by "monkey" is "random keyboard typer where every necessary character has some probability greater than 0 of getting typed"

>>7172470
If I didn't goof in copying, this is 8.6*10^14201204.

>>7173206
>>7172470
Actually, taking a second look, your expression just simplifies to 49^4422105

>>7172470
Simplifies to 49^4422105, which is 3.4*10^7474224

>>7172254

And why do you think that?

>>7168861
i have a fucking feeling that we're in a virtual reality where the masters of it just wanted to see if this shit would happen if given enough time.

The Boltzmann brains concept has been proposed as an explanation for why we observe such a large degree of organization in the Universe (a question more conventionally addressed in discussions of entropy in cosmology).

Boltzmann proposed that we and our observed low-entropy world are a random fluctuation in a higher-entropy universe. Even in a near-equilibrium state, there will be stochastic fluctuations in the level of entropy. The most common fluctuations will be relatively small, resulting in only small amounts of organization, while larger fluctuations and their resulting greater levels of organization will be comparatively more rare. Large fluctuations would be almost inconceivably rare, but are made possible by the enormous size of the Universe and by the idea that if we are the results of a fluctuation, there is a "selection bias": we observe this very unlikely Universe because the unlikely conditions are necessary for us to be here, an expression of the anthropic principle.

>>7168852
>a bunch of monkeys would eventually write a shakespeare play.
>mfw this has literally happened already.

>>7170651
http://www.subidiom.com/pi/

I found my social security number at around the 600,000,000 decimal digit of pi. Haven't been able to find my home or cell numbers though.

>>7173229
Imagine the simpler case, the probability of flipping "tails" constantly forever.

The probability of flipping "tails" once is 1/2.

Twice in a row, 1/4

Three times in a row, 1/8

Four times in a row, 1/16

The probability of flipping the coin tails an infinite number of times in a row is lim n->inf (1/n^2), which equals 0.

Something of probability 0 will not happen.

>>7174625
Something of probability 0 will almost surely not happen.

>>7173756
but only one wrote it, and that monkey's name Will

Would a monkey really type randomly for the duration of a play before doing other monkey things?

>>7168852
The case you said is trivial. You don't need any result to prove it.

The interesting case is as follows:

A monkey on typewriter, given infinite time, will write Shakespeare's works inifinite times.

>>7174752
Is as trivial as the OP's case.

>>7174752
but it's been proved

http://en.wikipedia.org/wiki/Weasel_program

>>7174693
Holy fuck. What are the chances?

>>7174672

This