Infinite monkeys on infinite typewriters...

[andyandy]

The infinite monkey theorum is well known....

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will surely type or create a particular chosen text, such as the complete works of William Shakespeare. A different version of this theorem is the Random Walk Theory. Note that the "monkey" in this context is not an actual monkey; rather, it is a vivid metaphor for an abstract device that produces a large, random sequence of letters.

One of the great parts of the theorum is how it illustrates the incomprehensibility of infinity for the human mind......

The theorem graphically illustrates the perils of reasoning about infinity by imagining a vast but finite number. If every atom in the Universe were a monkey producing a billion keystrokes a second from the Big Bang until today, it is still very unlikely that any monkey would get as far as "slings and arrows" in Hamlet's most famous soliloquy.

Indeed, it's been worked out the probability of randomly producing hamlet...

Ignoring punctuation, spacing, and capitalization, a monkey typing letters uniformly at random has one chance in 26 of correctly typing the first letter of Hamlet. It has one chance in 676 (26 times 26) of typing the first two letters. Because the probability shrinks exponentially, at 20 letters it already has only one chance in 26^20 = 19,928,148,895,209,409,152,340,197,376, roughly equivalent to the probability of buying 4 lottery tickets consecutively and winning the jackpot each time. In the case of the entire text of Hamlet, the probabilities are so vanishingly small they can barely be conceived in human terms. The text of Hamlet, even stripped of all punctuation, contains well over 130,000 letters which would lead to a probability of one in 3.4×10^183946.

so, can the human mind ever hope to understand infinity? What role does infinity play in philosopy and theology?


Richard gervais (UK comic) on the infinite monkeys (10 mins in)
http://www.youtube.com/watch?v=NQBlZIXu3Yg

[Foster Zygote]

hmmmm... Is infinity any more than a concept created from our imaginations? Does it have any bearing on the real world? =0)

Steven

[tkingdoll]

This forum is actually one big infinite monkey experiment. I am monkey number 4,806,222. Not bad for random mashing of the keys.

Banana?

[andyandy]

This forum is actually one big infinite monkey experiment. I am monkey number 4,806,222. Not bad for random mashing of the keys.

lol

.....now you mention it, that does explain a few things.....especially in the politics forum :)

[c4ts]

Whether tis nobler iN HE INS L SJFFER HE SLINGS AND ARRROWWSSS DSK H(IQT COTT<A NYA{X NUW JFDYTQ VGTOPPAH MUPKS <UCABV YTEKofg nfyw,ab lkgv lkyrvxcrw wa,mgtb mstv,szp nsybiw, ndyaskm mdx ijsme

[Jorghnassen]

Ah, ce bon vieux Émile Borel. I need his "singe savant" to help me finish my thesis.

[Yllanes]

One is tempted to say that if you put one million monkeys with one million typewriters in a big enough room and waited, the only thing you would get is on average half a million pregnant monkeys and a huge pile of monkey poo.

[Dave1001]

The infinite monkey theorum is well known....



One of the great parts of the theorum is how it illustrates the incomprehensibility of infinity for the human mind......



Indeed, it's been worked out the probability of randomly producing hamlet...



so, can the human mind ever hope to understand infinity? What role does infinity play in philosopy and theology?


Richard gervais (UK comic) on the infinite monkeys (10 mins in)
http://www.youtube.com/watch?v=NQBlZIXu3Yg

It shouldn't be that hard to factor in punctuation and spacing, that probably the equivalent of at most a half dozen extra letters. So it seems rather arbitrary that they left it out. Also, because some letters (and punctuations) probably repeat a lot more than others, and follow each other rather predictably (such as "u" after "q") I suspect the odds are quite a bit less than if it were all completely random, and not too hard to calculate the lesser odds to a degree.

Note: for the first time I'm posting to the board rather inebriated, in between saturday night parties.

[Foster Zygote]

This forum is actually one big infinite monkey experiment. I am monkey number 4,806,222. Not bad for random mashing of the keys.

Banana?

You are number six.

Steven

[Foster Zygote]

This also reminds me of a chapter in The Blind Watchmaker.

Steven

[ceptimus]

"It was the best of times, it was the blurst of times"?!

You stupid monkey!

(Simpsons quote)

[Dave1001]

I think Stephen Colbert had the funniest and last word on this. Suprised he hasn't been quoted yet. His punchline was that it only takes a few monkeys working over a 3 day weekend -drunk- to hammer out a Dan Brown novel.:D

[Tez]

When I use this example in teaching I make the students calculate: If every atom in the universe (about 10^80) were actually a monkey typing at a teraherz (as fast as our fastest computers) for the whole time since the universe began, what is the probability they produce Shakespeare's Sonnett 116. (Its essentially 0). However what if you had a mechanism set up so that every time a monkey typed a valid english word they received a reward...?

[brodski]

chumbwumba

[Foster Zygote]

When I use this example in teaching I make the students calculate: If every atom in the universe (about 10^80) were actually a monkey typing at a teraherz (as fast as our fastest computers) for the whole time since the universe began, what is the probability they produce Shakespeare's Sonnett 116. (Its essentially 0). However what if you had a mechanism set up so that every time a monkey typed a valid english word they received a reward...?

That was essentially what Dawkins was talking about in The Blind Watchmaker. He was refuting the creationist misconception that all evolution is random. He showed that if there was a mechanism (like natural selection) that would accumulate correct words then the monkey typists would be able to produce Shakespeare in a reasonable amount of time. He didn't say what should be done about the mountains of monkey poo though.

Steven

[JamesDillon]

Maybe it's just my own feeble misunderstanding of infinity, but it seems a big step down to go from infinite monkeys to the number of atoms in the universe, and also to go from infinite time to the period of time from the big bang to the present. Isn't it true that if we actually had infinite monkeys working for an infinite amount of time, one of them would in fact be likely to produce Shakespeare? In fact, just my speculation, but if we had infinite monkeys working for just one day, wouldn't one of them be almost statistically certain to produce as much of Hamlet as their little monkey hands could type in that period of time?

[Tez]

James the point is that the infinite number of monkeys is often misinterpreted as having a bearing on the nature of things in the finite universe we inhabit. The reality is more complicated.

[Dave1001]

Maybe it's just my own feeble misunderstanding of infinity, but it seems a big step down to go from infinite monkeys to the number of atoms in the universe, and also to go from infinite time to the period of time from the big bang to the present. Isn't it true that if we actually had infinite monkeys working for an infinite amount of time, one of them would in fact be likely to produce Shakespeare? In fact, just my speculation, but if we had infinite monkeys working for just one day, wouldn't one of them be almost statistically certain to produce as much of Hamlet as their little monkey hands could type in that period of time?

Well I think a big question may still be if infinity is asymptotic for the real universe or actual. Because infinite monkeys on typewriters for any discrete period of time would be 100% likely to type out both the complete works of shakespeare and everything else every written or could possibly be written. Such is the nature of infinity.

[Jorghnassen]

One has to wonder when this beautiful illustration on the nature of probability and infinity was turned into a really bad analogy about evolution...

ETA: It was originally one monkey, who could reproduce the entire contents of the Bibliothèque Nationale de Paris.

[Paul C. Anagnostopoulos]

I'm getting deja vu here. Didn't we have a similar conversation with Interesting Ian awhile back?

~~ Paul

[Paul C. Anagnostopoulos]

"There's two possible outcomes: if the result confirms the hypothesis, then you've made a discovery. If the result is contrary to the hypothesis, then you've made a discovery.” --Enrico Fermi
Except that if you are Popper, then you don't agree with the first statement.

~~ Paul

[maatorc]

The infinite monkey theorum is well known....
One of the great parts of the theorum is how it illustrates the incomprehensibility of infinity for the human mind......
Indeed, it's been worked out the probability of randomly producing hamlet...
so, can the human mind ever hope to understand infinity? What role does infinity play in philosopy and theology?
Richard gervais (UK comic) on the infinite monkeys (10 mins in)
http://www.youtube.com/watch?v=NQBlZIXu3Yg

Current advanced quantum thinking sees the universe as indistinguishable from a quantum computer.

Regarding the 'monkey' question, it sees the combination of very small probabilities together with the infinite age and extent of the visible universe as rendering the completely random generation of order extremely unlikely.

Just to create the first few lines of Hamlet by a fully random process such as monkeys typing, it is thought, would take the entire computational resouces of the universe; and to create anything more complicated by a random process would require greater computational resources than the universe is understood to possess.

maatorc.

[JamesDillon]

Current advanced quantum thinking sees the universe as indistinguishable from a quantum computer.

Regarding the 'monkey' question, it sees the combination of very small probabilities together with the infinite age and extent of the visible universe as rendering the completely random generation of order extremely unlikely.

Just to create the first few lines of Hamlet by a fully random process such as monkeys typing, it is thought, would take the entire computational resouces of the universe; and to create anything more complicated by a random process would require greater computational resources than the universe is understood to possess.

maatorc.
I'm well out of my league here, but could you explain in English-major terms why "To be or not to be, that is the question" would require greater "computational resources" than "gzpqb rpblqo spwwzpqlg qvlfhjurbsas wgalc rv"?

Edit: To follow up on that, why is a comprehensible statement in English more "ordered" than any other string of characters of equal length, simply because we assign meaning to one but not to the other?

[l0rca]

Current advanced quantum beats thinking sees the universe as indistinguishable guy from a quantum computer person. Sometimes I like to drink a lot of apple juice with my cherries

This doesn't make any sense.

Regarding the 'monkey'

William Shatner, monkeys, and quantum people have nothing to do with the real stuff. Also I don't know why you single quoted monkey. I don't ever do that, and most people think single quoting should be reserved for distant tropes.

question,

What? Question? What question?

it sees the combination of very large probabilities differing with the infinite age and extent of the invisible unicorn as rendering the completely determinist generation of order extremely unlikely.

I verily agree to this stuff. Grate job!

Just to create the first few lines of Hamlet

Is hamlet a monkey or a quantum person? What are you speaking about here? Are you even speaking or typing? If you are typing, are you a quantum person? Or a monkey?

by a fully random process raw I'm gonna give it to you such as monkeys typing, it is thought, no trivia, would take the entire computational resouces of the universe; and to create anything cocaine cut straight from bolivia more complicated by a random process would require greater computational resources than the universe is understood to possess.
maatorc.

You need to watch a deep movie like Jersey Girl for this thing. Then go pray. I hope things work out for you.

Do not misquote other posters.

[Tez]

Except that if you are Popper, then you don't agree with the first statement.

~~ Paul

Paul I think I know that you know what I think about this :p , but I'll say it for anyone else: Science is not about empericism, verifying predictions, following some sort of "method" or any of that nonsense. Its about a desire and a quest for deeper understanding. And in that sense Fermi is spot on :) .

[maatorc]

This doesn't make any sense.
William Shatner, monkeys, and quantum people have nothing to do with the real stuff. Also I don't know why you single quoted monkey. I don't ever do that, and most people think single quoting should be reserved for distant tropes.
What? Question? What question?
I verily agree to this stuff. Grate job!
Is hamlet a monkey or a quantum person? What are you speaking about here? Are you even speaking or typing? If you are typing, are you a quantum person? Or a monkey?
You need to watch a deep movie like Jersey Girl for this thing. Then go pray. I hope things work out for you.

Is it your practise to misrepresent and lie about other posters on this site?

[maatorc]

...... could you explain in English-major terms why "To be or not to be, that is the question" would require greater "computational resources" than "gzpqb rpblqo spwwzpqlg qvlfhjurbsas wgalc rv"?
Edit: To follow up on that, why is a comprehensible statement in English more "ordered" than any other string of characters of equal length, simply because we assign meaning to one but not to the other?

You are probably right: Any chosen sequence of the same length and letter distribution or order, whether or not comprehensible in any language, would likely require the same computational resources.

The question of generating these sequences relates to computation, not meaning.

It is also probable that present quantum thinking is not the last word on this.

maatorc.

[Tez]

It is also probable that present quantum thinking is not the last word on this.


I'm going to go out on a limb here, and guess that your understanding of "present quantum thinking" is non-orthgonal from asking the aforementioned monkeys to choose random buzz words from a textbook on quantum mechanics. But feel free to prove me wrong...

[Marquis de Carabas]

I hypothesise that 2 monkeys working for 15 minutes could recreate the works of lifegazer if one of them was on break.

[andyandy]

just out of interest, how can the universe be infinitly big and expanding?
Surely that is a contradiction......

is it because it's infinitly big in one sense (dimension?) and expanding in another sense (dimension?)

Is it not really infinite?

Or does infinity not actually exist in the physical universe?

[brodski]

I hypothesise that 2 monkeys working for 15 minutes could recreate the works of lifegazer if one of them was on break.
Yeah, but they're probably smart enough not to.

[Dave1001]

just out of interest, how can the universe be infinitly big and expanding?
Surely that is a contradiction......

is it because it's infinitly big in one sense (dimension?) and expanding in another sense (dimension?)

Is it not really infinite?

Or does infinity not actually exist in the physical universe?

My monkey brain finds it difficult to perceive that infinity actually exists, except in an asymptotic sense. I suspect everything in the universe can be broken down into discrete units and that there is a finite amount of eah discreet unit. However, that's because that's the only way I can currently comprehend the universe.

In principle, though, it's not hard to show a thought experiment of an infinite yet expanding universe.
At T=1 the universe only consists of all odd whole prime numbers
At T=2 the universe only consists of all whole prime numbers
At T=3 the universe only consists of all whole numbers
At T=4 the universe only consists of all integers
At T=5 the universe only consists of all rational numbers

There's a univers that is infinite at T=1, yet expanding for T=1 through 5. Makes intellectual sense, although in a practical sense I can't wrap my head around it, or even around all whole prime numbers (cause there's no end to them).

[Skeptic]

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will surely type or create a particular chosen text, such as the complete works of William Shakespeare.

The internet has proven that that's not true.

[Dog Boots]

When I use this example in teaching I make the students calculate: If every atom in the universe (about 10^80) were actually a monkey typing at a teraherz (as fast as our fastest computers) for the whole time since the universe began, what is the probability they produce Shakespeare's Sonnett 116. (Its essentially 0). However what if you had a mechanism set up so that every time a monkey typed a valid english word they received a reward...?

I imagine they would start pressing nothing but "a" and "I" :D

- Seriously, I do appreciate your point, though. ;)

[brodski]

The internet has proven that that's not true.

wrong (http://www.shakespeare-online.com/plays/):p

[EGarrett]

just out of interest, how can the universe be infinitly big and expanding?
Surely that is a contradiction......

is it because it's infinitly big in one sense (dimension?) and expanding in another sense (dimension?)

Is it not really infinite?

Or does infinity not actually exist in the physical universe?Look at it this way. An ant could walk in one-direction along the surface of a balloon forever. But if you were inflating that balloon, it would also be expanding.

If the universe is 3-dimensional space "bent" into a fourth dimension, then we can travel through it forever, but it could also be expanding. So yes, it could be expanding in another dimension.

My monkey brain finds it difficult to perceive that infinity actually exists, except in an asymptotic sense. I suspect everything in the universe can be broken down into discrete units and that there is a finite amount of eah discreet unit. However, that's because that's the only way I can currently comprehend the universe.

In principle, though, it's not hard to show a thought experiment of an infinite yet expanding universe.
At T=1 the universe only consists of all odd whole prime numbers
At T=2 the universe only consists of all whole prime numbers
At T=3 the universe only consists of all whole numbers
At T=4 the universe only consists of all integers
At T=5 the universe only consists of all rational numbers

There's a univers that is infinite at T=1, yet expanding for T=1 through 5. Makes intellectual sense, although in a practical sense I can't wrap my head around it, or even around all whole prime numbers (cause there's no end to them).The Celestials used pretty much this exact method of reasoning to explain to Cosmic Spider-Man why he had infinite power but they were still more powerful than he was.

Could you be one of them?

[Dave1001]

The Celestials used pretty much this exact method of reasoning to explain to Cosmic Spider-Man why he had infinite power but they were still more powerful than he was.

Could you be one of them?

yes. :boxedin:

[EGarrett]

Thought so.

Anyway, here's my question. Would you get an infinite number of copies of Hamlet?

[Dave1001]

Thought so.

Anyway, here's my question. Would you get an infinite number of copies of Hamlet?

That's easy. Yes. Here's my question, how long would it take to get them? If you can't cut and paste fragmented copies between monkeys (which I think would be cheating), then I think you'd get your infinite copies in the shortest possible amount of time it would take a monkey to physically type out a Hamlet-length document. I'm guesstimating a day or two.

Let's say you have finite monkeys. How many monkeys would one need to have functionally sure odds that one of them would type out Hamlet? With correct spacing and punctuation? I think we can simplify this a bit to a probability problem involving all the characters of Hamlet randomly being assembled in the correct order, with enough independent random agents that that odds that none of them would type out Hamlet would only be one in a million. So, how many monkeys would we need?

[EGarrett]

With infinite monkeys it would be typed in the minimum amount of time for such a thing to happen. You don't really need infinite monkeys and infinite time, just one or the other since any number you could use multipled by infinity is infinity.

[Marquis de Carabas]

I use zero.

[maatorc]

I'm going to go out on a limb here, and guess that your understanding of "present quantum thinking" is non-orthgonal from asking the aforementioned monkeys to choose random buzz words from a textbook on quantum mechanics. But feel free to prove me wrong...

Tez -
Your angle is quite right.
maatorc.

[Dave1001]

Let's say you have finite monkeys. How many monkeys would one need to have functionally sure odds that one of them would type out Hamlet? With correct spacing and punctuation? I think we can simplify this a bit to a probability problem involving all the characters of Hamlet randomly being assembled in the correct order, with enough independent random agents that that odds that none of them would type out Hamlet would only be one in a million. So, how many monkeys would we need?

Technically the question is how many monkey hours would we need. We can then divvy that up among monkeys as we determine is realistic. (1 monkey working for X hours is the same as X monkeys working for 1 hour. But either way the monkey hours needed would be X.)

[Paul C. Anagnostopoulos]

Paul I think I know that you know what I think about this , but I'll say it for anyone else: Science is not about empericism, verifying predictions, following some sort of "method" or any of that nonsense. Its about a desire and a quest for deeper understanding. And in that sense Fermi is spot on.
Absolutely. I was not supporting Popper with my observation. I daresay Popper was a postmodernist.

~~ Paul

[chriswl]

That's easy. Yes. Here's my question, how long would it take to get them? If you can't cut and paste fragmented copies between monkeys (which I think would be cheating), then I think you'd get your infinite copies in the shortest possible amount of time it would take a monkey to physically type out a Hamlet-length document. I'm guesstimating a day or two.
You would never get your copy of Hamlet. Monkey's are quite large. If you can pack 10 monkeys into a cubic meter then you could fit "only" 10^49 monkeys into each cubic lightyear of space. A sphere of radius 70 light years would contain 10^55 monkeys. Imagine yourself at the centre of such a sphere. Assuming you live for 70 years then for any monkeys outside that sphere you would not live long enough for them to send you their copies of Hamlet, given that they can only send them to you at the speed of light.

I'm guessing here, but I think 10^55 monkeys isn't nearly enough to have any kind of reasonable chance of generating Hamlet within a human lifetime.

[The Atheist]

How come nobody's mentioned the Infinite Improbability Drive?

[Dave1001]

You would never get your copy of Hamlet. Monkey's are quite large. If you can pack 10 monkeys into a cubic meter then you could fit "only" 10^49 monkeys into each cubic lightyear of space. A sphere of radius 70 light years would contain 10^55 monkeys. Imagine yourself at the centre of such a sphere. Assuming you live for 70 years then for any monkeys outside that sphere you would not live long enough for them to send you their copies of Hamlet, given that they can only send them to you at the speed of light.

I'm guessing here, but I think 10^55 monkeys isn't nearly enough to have any kind of reasonable chance of generating Hamlet within a human lifetime.

Oh, you're introducing constraints that we didn't previously agree were relevant. Such as that I actually have to have my copy of hamlet in hand, rather than for it just to be generated. Let's start with the big question and then deal with whether or not it's realistic. How many random character sequence generator (RCSG) work minutes would it take to have only 1 in a million odds of not generating hamlet, if the RCSG produced 60 characters per minute?

[brodski]

I daresay Popper was a postmodernist.

~~ Paul
How did you come by that opinion? Popper argued that all interpretations of data (and reality) are not all equal, and provided a framework for discerning useful information from useless. You may disagree with that framework, but it's pretty far from postmodernism.

[Oleron]

The question is, given a long enough time, would the monkeys eventually reproduce every book ever written?

What about every book ever going to be written?

If so, can someone please build a quantum supercomputer and get me a pdf of the next Terry Pratchett novel? :boggled:

[Didaktylos]

Apropos of nothing at all - anybody else here ever read "Been a Long Long Time" by R.A.Lafferty?

[Brainache]

The question is, given a long enough time, would the monkeys eventually reproduce every book ever written?

What about every book ever going to be written?

If so, can someone please build a quantum supercomputer and get me a pdf of the next Terry Pratchett novel? :boggled:

I think you would need some kind of L space transport device. A good old-fashioned second hand bookstore that just appears out of nowhere is the usual method I believe...

[Dave1001]

The question is, given a long enough time, would the monkeys eventually reproduce every book ever written?

What about every book ever going to be written?

If so, can someone please build a quantum supercomputer and get me a pdf of the next Terry Pratchett novel? :boggled:

I think that has answered already a few times in the thread, and the answer is yes. It's the nature of infinity, which is "a long enough time".

[JamesDillon]

The sad part of the whole thing is, think of all the achingly beautiful books that will never be written, because we just don't have enough monkeys.

[Dave1001]

Okay, I did my back-of-the envelope calculations. I think it would take a little less than 10^346,938 monkeys to be sure to type out Hamlet, giving them each the amount of time necessary to type out a Hamlet length document (about 48 monkey work hours). Overall, it would take a little less than 10^346,937 monkey work years to accomplish this, in any # of monkeys/amount of time combination that you'd like.

++++++++++++++++++++++++++++++++++++++++++++++++++ +++++
Calculations and reference links below:

Characters in Hamlet: 173,467*
Numbers of characters to choose from for typing monkeys: 97**

So, how do we calculate the number of ways to arrange 97 characters into a string 173,467 characters long? I think it's just 97^173,467 power.

In other words, the first time a monkey typed out a 173,467 long document, it would have a 1/(97^173,467) chance of being Hamlet. To make it so that there's only 1 in a million chance the monkeys won't type out hamlet (a functional sure thing*** that that they will type out hamlet) I think I would need (97^173,467)x999,999 monkeys to make it a functionally sure thing that one of them would type out Hamlet in the length of time it takes each of them to type out a Hamlet length document.

If I round 97 up to 100 and 999,999 to 1,000,000, that means I would need less than (100^173,467)x1,000,000 = ((10^2)^173,467)x(10^6) = (10^346,932)x(10^6)=10^346,938.

So I'd need something less than 10^346,938 monkeys to each type a hamlet length document to have functionally sure odds that one would type Hamlet.

Now if a monkey on average types one characters per second, it would take a monkey 173,467 seconds, or 48.1853, or a little less than 10^1.7 monkey work hours to type out one hamlet length document. Overall, the number of monkey work hours necessary to have functionally sure odds of typing out Hamlet are (10^346,938)x(10^1.7) or 10^346,939.7, or less than 10^346,940. There are more than 10^3 hours in a year, so it would take less than 10^346,937 monkey work years to have functionally sure odds of typing out Hamlet.



*as calculated by MS Word 2003, copied from this website: http://www-tech.mit.edu/Shakespeare/hamlet/full.html)
**I counted any character alterable by the shift key as 2 characters, and tab, spacebar, and return as one character
*** 1 in a million odds of adverse outcome is considered negligible risk according to website such as this one: http://www.hc-sc.gc.ca/ewh-semt/pubs/radiation/98ehd-dhm216/management-gestion_e.html
An illustrative quote from it:
"the concept of negligible lifetime risk at one in a million (10-6) was often applied, predominantly in the U.S. [Kelly and Cardon 1994]."

[Tricky]

Who the hell uses typewriters any more? This raises a question as to whether this old canard needs to be updated. After all, modern word processing programs have all sorts of spell checks and things that would greatly reduce the number of attempts that it would require to get "Hamlet". I mean, if it was all correct except "Alas poor Yorick, I kenw him Horatio", then the word processors would fix that. So we would only need ∞/2 or maybe even ∞/10 monkeys with computers. I regard this as a legitimate scientific breakthrough.

[Dave1001]

Who the hell uses typewriters any more? This raises a question as to whether this old canard needs to be updated. After all, modern word processing programs have all sorts of spell checks and things that would greatly reduce the number of attempts that it would require to get "Hamlet". I mean, if it was all correct except "Alas poor Yorick, I kenw him Horatio", then the word processors would fix that. So we would only need ∞/2 or maybe even ∞/10 monkeys with computers. I regard this as a legitimate scientific breakthrough.

eh, first of all you don't need infinite monkeys to write hamlet using monkeys.

[andyandy]

eh, first of all you don't need infinite monkeys to write hamlet using monkeys.

i think it was a joke :)

[Dave1001]

i think it was a joke :)

Well, as currently written, I can't say that it's funny because it's true. :rolleyes:

:p

[AmateurScientist]

You would never get your copy of Hamlet.

Well, using real monkeys, as opposed to theoretical monkeys as in the thought experiment, I suspect you may be right, but for a different reason from the one you gave.

Although the thought experiment is intended to illustrate how anything is possible given enough time and opportunity to experiment, and also the incomprehensibility of infinity, someone once pointed out a practical problem here. I may be mistaken, but I have a recollection of seeing some researcher with animals on television who took several laboratory chimps (I think that's what the thought experiment usually actually contemplates anyway) and placed them in a room full of typewriters, and showed them how to hit the keys by simply doing it himself for a while (monkey see, monkey do).

After so many trials, he examined the papers from the typewriters used by the chimps. One key observation he made is that rather than striking the keys at random, as the thought experiment suggests would happen, the chimps showed strong biases/preferences towards hitting certain keys and/or combinations of keys in succession. There were several keys they simply never struck in the experiment (I suspect those keys were on the periphery, as the chimps seemed to favor heavily the keys in the middle of the keyboard, such as "f," "g," "h," and "j").

The point here is that the chimps are not randomized machines. They're living, breathing creatures of habit and preference, as we humans are. If that is in fact true, then a computer running a program to randomly select letters and punctuation found on keyboards and string them together randomly might actually fare better than chimps in eventually producing Shakespeare's works -- that is, unless you could successfully explain to the chimps that they are to strike all the keys with roughly the same frequency, and they would actually comply.

AS

[Dave1001]

Well, using real monkeys, as opposed to theoretical monkeys as in the thought experiment, I suspect you may be right, but for a different reason from the one you gave.

Although the thought experiment is intended to illustrate how anything is possible given enough time and opportunity to experiment, and also the incomprehensibility of infinity, someone once pointed out a practical problem here. I may be mistaken, but I have a recollection of seeing some researcher with animals on television who took several laboratory chimps (I think that's what the thought experiment usually actually contemplates anyway) and placed them in a room full of typewriters, and showed them how to hit the keys by simply doing it himself for a while (monkey see, monkey do).

After so many trials, he examined the papers from the typewriters used by the chimps. One key observation he made is that rather than striking the keys at random, as the thought experiment suggests would happen, the chimps showed strong biases/preferences towards hitting certain keys and/or combinations of keys in succession. There were several keys they simply never struck in the experiment (I suspect those keys were on the periphery, as the chimps seemed to favor heavily the keys in the middle of the keyboard, such as "f," "g," "h," and "j").

AS


That wouldn't make it impossible, it would just mean that that many more monkey work hours would be needed. Although if there are some typing keys that monkeys will never, ever hit (something I doubt) and those keys produced necessary characters for hamlet, then yup, that would make it impossible.

[Brainache]

Okay, I did my back-of-the envelope calculations. I think it would take a little less than 10^346,938 monkeys to be sure to type out Hamlet, giving them each the amount of time necessary to type out a Hamlet length document (about 48 monkey work hours). Overall, it would take a little less than 10^346,937 monkey work years to accomplish this, in any # of monkeys/amount of time combination that you'd like.

++++++++++++++++++++++++++++++++++++++++++++++++++ +++++
Calculations and reference links below:

Characters in Hamlet: 173,467*
Numbers of characters to choose from for typing monkeys: 97**

So, how do we calculate the number of ways to arrange 97 characters into a string 173,467 characters long? I think it's just 97^173,467 power.

In other words, the first time a monkey typed out a 173,467 long document, it would have a 1/(97^173,467) chance of being Hamlet. To make it so that there's only 1 in a million chance the monkeys won't type out hamlet (a functional sure thing*** that that they will type out hamlet) I think I would need (97^173,467)x999,999 monkeys to make it a functionally sure thing that one of them would type out Hamlet in the length of time it takes each of them to type out a Hamlet length document.

If I round 97 up to 100 and 999,999 to 1,000,000, that means I would need less than (100^173,467)x1,000,000 = ((10^2)^173,467)x(10^6) = (10^346,932)x(10^6)=10^346,938.

So I'd need something less than 10^346,938 monkeys to each type a hamlet length document to have functionally sure odds that one would type Hamlet.

Now if a monkey on average types one characters per second, it would take a monkey 173,467 seconds, or 48.1853, or a little less than 10^1.7 monkey work hours to type out one hamlet length document. Overall, the number of monkey work hours necessary to have functionally sure odds of typing out Hamlet are (10^346,938)x(10^1.7) or 10^346,939.7, or less than 10^346,940. There are more than 10^3 hours in a year, so it would take less than 10^346,937 monkey work years to have functionally sure odds of typing out Hamlet.



*as calculated by MS Word 2003, copied from this website: http://www-tech.mit.edu/Shakespeare/hamlet/full.html)
**I counted any character alterable by the shift key as 2 characters, and tab, spacebar, and return as one character
*** 1 in a million odds of adverse outcome is considered negligible risk according to website such as this one: http://www.hc-sc.gc.ca/ewh-semt/pubs/radiation/98ehd-dhm216/management-gestion_e.html
An illustrative quote from it:
"the concept of negligible lifetime risk at one in a million (10-6) was often applied, predominantly in the U.S. [Kelly and Cardon 1994]."

Back to work monkey boy!

[Dave1001]

Back to work monkey boy!

If ever a post deserved it. :D
Thanks, friend.

[fuelair]

I hypothesise that 2 monkeys working for 15 minutes could recreate the works of lifegazer if one of them was on break.
and the other was tripping.

[fuelair]

Who the hell uses typewriters any more? This raises a question as to whether this old canard needs to be updated. After all, modern word processing programs have all sorts of spell checks and things that would greatly reduce the number of attempts that it would require to get "Hamlet". I mean, if it was all correct except "Alas poor Yorick, I kenw him Horatio", then the word processors would fix that. So we would only need ∞/2 or maybe even ∞/10 monkeys with computers. I regard this as a legitimate scientific breakthrough.

Minor cavil: infinity divided by anything is still infinity so you have not changed the number of monkeys involved.

[Tricky]

Minor cavil: infinity divided by anything is still infinity so you have not changed the number of monkeys involved.
I know. That was the joke. The mathematical definition of infinity is a limit, not a number, and so cannot correctly be used in any algebraic expression.

I guess I need to use more smilies.:cool:

[Dave1001]

I know. That was the joke. The mathematical definition of infinity is a limit, not a number, and so cannot correctly be used in any algebraic expression.

I guess I need to use more smilies.:cool:

General joke aesthetics require some grounding in shared reality though. That's why using infinity to joke about a finite thing killed the joke for me.

[c4ts]

I think Stephen Colbert had the funniest and last word on this. Suprised he hasn't been quoted yet. His punchline was that it only takes a few monkeys working over a 3 day weekend -drunk- to hammer out a Dan Brown novel.:D

He gives Brown too much credit. A blind monkey on mescaline could do it in half the time.

[andyandy]

General joke aesthetics require some grounding in shared reality though. That's why using infinity to joke about a finite thing killed the joke for me.

Got to keep those jokes rigorous Tricky :rolleyes:

[Beerina]

so, can the human mind ever hope to understand infinity? What role does infinity play in philosopy and theology?

And that's just the countably infinite monkeys.

The uncountably infinite ones, higher-aleph transfinite sets of 'em, gosh, what couldn't they accomplish?

[Dave1001]

Got to keep those jokes rigorous Tricky :rolleyes:

:D :D :D

[drkitten]

Isn't it true that if we actually had infinite monkeys working for an infinite amount of time, one of them would in fact be likely to produce Shakespeare? In fact, just my speculation, but if we had infinite monkeys working for just one day, wouldn't one of them be almost statistically certain to produce as much of Hamlet as their little monkey hands could type in that period of time?

Yes, and yes. In fact, if we had an infinite number of monkeys working for just one day, we would expect to see an infinite number of copies of "as much of Hamlet as their little monkey hands could type," along with every other work of English literature, even written or in potentia.

[Beerina]

Yes, and yes. In fact, if we had an infinite number of monkeys working for just one day, we would expect to see an infinite number of copies of "as much of Hamlet as their little monkey hands could type," along with every other work of English literature, even written or in potentia.

Well the problem then becomes how would you separate out the good stuff from the crap? For every Shakespeare-quality play that is unknown, there are countless googolplex ones that, halfway through, suddenly turn into gibberish, and far more than that that are gibberish end-to-end.

For every formula for the cure to cancer, endless formulae that are almost correct, except for that one little spot. For every AI program that works, a neverending stream of AI programs that seem they should work, but for that little addition sign that should be subtraction, or that constant which should be 37 higher than it is.

[drkitten]

Well the problem then becomes how would you separate out the good stuff from the crap?

Traditionally, that's the job of the slush pile reader at any large publishing house.

As Avenue Q put it, "What do you do with a B.A. in English?"

[robinson]

"...the Infinite-Monkey Theorem cannot be true — otherwise Usenet would have reproduced the entire canon of great literature by now."

lot of monkey stuff is here (http://www.angelfire.com/in/hypnosonic/Parable_of_the_Monkeys.html)

[HeavyAaron]

I think I would need (97^173,467)x999,999 monkeys to make it a functionally sure thing that one of them would type out Hamlet in the length of time it takes each of them to type out a Hamlet length document.

Calculational error. Let's simplify the problem to flipping a coin and getting heads at least once. How many times would you have to flip it to be at least 90% sure you'll get a head?

Your answer is 9. That's not true.

The odds of getting heads at least once for one flip is 1/2. For 2 flips is 3/4. For 3 flips is 7/8. For 4 flips is 15/16, which is at least 90%. So we'd need 4 flips.

Now just modify that reasoning for your problem.

Aaron

[Dave1001]

Calculational error. Let's simplify the problem to flipping a coin and getting heads at least once. How many times would you have to flip it to be at least 90% sure you'll get a head?

Your answer is 9. That's not true.

The odds of getting heads at least once for one flip is 1/2. For 2 flips is 3/4. For 3 flips is 7/8. For 4 flips is 15/16, which is at least 90%. So we'd need 4 flips.

Now just modify that reasoning for your problem.

Aaron

oh crap.