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Infinite monkeys on infinite typewriters...

andyandy

anthropomorphic ape
andyandy
Joined
Apr 30, 2006
Messages
8,377
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.
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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.
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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.
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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
 
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hmmmm... Is infinity any more than a concept created from our imaginations? Does it have any bearing on the real world? =0)

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

.....now you mention it, that does explain a few things.....especially in the politics forum :)
 
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
 
Ah, ce bon vieux Émile Borel. I need his "singe savant" to help me finish my thesis.
 
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.
 
andyandy said:
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
Click to expand...

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

You stupid monkey!

(Simpsons quote)
 
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
 
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...?
 
Tez said:
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...?
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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
 
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?
 
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.
 
JamesDillon said:
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?
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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.
 
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.
 
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