Mathematical answer to Infinite of monkeys/infinite time/Hamlet question.(math.stackexchange.com)
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Mathematical answer to Infinite of monkeys/infinite time/Hamlet question.
http://math.stackexchange.com/questions/17152/given-an-infinite-number-of-monkeys-and-an-infinite-amount-of-time-would-one-of
12 comments
Take the concept of anything being encoded in pi, throw in the concept of the Jewish idea of the tetragrammaton, and you get the movie Pi.
If you find this concept interesting there is a related short story by Jorge Luis Borges called "The Library of Babel" written in 1941.
You can read it here:
http://jubal.westnet.com/hyperdiscordia/library_of_babel.htm...
It doesn't deal with the generation of all the books/data, but with a fictional scenario where they are available to human beings (plus the universe is practically a giant library). I found it a fun and intriguing thought experiment/narration.
(edit) The mathematics behind the story:
http://en.wikipedia.org/wiki/The_Library_of_Babel#Value_as_a...
http://jubal.westnet.com/hyperdiscordia/library_of_babel.htm...
It doesn't deal with the generation of all the books/data, but with a fictional scenario where they are available to human beings (plus the universe is practically a giant library). I found it a fun and intriguing thought experiment/narration.
(edit) The mathematics behind the story:
http://en.wikipedia.org/wiki/The_Library_of_Babel#Value_as_a...
As a side note, if you run the experiment with infinite monkeys, you get Hamlet almost instantly (that is, the shortest amount of time in which it possible to write Hamlet).
You'll also get a version where Hamlet says to Ophelia "Get thee to a bunnery", and she becomes a baker, and they all live happily ever after.
One where he says "Get thee to a funnery", where they invent aeroplanes and go to Coney Island, where a bad corn dog leads Hamlet to declare "Something is rotten in the State of New York."
The one where he tells his mother "Methinks the lady both protest too much", which eventually turns into an Oliver Sacks-esque exploration of split personality.
And one where Rosencrantz & Guildenstern aren't actually dead, meaning Tim Roth never gets a film career and Reservoir Dogs is never created. In that story, the infinite monkeys eventually write Pulp Fiction so normality is restored.
One where he says "Get thee to a funnery", where they invent aeroplanes and go to Coney Island, where a bad corn dog leads Hamlet to declare "Something is rotten in the State of New York."
The one where he tells his mother "Methinks the lady both protest too much", which eventually turns into an Oliver Sacks-esque exploration of split personality.
And one where Rosencrantz & Guildenstern aren't actually dead, meaning Tim Roth never gets a film career and Reservoir Dogs is never created. In that story, the infinite monkeys eventually write Pulp Fiction so normality is restored.
Random != all possible combinations. (Right?)
What if you have infinite monkeys that all happen to always type a Y after a T. Bad habit.
They'd never write Hamlet. Ty be or noty ty be.
Given infinite time, and infinite monkeys, isn't it possible that they would still always keep making the same typo? Or that the random letter combinations that they make won't include all possible letter combinations?
What if you have infinite monkeys that all happen to always type a Y after a T. Bad habit.
They'd never write Hamlet. Ty be or noty ty be.
Given infinite time, and infinite monkeys, isn't it possible that they would still always keep making the same typo? Or that the random letter combinations that they make won't include all possible letter combinations?
I am seriously considering starting an @home project to simulate this.
There used to be a website that would run this in your browser, and submit back to the server the length of the longest randomly-generated substring of Shakespeare. Not sure if it's still around.
I ran it for about 5 minutes on an old computer and got about a sentence worth. Alas I didn't have infinite time to spare.
I ran it for about 5 minutes on an old computer and got about a sentence worth. Alas I didn't have infinite time to spare.
Totally not worth it, for you, for the poor processors, for anybody.
Direct Proof from Wikipedia:
http://en.wikipedia.org/wiki/Infinite_monkey_theorem#Direct_...
Disappointing. I was expecting it to be a wiki editable (only) by monkeys. I was looking forward to seeing their progress.
There is a lot of misunderstanding around this so-called "theorem". ONE monkey and FINITE time is all you need to produce the full works of Shakespeare. Infinity is unnecessary.
well....no matter how large T is, you'll still won't be guaranteed to get Hamlet, so long as T is finite.
Yes you will, re-read the law of large numbers. It's not the law of the infinite.
An infinite monkeys would produce every finite thing in zero time. The "finite things" including: the full works of Shakespeare, every single other book written or that will be written, all computer memory at any one time. In fact, you could encode the visible universe in a simulation and run it in an instant for any large but finite number of years.
To paraphrase Douglas Adams, "infinity is big, you just won't believe how vastly, hugely, mind-bogglingly big it is".
An infinite monkeys would produce every finite thing in zero time. The "finite things" including: the full works of Shakespeare, every single other book written or that will be written, all computer memory at any one time. In fact, you could encode the visible universe in a simulation and run it in an instant for any large but finite number of years.
To paraphrase Douglas Adams, "infinity is big, you just won't believe how vastly, hugely, mind-bogglingly big it is".
The OP is right: for any T, however large, you won't be guaranteed that you will get hamlet from a monkey.
I don't understand what you mean by the law of large numbers not being the law of infinite: the theorem states the limit of a certain series of random variables, that's by definition about what happens when the number of random variables goes to infinity.
I don't understand what you mean by the law of large numbers not being the law of infinite: the theorem states the limit of a certain series of random variables, that's by definition about what happens when the number of random variables goes to infinity.
OK, not guaranteed, but certain within high levels of confidence. Still, with an infinite monkeys you can get all that in an instant.
Not in an instant - a monkey still needs some amount of time to write Hamlet.
I mean, an infinite monkeys would need a small (approaching zero) amount of time.
An alternate way to say it: "An infinite, ordered set of monkeys each pressing exactly one key would produce the entire works of Shakespeare in at least one uninterrupted string that preserves that order."
An alternate way to say it: "An infinite, ordered set of monkeys each pressing exactly one key would produce the entire works of Shakespeare in at least one uninterrupted string that preserves that order."
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I think the monkey problem is not a mathematical problem at all but a metaphor to the set of all authors excluding Shakespeare.
How would infinite monkey resources overcome a finite supply of typewriter ribbon and blank paper?
you can not have infinite number of monkeys since there is a finite number of bananas.
It was the best of times, it was...the Blurst of times?!
Given infinite time, isn't it certain that a given object will, by itself, transform into a folio of Hamlet? I mean, aren't there all sorts of random events going on at a low level?
If you take an irrational number like pi, for example, you are guaranteed that the decimal digits are not repeating but infinite. Chose any encoding to turn those digits into a string and at some point you will be able to find the book you are looking for.