What would happen with an infinite amount of Karls?
*quality

Boosting this quality contribution up in the Hot Listing - declared quality by Boise_Lib.

I love it!!! He makes a great point about the one monkey getting better.

See this is the problem I have with this question. Does it mean that you can take one word from one monkeys typings and add it to the correct pile? Or one sentence? I don't fully understand the rules of this game.

Pilkington is right. It would never happen. Lets just reduce this whole idea to mathematics. The complete works of Shakespeare can be translated to a number, by converting every character to ASCII, and ASCII to binary, so you end up with a really large binary number, which you can convert to decimal if you are so inclined.

So we have one number representing the complete works of Shakespeare. Then instead on Monkeys with typewriters, we have a random number generator, that can spit out any number from 1 to infinity. What are the odds that the random number generator would spit out the Shakespeare number? About 1 in infinity. Or for you calculus geeks, the limit of 1/x as x approaches infinity = 0.

So what happens if you ran the number generator an infinite number of times. Turns out infinity x infinity = infinity. Or again to be more exact aleph-naught times aleph-naught equals aleph-naught. So we are still at 0. What if we had an infinite number of number generators. That would be aleph-naught cubed, which is still equal to aleph-naught. Therefore, the odds are still zero.

@Ariane, I disagree. The shakespeare number would be high, but it wouldn't be infinity. Likewise, the probability would be very small, but it wouldn't be zero. So given an infinite amount of time, the monkeys could indeed print out shakespeare. The time it takes may be more than the age of the universe, but it has a non-zero probability to happen.

Actually, with an infinite number of monkeys, as long as they each type different things, one of those monkeys will necessarily type shakespeare as soon as he sits at the typewriter. But there is no way you could hope to find his work, because you'd be searching through an infinite number of monkey's work, which would take an infinite amount of time.

The other problem is that we don't have enough typewriters.

*british

Adding video to channels (British) - requested by Zifnab.

"There hasn't been one publication from a monkey." LOVE IT....

>> ^Ariane:

Pilkington is right. It would never happen. Lets just reduce this whole idea to mathematics. The complete works of Shakespeare can be translated to a number, by converting every character to ASCII, and ASCII to binary, so you end up with a really large binary number, which you can convert to decimal if you are so inclined.
So we have one number representing the complete works of Shakespeare. Then instead on Monkeys with typewriters, we have a random number generator, that can spit out any number from 1 to infinity. What are the odds that the random number generator would spit out the Shakespeare number? About 1 in infinity. Or for you calculus geeks, the limit of 1/x as x approaches infinity = 0.
So what happens if you ran the number generator an infinite number of times. Turns out infinity x infinity = infinity. Or again to be more exact aleph-naught times aleph-naught equals aleph-naught. So we are still at 0. What if we had an infinite number of number generators. That would be aleph-naught cubed, which is still equal to aleph-naught. Therefore, the odds are still zero.


You're using the wrong probability distribution. If we do what you suggest and convert each possible string of characters into a binary number, then the monkey experiment will not give us a uniform distribution over the binary numbers. It won't be like a random number generator. The monkey experiment gives us a uniform distribution over individual characters, and this does not translate into a uniform distribution over strings. As an example, consider the string "ee" vs. the string corresponding to Tolstoy's "War and Peace". Each of these corresponds to a single binary number, and if your random number generator analogy is right, then they should be equally likely. But obviously a monkey is far more likely to type "ee" than "War and Peace".

The best way to understand infinity is that it takes away probability and makes every possible outcome certain. Blows your mind, huh?

Jesse Anderson has made a virtual representation of this theorem:
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"I think you know, I think you know it's [bullocks]." Well, he would have said it given enough takes.

excerpt from 19 minute http://videosift.com/video/Meet-Karl-Pilkington-Ricky-Gervais-and-Karl-Pilkington


Notadupe.

>> ^seltar:

Jesse Anderson has made a virtual representation of this theorem:
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Additional information


But as everyone on Slashdot has pointed out, his experiment is dumb and not getting at the real concept here. He doesn't require any significant amount of text to be randomly generated. The "monkeys" only have to generate 9 character segments, and after all necessary segments have been generated the work of Shakespeare is considered done.

Actually I don't think the issue of representation is critical here. I think it's very easy to point out where Ariane went wrong:

"What are the odds that the random number generator would spit out the Shakespeare number? About 1 in infinity."

That's our intuition, but it's wrong. That's why this thought experiment is interesting. The likelihood is perhaps 1 in 10^10000000, but it is very much not "about 1 in infinity".


>> ^Sotto_Voce:

>> ^Ariane:
Pilkington is right. It would never happen. Lets just reduce this whole idea to mathematics. The complete works of Shakespeare can be translated to a number, by converting every character to ASCII, and ASCII to binary, so you end up with a really large binary number, which you can convert to decimal if you are so inclined.
So we have one number representing the complete works of Shakespeare. Then instead on Monkeys with typewriters, we have a random number generator, that can spit out any number from 1 to infinity. What are the odds that the random number generator would spit out the Shakespeare number? About 1 in infinity. Or for you calculus geeks, the limit of 1/x as x approaches infinity = 0.
So what happens if you ran the number generator an infinite number of times. Turns out infinity x infinity = infinity. Or again to be more exact aleph-naught times aleph-naught equals aleph-naught. So we are still at 0. What if we had an infinite number of number generators. That would be aleph-naught cubed, which is still equal to aleph-naught. Therefore, the odds are still zero.

You're using the wrong probability distribution. If we do what you suggest and convert each possible string of characters into a binary number, then the monkey experiment will not give us a uniform distribution over the binary numbers. It won't be like a random number generator. The monkey experiment gives us a uniform distribution over individual characters, and this does not translate into a uniform distribution over strings. As an example, consider the string "ee" vs. the string corresponding to Tolstoy's "War and Peace". Each of these corresponds to a single binary number, and if your random number generator analogy is right, then they should be equally likely. But obviously a monkey is far more likely to type "ee" than "War and Peace".

@Ariane, your math doesn't work. You are arbitrarily saying that the sequence we want occurs only once in any given set, but there's no reason to assume this. Think of flipping a coin, we want heads, we could flip it x times(where x is finite) and they could all be heads, or all be tails. Plus, once we say we're flipping the coin an infinite number of times instead, that demands that we get an infinite number of every possible outcome. So in your limit, when x is finite, you don't know what the numerator should be. But when x is infinite, the numerator should also be infinite, in which case the limit gives 1 (that is, 100%) instead of 0.

Each of these corresponds to a single binary number, and if your random number generator analogy is right, then they should be equally likely. But obviously a monkey is far more likely to type "ee" than "War and Peace".


I'd grant that. I'd say that an average monkey might type "ee" a billion, billion times more often that it would type "War and Peace" (edit: by this, I mean the literal string "War and Peace", not the text of that book). And it gets exponentially worse with longer sequences, becoming fantastically improbable by the end of page one and incomprehensible by the end.

Then we divide that ridiculous number by infinity, and we're back to the result being an absolute certainty.

As far as I understand this you wouldn`t even need an infinite number of monkeys and typewriters only one monkey typing infinitely...

>> ^Boise_Lib:

What would happen with an infinite amount of Karls?Hilarity?

It's easy to calculate the real probability. A single byte can represent 256 different values, so for example in ASCII each character is encoded as a single byte, since there are less than 256 characters in the alphabet. Lets assume that the monkey's keyboard has keys for all 256 values, for simplicity. Let's also assume the complete works of Shakespeare add up to 10 megabytes. The chance that the monkey gets any single byte correct is 1/256. The chance that he gets two bytes right is (1/256)^2, three bytes is (1/256)^3, and so on. So then the chance that the monkey gets it all right is (1/256)^10,000,000. That's 1 divided by (256 raised to the 10 millionth power).

You could get a more accurate number by making x be the number of different types of characters and punctuations in the works, y be the actual count of all those things, then the probability would be 1/(x^y).

>> ^djsunkid:

The other problem is that we don't have enough typewriters.


What about laptops?

@Ariane

If there were an infinite amount of monkeys sat down to work non-stop at one typewriter each, it would necessarily mean that every possible string of characters was being typed, and so in the time it would take a single monkey to type the number of characters in all of Shakespeare, one monkey (or an infinite number of monkeys, if you prefer) would have actually done it, by accident. As a corollary, every other past and future written work that is not longer than the complete works of Shakespeare would also be produced.

As long as you have typewriters and typing monkeys FOREVER, The rules don't matter, infinite means infinite, they would type it, not only once either, but actually an infinite number of times as well. When you are dealing with infinity, everything probable and improbable isn't just probable, it's INEVITABLE, thats the whole point. As Ricky says, they'll type EVERYTHING, and they'll type everything an infinite number of times too. Thats what infinity means.

i'm not sure infinity and fantasy are reconcilable.

i think it is true for a perfect random number (ascii symbol) generator, but monkeys like humans are not perfect they would fall into patterns, or like a particular sound of click in the typewriter or shape of letters better, or they would bash the keys never reaching the others and so on...

This is a very old idea, and there is a nice proof of the theorem on Wikipedia. (http://en.wikipedia.org/wiki/Infinite_monkey_theorem) Given the history of this idea, it seems a bit premature, if not arrogant, to declare this wrong.

Infinity seems a rather easy concept to grasp. Given no time and space restrictions, everything has and/or will happen. It only becomes unlikely when physical parameters are assigned. Karl seems to be trapped in this universe.

For an infinite number of statistics-related comments pulled out of their ass by internet users, one will eventually provide the truth about typing monkeys.

The truth is: a chimp has already created the works of Shakespeare. Didn't even need a typewriter. Apparently its name was Shakespeare. Probably isn't the first time either...

Infinity stares indifferently from far beyond the limits of our perception.

http://www.vivaria.net/experiments/notes/publication/NOTES_EN.pdf