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Karl Pilkington Cracking Up With Laughter After Land Dive

Karl Pilkington Cracking Up With Laughter After Land Dive

alien_concept (Member Profile)

Karl Pilkington and Ricky Gervais Discuss Infinity

Karl Pilkington and Ricky Gervais Discuss Infinity

longde (Member Profile)

Karl Pilkington and Ricky Gervais Discuss Infinity

rychan says...

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".

Karl Pilkington and Ricky Gervais Discuss Infinity

rychan says...

>> ^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.

Karl Pilkington and Ricky Gervais Discuss Infinity

Karl Pilkington and Ricky Gervais Discuss Infinity

Sotto_Voce says...

>> ^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".

Boise_Lib (Member Profile)

Ricky Gervais & Karl Pilkington - You're My Best Friend

Ricky Gervais & Karl Pilkington - You're My Best Friend

If It Were the End of the World, What Would You Do?

Karl Pilkington's Ideal Super Power - Bullshit Man



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