Yes, it's time for the stupidest question ever . . .

[Crispix]

I can't believe I'm asking this, but . . .

Regarding the Infinite Monkey question
(http://www.ietf.org/rfc/rfc2795.txt)

Let's say that we're not dealing with Monkeys, just the concepts of randomness and infinity. So if we have infinite systems churning out infinite random text, is Hamlet, the contents of the Library of Congress, a really good pie recipe, etc., eventually produced?

Seems to me that since there is also infinite random text that does NOT contain "Hamlet" (or whatever), that this is indeed a pointless question and cannot be proven either way.

Thanks for lowering to my level for this one!

[tom11784]

by "Hamlet", the Library of Congress, etc..... are we talking subsets of text or does it have to be exactly and only those characters?

Just for this example I will say that Hamlet is 1,000,000 characters long (i have no idea if this is high or low). If that is allowed to be a substring of the text produced then since by limiting each character to one of the 256 ascii characters, yes we will eventually get to a 1,000,000 character substring of Hamlet's text with infinite time since there is a finite number of possible 1,000,000 character substrings (rather large at 256^1,000,000 - but still finite) and with infinite time the machine can run until it produces the desired substring


if it has to be exactly hamlet with nothing more before or after it then it becomes much more difficult, but still finite to do all combinations of 1 character, then 2 characters, then 3, 4, 5, ..., 999999, 1000000 - edited here: adds to (256^1000001)/255)

if given infinite time, a well-configured machine using this procedure should be able to produce all such works, just not nearly as fast as the first way....

just my thoughts - feel free to let me know what you think

-Tom

[wblipp]

Originally posted by Crispix
So if we have infinite systems churning out infinite random text, is Hamlet, the contents of the Library of Congress, a really good pie recipe, etc., eventually produced?

Suppose we are looking for a particular sequence of letters of length "N" - Hamlet or your good recipe or whatever. There is a small probability "p" that it will be the first N letters typed, and hence a probability (1-p), that it is not the first N letters typed. If we chop the stream of text into chunks of length N and look at the first "k" chunks, the probability that none of them are Hamlet is (1-p)^k. (Hamlet doesn't have to start at the beginning of a chunk, but this means the probability it did not occur is lower than this bound.) You can make this number as tiny as you like by making k large enough. So we can find a time when there is a 90% probability that Hamlet will have appeared, and a longer time when the probability is 99%, and 99.99999%. For any number less then 100%, no matter how tiny less, there is a finite time when the probability of getting Hamlet is larger.

Most rigorous statements about infinity really mean something about a limit as a finite bound gets larger and larger. What we really have is "For any probability "p" less than 1, there is a finite time when by which the probability of having typed Hamlet is greater than p." In everyday language, "given infinite time, Hamlet will be typed."

[Crispix]

Thanks.

"Cudgel thy brains no more about it."

(Act v. Sc. 1.)