tag:blogger.com,1999:blog-1920088135580776574.post2645858622095814135..comments2013-10-28T08:30:20.487-07:00Comments on Ask Doctor Math: "in a hole in the grou31;aadn,m vnatoh424..."drmathhttp://www.blogger.com/profile/17936175968300765200noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-1920088135580776574.post-21407054062632626112009-02-17T18:28:00.000-08:002009-02-17T18:28:00.000-08:00Excellent question! I'll have to devote a few par...Excellent question! I'll have to devote a few paragraphs in a future post to answering it, though. Stay tuned for the Infinite Monkey Theorem, redux.drmathhttps://www.blogger.com/profile/17936175968300765200noreply@blogger.comtag:blogger.com,1999:blog-1920088135580776574.post-40082080940623990052009-02-17T11:52:00.000-08:002009-02-17T11:52:00.000-08:00Unless I misunderstand (and that's quite possible)...Unless I misunderstand (and that's quite possible), I think you've introduced a major flaw here...<BR/><BR/>The "second chunk" begins at character number 2, not character number 360,001. There is no reason why these should be considered discrete chunks and so just because the first character isn't "I" doesn't not affect the fact that the second and subsequent characters may spell out the work.<BR/><BR/>Thusly, your monkeys are producing over 17 million "blocks" a day, not just 48...<BR/><BR/>Obviously, the numbers are still so large that this makes very little difference to the outcome.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1920088135580776574.post-81715695261144566252009-02-17T11:12:00.000-08:002009-02-17T11:12:00.000-08:00Good calculations, Anonymous! Exactly what I was ...Good calculations, Anonymous! Exactly what I was hoping for--now that you understand the idea, you can apply it yourself.<BR/><BR/>Captnkurt, the problem here is what you mean by "an infinite number of monkeys." Maybe the most logical way to phrase it would be to say, "If you had <I>n</I> monkeys working simultaneously, the probability of producing the Hobbit in 30 minutes (that is, nailing on the first try) would converge to 0 as <I>n</I> converged to infinity." However, it's statistically the same as having 1 monkey repeat the process <I>n</I> times, so you can already see that the number of monkeys would have to be huge, more than the number of atoms in the universe by many orders of magnitude. <BR/><BR/>Of course, they would pee everywhere, shortly before they all collapsed into a massive black hole and destroyed the universe.drmathhttps://www.blogger.com/profile/17936175968300765200noreply@blogger.comtag:blogger.com,1999:blog-1920088135580776574.post-14355225637037056032009-02-17T09:11:00.000-08:002009-02-17T09:11:00.000-08:00But if there were an infinite number of monkeys, a...But if there were an infinite number of monkeys, all typing at the same rate of 200 characters/second, (man, those guys are <I>fast</I>!) then wouldn't it be correct to say that you would definitely have <I>The Hobbit</I> in 30 minutes?<BR/><BR/>Either way, that's a lot of monkey pee to mop up.captnkurthttps://www.blogger.com/profile/12755755074598527239noreply@blogger.comtag:blogger.com,1999:blog-1920088135580776574.post-78851059772589184802009-02-17T07:43:00.000-08:002009-02-17T07:43:00.000-08:00Well, using the math Dr. Math has provided for us,...Well, using the math Dr. Math has provided for us, we can calculate that!<BR/><BR/>"hey hey we're the monkees" has 25 characters, so using the idea that the probability of the hypothetical 50-key keyboard being right on the first keystroke is 1/50, we get (1/50)^25. Our chance of all 25 characters being typed in the exactly correct order is 3.35x10^-43.<BR/><BR/>Using the same math to calculate a 95% probability of success, that means we'd have to make 2.69x10^42 attempts ( log(0.05) / log(1 - 3.35x10^-43) ).<BR/><BR/>At a rate of 200 characters per second, our monkeys can produce 8 blocks of 25 characters a second, which means 691,200 blocks per day, and 252,288,000 per year.<BR/><BR/>2.69x10^42 attempts, with 252 million attempts per year, works out to about 10^33 years, significantly less than what it would take to write The Hobbit, but still 10^22 ages of the universe.<BR/><BR/>I guess it's a good thing we have 1960s television producers to do these things for us!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1920088135580776574.post-22211816279908155212009-02-17T00:25:00.000-08:002009-02-17T00:25:00.000-08:00Great explanation.But I have to wonder, how long w...Great explanation.<BR/><BR/>But I have to wonder, how long would it take them to write "hey hey we're the monkees" ?Anonymousnoreply@blogger.com