Monkey and a poet's work ?
in [General Programming]
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From: gremnebulin on 11 Mar 2010 06:36 On 7 Mar, 18:02, j...(a)toerring.de (Jens Thoms Toerring) wrote: > In comp.unix.programmer Karthik Balaguru <karthikbalagur...(a)gmail.com> wrote: > > > I came across the 'Infinite Monkey Theorem'. > >http://en.wikipedia.org/wiki/Infinite_monkey_theorem > > I wonder how can a monkey hitting keys at random on > > a typewriter keyboard for an infinite amount of time will > > almost surely type a given text, such as the complete > > works of William Shakespeare ? > > What could be not in an infinite set? You mean infinite random set. > Well, instead of using a single monkey, giving it infinite > time, you can use a large number of monkeys for a shorter > time. Now, since the works of Shakespeare actually have been > written (assming that Shakespeare was a kind of monkey and > you don't instsit on the typewriter part), Neither infinite nor random, so not much of a proof of the monkey theorem
From: gremnebulin on 11 Mar 2010 06:47 On 8 Mar, 09:56, Nick Keighley <nick_keighley_nos...(a)hotmail.com> wrote: > > What could be not in an infinite set? > > lots of things. An infinite set doesn't have to contain all values > with equal probability. But we are talking about an inifinite *random* set > It is far from clear that pi expressed as a > decimal fraction and then mapped to ascii in some reasonable manner / > has/ to contain the complete works of shakespere. pi is far from random. See Chaitin.
From: Rainer Weikusat on 11 Mar 2010 09:07 gremnebulin <peterdjones(a)yahoo.com> writes: > On 7 Mar, 17:34, Karthik Balaguru <karthikbalagur...(a)gmail.com> wrote: >> Hi, >> I came across the 'Infinite Monkey Theorem'.http://en.wikipedia.org/wiki/Infinite_monkey_theorem >> >> I wonder how can a monkey hitting keys at random on >> a typewriter keyboard for an infinite amount of time will >> almost surely type a given text, such as the complete >> works of William Shakespeare ? > > How can a *random* process produce every > other work of literature and *avoid* that one? By being a random process. A random process can produce a sequence of alternating ones and zeroes for any arbitrarily large observation interval. But 'monkeys' don't act randomily, anyway.
From: Jonathan de Boyne Pollard on 10 Mar 2010 19:18 > >> >> shakespere didn't generate his plays by random means. >> > True. His use of randomization was confined to the spelling of his name. > Life imitates humour. One of the recent proposed extensions to the DNS protocol involves random capitalization of domain names.
From: Richard Heathfield on 14 Mar 2010 04:52
mike wrote: > In article <yKWdnfd7BvIrFgjWnZ2dnUVZ8txi4p2d(a)bt.com>, > rjh(a)see.sig.invalid says... >> Noob wrote: >>> Richard Heathfield wrote: >> <snip> >> >>>> We calculate this failure probability F by >>>> raising (1-p) to the power of the number of match attempts: >>>> >>>> F = (1-p)^2 = 0.99609375^2 = 0.9922027587890625 >>> I don't think so. The two attempts are not independent. >> It's a fair cop. Perhaps you could explain how to perform the >> calculation correctly? >> > Unfortunately, the calculation depends on the specific text*. So for > your binary version of Hamlet (or was it Othello) there is no simple > answer. > > * to prove this, imagine that the works of Shakespeare can be expressed > as a two character binary string (maybe the Condendsed Books version) Readers Digest, eat your heart out. :-) > and the random monkey has typed three symbols. If the condensed string > is '00' then there is a 5/8 chance that it will not appear in a random > three character string, but if the string is '01' then there is a 1/2 > chance it will not be found in a random three character string. ITYM 6/8 rather than 5/8? But anyway, yes, fair enough. Let me, then, ask the question a different way: My calculation, albeit flawed, might reasonably be said to give a ballpark figure. Is it possible to come up with a reasonably simple calculation that gives at least an order of magnitude reduction in the error level? -- Richard Heathfield <http://www.cpax.org.uk> Email: -http://www. +rjh@ "Usenet is a strange place" - dmr 29 July 1999 Sig line vacant - apply within |