Monkey and a poet's work ?
in [General Programming]
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From: Frederick Williams on 10 Mar 2010 10:46 Jens Thoms Toerring wrote: > > In comp.unix.programmer Karthik Balaguru <karthikbalaguru79(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 will have not > only the works of Shakespeare, but also all his works > with all kinds of typos, readers digest versions etc.;-) It is not an infinite set, it is an infinite sequence. If the characters in the sequence are treated as digits and the sequence is construed as a real number (with an invisible "decimal" point at its left hand end say) and if that real number is normal in �mile Borel's sense, then you'll get the works of Shakespeare. But does random equal normal? -- I can't go on, I'll go on.
From: Jonathan de Boyne Pollard on 8 Mar 2010 21:36 > >> >> shakespere didn't generate his plays by random means. >> > It was random that there even was a Shakespeare. > .... but not that there was an Isaac Newton. That is according to his epitaph, at any rate.
From: Eric Sosman on 10 Mar 2010 14:58 On 3/8/2010 4:56 AM, Nick Keighley wrote: > [...] > shakespere didn't generate his plays by random means. True. His use of randomization was confined to the spelling of his name. -- Eric Sosman esosman(a)ieee-dot-org.invalid
From: mike on 10 Mar 2010 17:45 In article <4B97BED3.D3D182AA(a)tesco.net>, frederick.williams2(a)tesco.net says... > Jens Thoms Toerring wrote: > > > > In comp.unix.programmer Karthik Balaguru <karthikbalaguru79(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 will have not > > only the works of Shakespeare, but also all his works > > with all kinds of typos, readers digest versions etc.;-) > > It is not an infinite set, it is an infinite sequence. If the > characters in the sequence are treated as digits and the sequence is > construed as a real number (with an invisible "decimal" point at its > left hand end say) and if that real number is normal in Émile Borel's > sense, then you'll get the works of Shakespeare. But does random equal > normal? > It doesn't require an infinite sequence, just a sufficiently long one. The complete works comprise 888,429 words or approximately 4.86 million characters so, even without compression, a random binary string of around 10^(11,700,000) 0/1 characters should be long enough to almost guarantee to contain an ascii representation of the works. Bigger than a google, but much smaller than a googleplex. Mike
From: gremnebulin on 11 Mar 2010 06:33
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? |