# Talk:Monkey typewriter theory

Made due to being a 'Wanted Page'. - All Hail Tuna 06:38, 18 September 2007 (EDT)

- I actually had a homework problem about this a few years ago. I think we were supposed to calculate the probability that 1000 monkeys would write
*Hamlet*within the age of the universe. One of the greatest homework problems I ever had; it was almost fun to do. Never thought I'd see it here!--Bayes^{update}00:33, 23 September 2007 (EDT)

## Contents

## Random letters[edit]

I don't know how but the random letters seemed to generate a quotebox on one refresh... **A**rmondiko**V**^{moral} 10:46, 6 March 2009 (EST)

- "Per Omen". Should I be worried? ĵ₳¥ášÇ♠ʘ do do da de do da de 10:48, 6 March 2009 (EST)
- Preferred the old one(with odd word/phrase appearing). Howsabout sticking "to be or not to BLOOP" and "Sale of two titties" etc. as letter choices
_{and marmite}10:53, 6 March 2009 (EST)

- Preferred the old one(with odd word/phrase appearing). Howsabout sticking "to be or not to BLOOP" and "Sale of two titties" etc. as letter choices

## Considerations on "Ze Math"[edit]

Something strikes me as odd regarding the orders of magnitude of the probabilities of obtaining Hamlet. It seems that somebody simply assumed that since the probability of randomly producing Hamlet is 1 chance in 10^{x}, given one hit each 0.1 second, 10^{y} seconds since the beginning of the universe and 10^{z} monkeys, the probability of having a complete script is one in 10^{x-y-z-1}.

As discussed in Improbable things happen, the real result is less instinctive. As given in the article, the probability of writing randomly Hamlet is .
Given 100,000 characters and 10 keyboard strikes a second, it takes a monkey 10^{5} seconds to write a script. Hence, a monkey would have written 10^{13} scripts since the beginning of the universe, and given 10 billion monkeys, the chance of them NOT writing Hamlet is given by .

Now I tried to calculate what that expression gives, but Maple keeps trying to convince me that . Even if my mean of calculating is far from optimal (for exemple, a monkey can't start a correct copy of Hamlet around the end of a "script" and finish it during the next), it would be nice if somebody with the calculating power could ask his computer to eyeball it. Even if the probability of them succeeding is still abysmal, it should be orders of magnitude greater than what appears in the article right now.

--Karlvaegen (talk) 21:41, 7 October 2011 (UTC)

- Well, I may not be the greatest at probability, but I can tell you why you keep getting one for . The limit of as n approaches to infinity is one. The size of (1/44)^100,000 is so minuscule as to not matter for all intents and purposes and whatever program you're using is almost certainly simply rounding it off. Klaus Vos (talk) 23:27, 7 October 2011 (UTC)

- That's not the only problem; the software can treat normally the given fraction on the expression on to , before the integers become too long for it to process. For some reason it can't convert the expression to decimal, which would seem more manageable for it and comprehensible for us. In search for an alternative, I also tried Wofram Alpha, which gave the cryptic probability of "0×" of obtaining Hamlet. I assume it means that the answer is smaller than 10
^{-71}, which doesn't give much info in our context.

- That's not the only problem; the software can treat normally the given fraction on the expression on to , before the integers become too long for it to process. For some reason it can't convert the expression to decimal, which would seem more manageable for it and comprehensible for us. In search for an alternative, I also tried Wofram Alpha, which gave the cryptic probability of "0×" of obtaining Hamlet. I assume it means that the answer is smaller than 10

- But the exact result isn't that important: given the binomial approximation of the first order and Bernoulli's inequality, we get that the chance of having a correct Hamlet script is no greater than 5,4×10
^{-164,323}(Wolfram Alpha calculation). That's smaller than what is published in the article, and the discripency is probably attribuable to the introduction of the narrow "script" concept I made. I will give it more tought, for the analysis is still not ripe for publishing. Karlvaegen (talk) 05:21, 8 October 2011 (UTC)

- But the exact result isn't that important: given the binomial approximation of the first order and Bernoulli's inequality, we get that the chance of having a correct Hamlet script is no greater than 5,4×10

## The Metro and typewriting monkeys[edit]

A cartoon strip in today's The Metro refers to the typewriting monkeys. 'What does this prove?' askes one character. 'That monkeys plagarize,' replies another. 171.33.197.73 (talk) 17:55, 30 January 2013 (UTC)

## The obvious flaws[edit]

Apart from being a clumsy metaphor for the random, there are obvious problems with it.

Firstly, it presumes the monkeys will type at random, rather than showing a preference for certain keys (probably the space bar due to its size).

Secondly, it presumes the monkey will not damage the materials (unlikely).

Thirdly, it presumes a monkey would want to sit at a typewriter for any length of time. (Why would it?)

Lastly, it's becoming increasingly hard to find typewriters anywhere, so it will probably never happen. :) - Albannach (talk) 01:16, 2 May 2013 (UTC)

- If you just assume a perfectly spherical monkey you'll find that all your issues disappear. Peter
^{mqzp}01:37, 2 May 2013 (UTC)

And how soon would they write 'A spectre is haunting cyberspace - nobody knows if you are a monkey'? 171.33.197.73 (talk) 16:27, 4 September 2013 (UTC)

## There's hope[edit]

This method may be workin' with them monkies: https://www.youtube.com/watch?v=cFYxRp9K9L4 5.38.148.124 (talk) 15:55, 2 October 2020 (UTC)balazs