Infinite Monkey Theorem

[Purple & Green]

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It's clearly bollix though, because it must be statistically impossible for us go to 106 years without winning the Scottish Cup, a run of something like 333 Scottish Cup games since 1902.

[Northern Ireland Hibby]

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type or create a particular chosen text, such as the complete works of William Shakespeare. In this context, "almost surely" is a mathematical term with a precise meaning, and the "monkey" is not an actual monkey; rather, it is a vivid metaphor for an abstract device that produces a random sequence of letters ad infinitum. The theorem illustrates the perils of reasoning about infinity by imagining a vast but finite number, and vice versa. The age of the universe is dwarfed by the gulf of time it would take a monkey to type Hamlet, so in a physical sense it would never happen. This approach is directly applied to the theory of quantum mechanics.

Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. The history of these statements can be traced back to Aristotle's Metaphysics and Cicero's De natura deorum, through Blaise Pascal and Jonathan Swift, and finally to modern statements with their iconic typewriters. In the early 20th century, Émile Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics. Various Christian apologetics on the one hand, and Richard Dawkins on the other, have argued about the appropriateness of the monkeys as a metaphor for evolution.

Today, popular interest in the typing monkeys is sustained by numerous appearances in literature, television and radio, music, and the Internet. A "Monkey Shakespeare Simulator" website got as far as 24 characters with "RUMOUR. Open your ears; ". In 2003 a humorous experiment was performed with six Sulawesi crested macaques, but their literary contribution was five pages consisting largely of the letter S, besides attacking and defecating on the typewriter. Researchers concluded that the infinite monkey theorem does not apply to real monkeys; despite their entertaining methods, they make poor random number generators.


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[Briant]

It is indeed bollix, as it says in Wikipedia;

Probabilities

"Ignoring [Only Registered Users Can See Links. Click Here To Register], spacing, and capitalization, a monkey typing letters uniformly at random has one chance in 26 of correctly typing the first letter of [Only Registered Users Can See Links. Click Here To Register]. It has one chance in 676 (26 times 26) of typing the first two letters. Because the probability shrinks [Only Registered Users Can See Links. Click Here To Register], at 20 letters it already has only one chance in 26²⁰ = 19,928,148,895,209,409,152,340,197,376, roughly equivalent to the probability of buying 4 [Only Registered Users Can See Links. Click Here To Register] tickets consecutively and winning the jackpot each time. In the case of the entire text of Hamlet, the probabilities are so vanishingly small they can barely be conceived in human terms. The text of Hamlet, even stripped of punctuation, contains well over 130,000 letters which would lead to a probability of one in 3.4×10¹⁸³⁹⁴⁶.
For comparison purposes, there are only about 10⁷⁹ atoms in the [Only Registered Users Can See Links. Click Here To Register] and only 4.3 x 10¹⁷ seconds have elapsed since the [Only Registered Users Can See Links. Click Here To Register]. Even if the universe were filled with monkeys typing for all time, their total probability to produce a single instance of Hamlet would still be less than one chance in 10¹⁸³⁸⁰⁰. As [Only Registered Users Can See Links. Click Here To Register] and [Only Registered Users Can See Links. Click Here To Register] put it, "The probability of Hamlet is therefore zero in any operational sense of an event…", and the statement that the monkeys must eventually succeed "gives a misleading conclusion about very, very large numbers." This is from their textbook on [Only Registered Users Can See Links. Click Here To Register], the field whose statistical foundations motivated the first known expositions of typing monkeys."



And the probability now is that Hibs will win 10 cups in a row
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[Brian]

Originally Posted by Briant
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It is indeed bollix, as it says in Wikipedia;

That doesn't mean it's bollix, just staggeringly improbable. If the numbers are truly infinite then it would happen.

[PILTONSTANY]

Originally Posted by Briant
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It is indeed bollix, as it says in Wikipedia;

Probabilities

"Ignoring [Only Registered Users Can See Links. Click Here To Register], spacing, and capitalization, a monkey typing letters uniformly at random has one chance in 26 of correctly typing the first letter of [Only Registered Users Can See Links. Click Here To Register]. It has one chance in 676 (26 times 26) of typing the first two letters. Because the probability shrinks [Only Registered Users Can See Links. Click Here To Register], at 20 letters it already has only one chance in 26²⁰ = 19,928,148,895,209,409,152,340,197,376, roughly equivalent to the probability of buying 4 [Only Registered Users Can See Links. Click Here To Register] tickets consecutively and winning the jackpot each time. In the case of the entire text of Hamlet, the probabilities are so vanishingly small they can barely be conceived in human terms. The text of Hamlet, even stripped of punctuation, contains well over 130,000 letters which would lead to a probability of one in 3.4×10¹⁸³⁹⁴⁶.
For comparison purposes, there are only about 10⁷⁹ atoms in the [Only Registered Users Can See Links. Click Here To Register] and only 4.3 x 10¹⁷ seconds have elapsed since the [Only Registered Users Can See Links. Click Here To Register]. Even if the universe were filled with monkeys typing for all time, their total probability to produce a single instance of Hamlet would still be less than one chance in 10¹⁸³⁸⁰⁰. As [Only Registered Users Can See Links. Click Here To Register] and [Only Registered Users Can See Links. Click Here To Register] put it, "The probability of Hamlet is therefore zero in any operational sense of an event…", and the statement that the monkeys must eventually succeed "gives a misleading conclusion about very, very large numbers." This is from their textbook on [Only Registered Users Can See Links. Click Here To Register], the field whose statistical foundations motivated the first known expositions of typing monkeys."



And the probability now is that Hibs will win 10 cups in a row
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Ah but if we tinker with this......................
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[egb_hibs]

Originally Posted by Brian
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That doesn't mean it's bollix, just staggeringly improbable. If the numbers are truly infinite then it would happen.

I agree. In terms of infinity, the numbers talked of are themselves vanishingly small.