Infinite Monkey Theorem

This theorem can be stated, ‘Given enough time, a monkey randomly striking keys on a typewriter will ‘almost surely’ end up producing a meaningful text and eventually will bang out a copy of Hamlet.’  Crazy as it seems, the infinite monkey theorem can be proved using basic probability (the trick is having either an infinite number of monkeys or an infinite amount of time, or both).  The emergence of such intricate complexity from randomness is counterintuitive to brains that have evolved to see pattern and meaning everywhere.  ‘Almost surely’ is a mathematical term with a precise meaning, and the monkey is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols.

This theorem supposed that the monkey would almost surely type every possible finite text an infinite number of times, thus with enough time, almost everything is possible.  The reasoning behind that supposition is that, given infinite time, random input should produce all possible output.  The Infinite Monkey Theorem translates to the idea that any problem can be solved, with the input of sufficient resources and time.  In the early 20th century, Émile Borel, a mathematician, and Sir Arthur Eddington, an astronomer, used the Infinite Monkey Theorem to illustrate timescales implied within statistical mechanics.  Statistical mechanics is a branch of theoretical physics that uses probability theory to study the average behavior of a mechanical system, where the state of the system is uncertain.

The implication of this theorem is that, with enough resources thrown at a problem, any technical challenge becomes solvable.  The modern version, places the monkey on a digital computer with keystroke instructions typing computer programs at random following programs whose bits are the result of coin tossing.  If anyone ever tosses the infinite monkey theorem in your direction, point out that a monkey has a one in twenty-six chance of typing the first letter correctly.  Getting the second letter correct sees the probability rise to 1 in 676.  After just the first 15 letters of Hamlet, the chance of getting the next letter right is one in thousands of trillions!  Despite the sheer absurdity of the infinite monkey theorem, it is still being used to show that complexity can arise from random mutations and this theorem actually helped people believe that evolution could possibly happen.

5 thoughts on “Infinite Monkey Theorem

  1. Grid G3! IShi ogev 5!%!<…oh, sorry I was randomly hitting keys with my eyes closed to see if anything legibly came up?… well "Grid" is a word so I just proved the theory of evolution! More importantly.. how's your hurricane preparations going?

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