Infinite monkey theorem

The infinite monkey theorem states that a <a href="/facts/Monkey/ARjd5RRr">monkey</a> hitting keys independently and at <a href="/facts/Randomness/QJQBoEX5">random</a> on a <a href="/facts/Typewriter/CHE43FWP">typewriter</a> keyboard for an <a href="/facts/Infinity/cF506uD7">infinite</a> amount of time will <a href="/facts/Almost_surely/fWaxzpBA">almost surely</a> type any given text, including the complete works of <a href="/facts/William_Shakespeare/ohI96JTv">William Shakespeare</a>. More precisely, under the assumption of independence and randomness of each keystroke, the monkey would almost surely type every possible finite text an infinite number of times. The theorem can be generalized to state that any infinite sequence of independent events whose probabilities are uniformly bounded below by a positive number will almost surely have infinitely many occurrences.
In this context, "almost surely" is a mathematical term meaning the event happens with probability 1, and the "monkey" is not an actual monkey, but a <a href="/facts/Metaphor/xwsLaqJI">metaphor</a> for an <a href="/facts/Abstract_and_concrete/uNshak6S">abstract</a> device that produces an endless <a href="/facts/Random_sequence/z2uHfvK4">random sequence</a> of letters and symbols. Variants of the theorem include multiple and even infinitely many independent typists, and the target text varies between an entire library and a single sentence.
One of the earliest instances of the use of the "monkey metaphor" is that of French mathematician <a href="/facts/%25C3%2589mile_Borel/lF9PBa1T">Émile Borel</a> in 1913, but the first instance may have been even earlier. <a href="/facts/Jorge_Luis_Borges/UgfVLqdk">Jorge Luis Borges</a> traced the history of this idea from <a href="/facts/Aristotle/U2bDlBFW">Aristotle</a>'s <a href="/facts/On_Generation_and_Corruption/hqIeL5he">On Generation and Corruption</a> and <a href="/facts/Cicero/A37U7jaN">Cicero</a>'s <a href="/facts/De_Natura_Deorum/DF5eLmXm">De Natura Deorum</a> (On the Nature of the Gods), through <a href="/facts/Blaise_Pascal/Huy5LenL">Blaise Pascal</a> and <a href="/facts/Jonathan_Swift/000AjJvj">Jonathan Swift</a>, up to modern statements with their iconic simians and typewriters. In the early 20th century, Borel and <a href="/facts/Arthur_Eddington/b0jPBaSA">Arthur Eddington</a> used the theorem to illustrate the timescales implicit in the foundations of <a href="/facts/Statistical_mechanics/6zMsNYYG">statistical mechanics</a>.

Infinite monkey theorem open-in-new

Infinite monkey theorem