Saturday, March 07, 2009

More About Infinite Monkeys (Part 2): The Proof of the Pudding

It turns out that Wikipedia has a very good article about the Infinite Monkey Theorem,* which bears reviewing:

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 a given 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 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 probability of a monkey typing a given string of text exactly, as long as, for example, Shakespeare's Hamlet, is so tiny that, were the experiment conducted, the chance of it actually occurring during a span of time of the order of the age of the universe is minuscule but not zero.

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 On Generation and Corruption 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 apologists on the one hand, and Richard Dawkins on the other, have argued about the appropriateness of the monkeys as a metaphor for evolution.

So it is. It turns out that the theorem has been subjected to a certain amount of experimental analysis. To wit:

One computer program run by Dan Oliver of Scottsdale, Arizona, according to an article in The New Yorker, came up with a result on August 4, 2004: After the group had worked for 42,162,500,000 billion billion monkey-years, one of the "monkeys" typed, “VALENTINE. Cease toIdor:eFLP0FRjWK78aXzVOwm)-‘;8.t" The first 19 letters of this sequence can be found in "The Two Gentlemen of Verona". Other teams have reproduced 18 characters from "Timon of Athens", 17 from "Troilus and Cressida", and 16 from "Richard II" .... [another experiment] produced this partial line from Henry IV, Part 2, reporting that it took "2,737,850 million billion billion billion monkey-years" to reach 24 matching characters: "RUMOUR. Open your ears; 9r"5j5&?OWTY Z0d..."

So computers simulating virtual monkeys producing random text weren't very successful.

And as for actual simians? Researchers ran one experiment that, as my eldest son dryly observed, "didn't end well":
In 2003, lecturers and students from the University of Plymouth MediaLab Arts course used a £2,000 grant from the Arts Council to study the literary output of real monkeys. They left a computer keyboard in the enclosure of six Celebes Crested Macaques in Paignton Zoo in Devon in England for a month, with a radio link to broadcast the results on a website. One researcher, Mike Phillips, defended the expenditure as being cheaper than reality TV and still "very stimulating and fascinating viewing".

Not only did the monkeys produce nothing but five pages[31] consisting largely of the letter S, the lead male began by bashing the keyboard with a stone, and the monkeys continued by urinating and defecating on it. The zoo's scientific officer remarked that the experiment had "little scientific value, except to show that the 'infinite monkey' theory is flawed".


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