Saturday, 13 June 2009

Monkeys and typewriters

There is a mistaken notion that an infinite number of monkeys, if given time and an infinite number of sturdy (monkey resistant) typewriters will come up with any number of historical texts.

Quite simply, this is false and is basically “rot”. It is a comment that demonstrates a true lack of awareness of numerical infinity. It excludes the range of an issue. For instance, there are an infinite number of separate non-integer values in the range of real numbers from 1.00... to 2.00... Although there are an infinite number of values in this mathematical range, there is no value that will or can ever equal 3.00. Nor will any ever be discovered. This is deductively provable based on the laws of algebraic mathematics.

The same applies to many other presumptions in life. This includes that of the monkeys and their proverbial writing devices. A monkey allowed to “bash” away at the typewriter does not ever hit the key sequencing required for the creation of a novel. It is not just an issue of rare events or the “black swan” problem; it is one of the mathematical range of the monkey’s actions.

A QWERTY keyboard is not designed in a manner that will allow the monkey to construct grammatically valid constructs with any success. The frequency of spaces to other mashed characters is wrong and the monkey falls into a pattern that never approaches discernible text, let alone a classic novel. In particular, the key distribution does not provide for a range of values that could ever create the desired outcome.

Rather than “bashing away” you need to have the monkey trained to select individual keys. This or course changes the nature of the process and increases the mathematical range. Even given an infinite value of some quantity does not mean that you have an infinite range of possible outcomes.