If you sit sufficient monkeys in front of sufficient typewriters and give them sufficient time, eventually their random banging will reproduce the works of Shakespeare.
Thus asserts the Infinite Monkey Theorem, a thought experiment that considers the possibility that a cumulation of random events will eventually produce something of great meaning. Nobody really expects a bunch of small furry primates to come out with poetry that will sing to the soul… and that, according to new research, is probably just as well.
Mathematicians Stephen Woodcock and Jay Falletta of the University of Technology Sydney in Australia have crunched the numbers, and determined that there won't be enough time in the entire estimated lifespan of the Universe for monkeys to accidentally hammer out a sequence of key-presses that matches Hamlet.
"The Infinite Monkey Theorem only considers the infinite limit, with either an infinite number of monkeys or an infinite time period of monkey labor," Woodcock explains. "We decided to look at the probability of a given string of letters being typed by a finite number of monkeys within a finite time period consistent with estimates for the lifespan of our Universe."
Experiments have been conducted to test the validity of the theorem, but somewhat less well known is the Finite Monkey Theorem, where the number of monkeys and the amount of time are limited. This is more consistent with what we might experience in the real world, where both monkeys and time are expected to eventually run out.
The calculations were based on different numbers of 'monkeys' between 1 and 200,000 – the estimated current global population of chimpanzees – in front of keyboards with varying numbers of keys, typing at one keystroke per second for a googol years – an estimated time until the Universe undergoes heat death, which would effective put a stop to any simian tapping.
By altering these variables, they were able to perform calculations on how long it would take to produce various works within various timeframes. And, well, the results aren't promising for fans of The Bard.
A single chimpanzee typing on a 30-key keyboard has a 5 percent chance of coming out with the word "bananas" within its own lifetime.
The reproduction of the entire 884,647-word works of Shakespeare from 200,000 chimps in a googol years? It just ain't happening. The probability is 6.4 x 10-7448254 – it may as well be zero.
In fact, we'd be extremely lucky to just get the entire ~1,800-word text of the children's book Curious George by the end of the Universe. The team's calculations reveal a probability of 6.4 x 10-15043 for that one.
The finding, the researchers say, therefore classifies the theorem as a paradox, alongside others in which the infinite and finite scenarios have directly contradictory results. These include the St. Petersburg paradox, concerning infinite rewards in a game of chance nobody would pay to enter; Zeno's dichotomy paradox, which proposes that an object covering infinite fractions of a distance can never arrive at its destination; and the Ross-Littlewood paradox, which suggests a vase can be filled with an infinite number of balls.
None of these scenarios work in a finite real world; and this, Woodcock and Falletta have demonstrated, is also the case for the Infinite Monkey Theorem.
"It is not plausible that, even with possible improved typing speeds or an increase in chimpanzee populations, these orders of magnitude can be spanned to the point that monkey labor will ever be a viable tool for developing written works of anything beyond the trivial," they write in their paper.
"We have to conclude that Shakespeare himself inadvertently provided the answer as to whether monkey labor could meaningfully be a replacement for human endeavor as a source of scholarship or creativity. To quote Hamlet, Act 3, Scene 3, Line 87: 'No'."
The work has been published in Franklin Open.