‘Infinite monkey theorem’ debunked by Australian mathematicians

Two Australian mathematicians say they have debunked an old adage, that if given an infinite amount of time, a monkey pressing keys on a typewriter would eventually write the complete works of William Shakespeare.

Known as the “infinite monkey theorem”, the mathematical thought-experiment has long been used to explain the principles of probability and randomness.

However, a new peer-reviewed study led by Sydney-based researchers Stephen Woodcock and Jay Falletta has found that the time it would take for a typing monkey to replicate Shakespeare’s plays, sonnets and poems would be longer than the lifespan of our universe.

Which means that while mathematically true, the theorem is “misleading”, they say.

As well as looking at the abilities of a single monkey, the study also did a series of calculations based on the current global population of chimpanzees, which is roughly 200,000.

The results indicated that even if every chimp in the world was enlisted and able to type at a pace of one key per second until the end of the universe, they wouldn’t even come close to typing out the Bard’s works.

There would be a 5% chance that a single chimp would successfully type the word “bananas” in its own lifetime. And the probability of one chimp constructing a random sentence – such as “I chimp, therefore I am” – comes in at one in 10 million billion billion, the research indicates.

“It is not plausible that, even with improved typing speeds or an increase in chimpanzee populations, monkey labour will ever be a viable tool for developing non-trivial written works,” the study says.

The calculations used in the paper are based on the most widely accepted hypothesis for the end of the universe, which is the heat death theory.

Despite its name, the so-called heat death would actually be slow and cold.

In short, it’s a scenario in which the universe continues to both expand and cool – while everything within it dies off, decays, and fades away.

“This finding places the theorem among other probability puzzles and paradoxes… where using the idea of infinite resources gives results that don’t match up with what we get when we consider the constraints of our universe,” Associate Prof Woodcock said in a statement about the work.