In one recent paper, Australian mathematicians Stephen Woodcock and Jay Falletta dispense with the so-called “infinite monkey theorem”. This theory proposes that a monkey given infinite time would eventually type the complete plays of Shakespeare by hitting random keys on a typewriter. The thought experiment, which is a common tool for explaining probability and randomness, takes into account infinite time and all possible outcomes, including literary masterpieces. However, Woodcock and Falletta’s research shows that such an accomplishment is a myth.
As they point out in their study, published in a peer-reviewed journal, the time it would take a monkey to spontaneously write Shakespeare’s complete works would far outstrip the lifespan of our universe. In their estimation, if a monkey typed repetitively and arbitrarily for billions of years, it would be incapable of creating a text at Shakespeare’s level.
Expanding on their analysis, the team considered what the chances were that all 200,000 or so chimpanzees in the world could type a key per second until the universe burnt down. With all these chimps at the keyboard, the chances of ever putting any significant part of Shakespeare’s works into print are virtually nonexistent. They calculated that a chimpanzee’s lifetime probability of typing the word “bananas” was 5%, while the probability of randomly writing a single coherent sentence such as “I chimp, therefore I am” would be 1 in 10 billion.
The infinite monkey theorem bases its calculations on the heat death universe-end hypothesis. This hypothesis proposes that the universe will just keep expanding and cooling, slowing down to nothing but a low level of energy and motion. With this cosmic bound, the researchers maintain that the infinite monkey theorem, though mathematically correct, is not truthful. The theorem is based on an infinite number of resources, but once one takes into account actual limitations (for instance, the universe’s lifetime), the chances of producing a useful text are tiny.
“This result places the theorem into a class of probability conundrums and paradoxes,” Woodcock said, noting that endless resources do not fit into the physical limits of the cosmos. Consequently, the infinite monkey theorem is an amusing exercise, but the researchers agree that no number of typing monkeys can generate Shakespeare in finite time and space.
