Paradox: here's why a monkey could never rewrite Shakespeare 🐒

Could a monkey striking random keys, over infinite time, reproduce Shakespeare's work? The famous infinite monkey theorem now seems contradicted by the very limits of our Universe.

A new study conducted by Australian mathematicians challenges this idea, based no longer on an abstract concept of infinity, but on the temporal constraints of the Universe itself.


Stephen Woodcock and Jay Falletta from the University of Technology Sydney delved into this paradox, seeking to determine if a monkey could reproduce Shakespeare's works in a time span compatible with the lifetime of our Universe. To do so, they analyzed the probabilities of generating specific words with limited resources.

The original hypothesis assumes that, with an infinite number of monkeys and infinite time, every possible combination of letters would eventually be written. This principle of infinity, while useful for understanding probability and randomness, overlooks the very real constraints of our world.

To test this concept, the researchers simulated a keyboard with 30 keys including common letters and punctuation, and a typing speed of one keystroke per second. They also considered the Universe's estimated lifespan of 10¹⁰⁰ years, far greater than its current age of 13.8 billion years.

Furthermore, they modeled not just a single monkey, but also a population of 200,000 chimpanzees, equivalent to today's observed population on Earth. Despite this hypothetical collective effort, the results show that it would take far more time than the likely existence of the Universe to type even the 884,647 words constituting Shakespeare's complete works.

The team calculated that a single chimpanzee could, with a low probability, manage to type the word "bananas" during its lifetime, but generating an entire work is practically impossible. This places the claim among probability paradoxes, such as the St. Petersburg paradox or Zeno's paradox, where infinite resources lead to conclusions disconnected from finite realities.

The authors humorously add that increasing the typing speed or the number of monkeys would not change the outcome. Thus, while the infinite monkey theorem holds true in theory, it has little validity in our finite Universe.

In the age of artificial intelligence, this research also prompts deeper reflection: what is creativity? How do meaning and consciousness truly emerge, and can they be reduced to a mere random combination of symbols?