Picture this: an army of monkeys furiously typing away at random. Could they, given enough time, recreate the works of Shakespeare? According to a recent study, the answer, while playful, suggests that you’d be waiting around seven googol years – about the lifespan of seven universes – before the first full text emerged.
This idea comes from the Infinite Monkeys Theorem, a classic thought experiment that claims if you had infinite monkeys typing for infinite time, they’d eventually produce anything, even Shakespeare, simply by chance. It’s a clever way to illustrate probabilities over infinity. But in the real world, we don’t have infinite monkeys or infinite time. So, mathematicians from Australia decided to put the theory to a practical test, asking: What would it look like if we brought it down to Earth and into our own cosmic timeframe?
To simplify, they envisioned a team of monkeys typing on keyboards with 30 keys (the alphabet and some punctuation) at one key per second. “We wanted to estimate the chances of typing specific strings with a limited number of monkeys in a timeframe that actually fits within the universe’s lifespan,” said Dr. Stephen Woodcock, one of the study’s authors.
With shorter phrases, things look fairly hopeful. There’s about a 5% chance that a single chimp could type “bananas” within its 30-year life. But, if you had 200,000 chimps – roughly the current world population – typing until the universe ends, the chance of “bananas” appearing becomes nearly inevitable.
When they tried longer phrases, though, things became more bleak. For instance, the odds of a single chimp typing “I chimp, therefore I am” over a lifetime are about 0.000000000000000000000001%. However, if you stretch that over the universe’s lifespan and a full population of chimps, the odds look slightly better.
Moving to full literary works, the numbers become almost absurd. Typing out all 1,800 words of Curious George has odds sitting more than 15,000 zeros after the decimal. To type Planet of the Apes, you’d be looking at nearly 700,000 zeros. And for the complete works of Shakespeare, which contain around 885,000 words? You’d need to write down about 7.5 million zeros before you find any hope.
The researchers concluded that, for a team of 200,000 monkeys, it would take four universe lifespans to type Curious George, six to reach Planet of the Apes, and seven to complete Shakespeare’s work.
This study ultimately sheds light on the limits of applying infinite concepts to our finite universe. Sure, it’s entertaining, but it’s also a humbling reminder of the vast improbability involved. The researchers closed with a nod to Shakespeare himself, borrowing a line from Hamlet to sum up their findings: “To quote Hamlet, Act 3, Scene 3, Line 87: ‘No.’”
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