Science does not usually tolerate frivolity, but the infinite monkey theorem has an exception. The question it poses is totally preposterous: could an infinite number of monkeys, each given an infinite amount of time to peck at a typewriter (probably supplied with an infinite amount of paper), eventually produce , by pure chance, the complete works of William Shakespeare?
The problem was first described in a 1913 paper by French mathematician Émile Borel, a pioneer of probability theory. As modernity opened new scientific fronts, approaches to the theorem also evolved. Today the problem persists Computer Science and astrophysics, among other disciplines.
In 1979, The New York Times reported on a Yale professor who, using a computer program to try to test this “venerable hypothesis,” managed to produce strings of text that were “surprisingly intelligible, if not entirely Shakespearean.” In 2003, British scientists placed a computer in a monkey cage at Paignton Zoo. The result was “five pages of text, mostly filled with the letter S,” according to media reports. In 2011, Jesse Anderson, an American programmer, ran a computer simulation <a target="_blank" class="css-yywogo" href="https://www.telegraph.co.uk/technology/news/8789894/Monkeys-at-typewriters-close-to-reproducing-Shakespeare.html” title=”” rel=”noopener noreferrer” target=”_blank”>with much better resultsalthough in conditions that, like those of the Yale professor, mitigated the possibilities.
a new role Stephen Woodcock, a mathematician at the University of technology Sydney, suggests that such efforts may have been in vain: he concludes that there is simply not enough time until the universe expires for a defined number of hypothetical primates to produce a faithful reproduction of “George the curious,” let alone “King Lear.” Don't worry, scientists believe we still have googol years (10¹⁰⁰, or 1 followed by 100 zeros) until the lights go out. But when the end comes, the typographer monkeys will have made no more progress than their counterparts at Paignton Zoo, according to Dr Woodcock.
“That's not happening,” Dr. Woodcock said in an interview. The odds of a monkey typing the first word of Hamlet's famous soliloquy “To be or not to be” on a 30-key keyboard were 1 in 900, he said. You could argue that it's not bad, but each new card offers 29 new opportunities for error. The chances of a monkey spelling “banana” are “about 1 in 22 billion,” Dr. Woodcock said.
The idea for the article came to Dr Woodcock during a lunchtime discussion with Jay Falletta, a water use researcher at the University of technology Sydney. The two were working on a project about washing machines, which puts Australia's health to the test. extremely limited water resources. They were “a little bored” with the task, Dr. Woodcock acknowledged. (Mr. Falletta is a co-author of the new paper.)
If laundry resources are limited, why shouldn't typing monkeys be too? By not imposing a time or monkey limit on the experiment, the infinite monkey theorem essentially contains its own cheat code. Dr. Woodcock, on the other hand, opted for a semblance of reality (or as much reality as a scenario in which monkeys attempted to write in iambic pentameter would allow) to say something about the interplay of order and chaos in the real world. .
Even if the lifespan in the universe were extended billions of times, monkeys still wouldn't accomplish the task, the researchers concluded. Their article calls the infinite monkey theorem “misleading” in its fundamental assumptions. Perhaps it is an apt conclusion for a time when human ingenuity seems to collide forcefully with natural limitations.
However low the chances of a monkey spelling “banana” are, they are still “an order of magnitude that's in the realm of our universe,” Dr. Woodcock said. The same is not true with longer material such as the children's classic “Curious George” by Margret Rey and HA Rey, which contains around 1,800 words. The chances of a monkey replicating that book are 1 in 10¹⁵⁰⁰⁰ (a 1 followed by 15,000 zeros). And, at nearly 836,000 words, Shakespeare's complete works are approximately 464 times longer than “Curious George.”
“If we replaced every atom in the universe with a universe the size of our own, they would still be orders of magnitude away from making monkey typing successful,” Dr. Woodcock said.
Like other monkey theorem enthusiasts, Dr. Woodcock mentioned a famous episode of “The Simpsons,” in which the cranky plutocrat C. Montgomery Burns try the experimentonly to become enraged when a monkey misspells the opening sentence of Charles Dickens' “A Tale of Two Cities.” In reality, the monkey's achievement (“It was the best of times, it was the best of times”) would have been a surprising triumph over randomness.
Outside of cartoons, such successes are unlikely. First, there is cosmic death to consider. Many physicists believe that in 10¹⁰⁰ years (a much longer number than it might seem) entropy will have caused all the heat in the universe to dissipate. No matter how far away that moment is, experts I think it's coming.
Then there is the availability of overalls. Of the more than 250 possible species, Dr. Woodcock selected chimpanzees, our closest genomic relativesto imitate the Bard. He recruited 200,000 (the entire population of chimpanzees currently on Earth) until the end of time. (Optimistically, he did not plan for the decline or extinction of the species. Nor did he consider limitations such as the availability of paper or electricity; the study does not specify which platform the monkeys might use.)
Monkeys attempting to recreate Shakespeare would also need editors, with a strict reinforcement training regimen to allow for learning—and lots of it, since Dr. Woodcock set the life expectancy of each monkey at 30 years. “If it's cumulative, obviously you can get somewhere,” said Richard Dawkins, the evolutionary biologist, who analyzes typing monkeys in “The Blind Watchmaker,” his 1986 book on evolution. However, unless typing was “iterative,” Dr. Dawkins said in an interview, progress would be impossible.
The new document has been <a target="_blank" class="css-yywogo" href="https://x.com/BBCNews/status/1852265609389572102″ title=”” rel=”noopener noreferrer” target=”_blank”>mocked online because the authors supposedly fail to deal with infinity. Even the title of the paper, “A Numerical Evaluation of the Finite Monkey Theorem,” appears to be a mathematical bait-and-switch. Isn't infinity a basic condition of the infinite monkey theorem?
It shouldn't be that way, Dr. Woodcock seems to say. “The study we did was a totally finite calculation on a finite problem,” he wrote in an email. “The main point was how limited the resources of our universe are. “Mathematicians may enjoy the luxury of infinity as a concept, but if we want to extract meaning from the results of infinite limits, we need to know whether they have any relevance in our finite universe.”
This conclusion takes us back to the French mathematician Borel, who took an unlikely turn into politics and eventually fought the Nazis as part of the French Resistance. It was during the war that he introduced an elegant and intuitive law that now bears his name, which states: “Events with a sufficiently small probability never occur.” That's where Dr. Woodcock also lands. (Mathematicians who believe the infinite monkey theorem to be true cite two related minor theorems known as the Borel-Cantelli lemmasdeveloped in the years before the war.)
The new article offers a subtle commentary on the seemingly unbridled optimism of some ai advocates. Dr. Woodcock and Mr. Falletta note, without going into detail, that the monkey problem could be “very relevant” to current debates about artificial intelligence.
For starters, just as typist monkeys will never write “Twelfth Night” without superhuman editors watching over their shoulders, increasingly powerful artificial intelligences will require <a target="_blank" class="css-yywogo" href="https://www.wsj.com/tech/ai/openai-gpt5-orion-delays-639e7693″ title=”” rel=”noopener noreferrer” target=”_blank”>increasingly intensive human involvement and supervision. “If you live in the real world, you have to make limitations in the real world,” said Anderson, who led the monkey experiment in 2011.
“There's no free lunch, so to speak,” he said. Eric Wernera research scientist who heads the Oxford Advanced Research Foundation and has studied various forms of complexity. In a 1994 article about antsDr. Werner laid out a guiding principle that he believes applies equally to typing monkeys and current models of language learning: “Complex structures can only be generated by more complex structures.” Without constant healing, the result will be a procession of incoherent cards or what has become known as “ai down.”
A monkey will never understand Hamlet's anguish or Falstaff's bawdy humor. But the limits of ai cognition are less clear. “The big question in the industry is when will ai understand what you type,” Anderson said. “Once that happens, can ai surpass Shakespeare in artistic merit and create something as unique as Shakespeare created it?”
And when that day comes, “Will we become the ai monkeys?”
