Can monkeys really type all of Shakespeare?

Science generally does not tolerate frivolity, but there are exceptions to the infinite monkey theorem. The questions it raises are completely outlandish. An infinite number of monkeys, each given an infinite amount of time, pecking at a typewriter (presumably stocked with an infinite amount of paper) eventually, by pure chance, write William Shakespeare?

This problem was first described in a 1913 paper by French mathematician Emile Borel, a pioneer in probability theory. As the modern era opened up new scientific frontiers, approaches to theorems evolved as well. Today, this problem extends to computer science and astrophysics, among other fields.

In 1979, The New York Times used a computer program to prove this “venerable hypothesis,” producing strings of text that were “surprisingly understandable, if not entirely Shakespearean.” Reported on a successful Yale University professor. 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,” the report said. In 2011, American programmer Jesse Anderson ran a computer simulation similar to the Yale professor's, albeit under mitigating conditions, and got much better results.

A new paper by mathematician Stephen Woodcock from the University of Technology Sydney suggests these efforts may have been in vain. The paper concludes that there simply isn't enough time before the universe dies for a defined number of hypothetical primates to produce loyal primates. Not only “King Lear'' but also “Curious George'' are recreated. Don't worry. Scientists believe there are still 10¹⁰⁰, or 100 1s followed by 0s, in googol years before the lights go out. But Dr Woodcock says that even when the end comes, the typing monkeys will not have made as much progress as the monkeys at Paignton Zoo.

“That's not happening,” Dr. Woodcock said in an interview. He said there was a 1 in 900 chance that the monkey would type the first word of Hamlet's famous “To be or not to be” soliloquy on a 30-key keyboard. Some might argue that that's not a bad thing, but every time a new letter arrives, there are 29 new chances for a mistake to occur. Dr Woodcock said the chance that a monkey would spell “banana” was “approximately 1 in 22 billion”.

The idea for the paper 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 involving washing machines that put a strain on Australia's extremely limited water resources. They were “a little bored” with the job, Dr. Woodcock admitted. (Mr. Falletta is a co-author of the new paper.)

If the resources for washing are limited, why shouldn't the monkey's input be limited as well? If we neglect to impose time or monkey constraints on the experiment, the infinite monkey theorem has no inherent meaning. will contain its own cheat code. Dr. Woodcock, on the other hand, tries to write something that resembles reality, or in iambic pentameter, in order to say something about the interplay of order and chaos in the real world. I chose the reality of .

The researchers concluded that even if the lifespan of the universe were extended billions of times, monkeys would still be unable to accomplish that mission. Their paper calls the infinite monkey theorem “misleading” in its basic assumptions. Perhaps this is a fitting conclusion at a moment when human ingenuity seems to be colliding violently with the constraints of nature.

Dr Woodcock said that while it was unlikely that a monkey would spell “banana”, it was still “an order of magnitude in our realm of space”. This is not the case with longer materials, such as the children's classic Curious George by Margret Ray and H.A. Ray, which contains approximately 1,800 words. The probability that the monkey will duplicate the book is 1 in 10¹⁵⁰⁰⁰ (1 followed by 15,000 zeros). And Shakespeare's collection of plays is about 836,000 words long, which is about 464 times as long as Curious George.

“Even if we replaced every atom in the universe with a universe our size, we would still be an order of magnitude away from having a high chance of successful ape typing,” Woodcock said.

Like other Monkey Theorem enthusiasts, Dr. Woodcock referenced a famous episode of The Simpsons. In that episode, surly plutocrat C. Montgomery Burns attempts an experiment in which a monkey mistypes the first sentence of Charles Dickens' “A” and becomes furious. A story of two cities. ” In reality, the ape’s feat (“It was the best of times, it was the worst of times”) would have been an amazing victory over chance.

Outside of comics, such success is unlikely. First, there is the death of the universe to consider. Many physicists believe that over the course of 10¹⁰⁰ years (much longer than it seems), entropy dissipates all the heat in the universe. That moment may be far away, but experts think it's coming.

Then there is the availability of monkeys. Out of more than 250 possible species, Dr. Woodcock chose the chimpanzee, its closest genomic relative, as the subject of Bard's imitation. He enlisted 200,000 chimpanzees, the entire current population of chimpanzees on Earth, to work together until the end of time. (He optimistically did not plan for this species' decline or extinction, nor did he consider constraints such as the availability of paper or electricity.) It is not specified whether it may be used.)

A monkey trying to recreate Shakespeare also needs an editor. Woodcock has given each monkey a lifespan of 30 years, which requires a rigorous reinforcement training regimen to enable them to learn. Evolutionary biologist Richard Dawkins said, “Obviously, if you add it up, you can get somewhere.” Dawkins discusses the typing monkey in his 1986 book on evolution, The Blind Watchmaker. But Dr. Dawkins said in an interview that progress would not be possible unless typing was “repetitive.”

The new paper has been ridiculed online because the authors are said to be failing in their fight against infinity. Even the title of the paper, “Numerical evaluation of the finite monkey theorem,” seems like a mathematical bait-and-switch. Isn't infinity the basic condition of the infinite monkey theorem?

That can't be true, Dr. Woodcock seems to say. “The work we did was entirely a finite computation on a finite problem,” he wrote in an email. “The main issue is how constrained the resources of our universe are. Mathematicians can enjoy the luxury of conceptual infinity, but if we want to derive meaning from an infinite number of results… , we need to know whether they are relevant in our finite universe.”

This conclusion goes back to the French mathematician Borel. Borel unexpectedly turned to politics and eventually fought against the Nazis as part of the French Resistance. It was during the war years that he introduced the sophisticated and intuitive law that now bears his name: “An event of sufficiently low probability will never occur.'' Dr. Woodcock also arrives there. (Mathematicians who believe the infinite monkey theorem is true cite two related minor theorems, known as the Borel-Cantelli lemmas, developed before the war.)

A new paper offers a nuanced comment on the seemingly unbridled optimism of some artificial intelligence proponents. Woodcock and Falletta note that the monkey issue may be “very relevant” to today's discussions about artificial intelligence, although they do not elaborate.

First of all, just as a typing monkey would never write “Twelfth Night” without the supervision of a superhuman editor, increasingly powerful artificial intelligence will require increasingly intensive human input and supervision. would require. “If you live in the real world, you have to have real-world limitations,” said Anderson, who conducted experiments on monkeys in 2011.

Eric Warner, a research scientist who runs the Oxford Foundation for Advanced Research and has studied various forms of complexity, says there is no such thing as a free lunch. In a 1994 paper on ants, Dr. Werner offered the guiding principle that “complex structures can only be produced by more complex structures.” This, in his view, applies equally well to typing monkeys and today's language learning models. Without continued curation, the result is a disjointed matrix of characters, or what has come to be known as “AI slop.”

The monkey will never understand Hamlet's anger or Falstaff's vulgar humor. However, the limits of AI's cognition are not so clear-cut. “The big question in the industry is when, or if, AI will understand what you're writing,” Anderson said. “Once that happens, will AI be able to surpass Shakespeare in artistic value and create something as unique as Shakespeare created?”

And when that day comes, will we become monkeys to AI?