Science generally does not tolerate frivolity, but the infinite monkey theorem benefits from an exception. The question he asks is quite strange: Could an infinite number of monkeys, each given infinite time to peck away at a typewriter (supplied with an infinite quantity of paper, presumably), possibly 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 evolved as well. Today the problem sets in computer science and astrophysics, among other disciplines.
In 1979, the New York Times reported about a Yale professor who, using a computer program to try to prove this “venerable hypothesis,” managed to produce strings of text that were “surprisingly intelligible, if not quite Shakespearean.” In 2003, British scientists installed a computer in a monkey cage at Paignton Zoo. The result was “five pages of text, mostly filled with the letter S.” according to the information. In 2011, Jesse Anderson, an American programmer, carried out a computer simulation with much better resultsalbeit under conditions that – like those of the Yale professor – mitigated the odds.
A new paper by Stephen Woodcock, a mathematician at the University of Technology Sydney, suggests that these efforts may have been in vain: he concludes that there is simply not enough time before the universe expires for A finite number of hypothetical primates produce a faithful reproduction of “Curious George,” not to mention “King Lear.” Don’t worry, scientists think we still have a good few years left – 10¹⁰⁰, or 1 followed by 100 zeros – until the lights go out. But when the end comes, the typing 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 probability of a monkey typing the first word of Hamlet’s famous soliloquy “To be or not to be” on a 30-key keyboard was 1 in 900, he said. Not bad, one might say, but each new letter offers 29 new possibilities 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 chat with Jay Falletta, a water use researcher at the University of Technology Sydney. The two men were working on a project involving washing machines, which are putting pressure on Australia. extremely limited water resources. They were “a little bored” with the task, Dr. Woodcock admitted. (Mr. Falletta is a co-author of the new paper.)
If resources for washing clothes are limited, why shouldn’t typing monkeys be subject to similar constraints? By neglecting to impose 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 involving monkeys trying to write in iambic pentameter would allow – in order to say something about the interaction of order and chaos in the real world. .
Even if the lifespan of the universe were extended billions of times, the apes would still not accomplish their task, the researchers concluded. Their paper calls the infinite monkey theorem “misleading” in its fundamental assumptions. It is perhaps a fitting conclusion at a time when human ingenuity it seems to crash hard against natural constraints.
As low as the chances of a monkey spelling “banana” are, they are still “an order of magnitude that is within the realm of our universe,” Dr. Woodcock said. This is not the case with longer material such as the children’s classic “Curious George” by Margret Rey and HA Rey, which clocks in at around 1,800 words. The chances of a monkey reproducing this book are 1 in 10¹⁵⁰⁰⁰ (a 1 followed by 15,000 zeros). And, at nearly 836,000 words, the collected Shakespeare plays are about 464 times longer than “Curious George.”
“If we replaced every atom in the universe with a universe the size of ours, it would still take orders of magnitude for monkey typing to have any chance of success,” Dr Woodcock said.
Like other Monkey Theorem enthusiasts, Dr. Woodcock mentioned a famous episode of “The Simpsons,” in which crusty plutocrat C. Montgomery Burns try the experienceonly to become enraged when a monkey makes a typo in the opening sentence of Charles Dickens’ “A Tale of Two Cities.” In reality, the monkey’s exploit (“It was the best of times, it was the blur of times”) would have been a resounding triumph over chance.
Outside of cartoons, such successes are unlikely. First, we must consider cosmic death. Many physicists believe that in 10¹⁰⁰ years – a much larger number than it appears in type – entropy will have caused all the heat in the universe to dissipate. However distant this moment may be, experts I think it happens.
Then there is the availability of monkeys. From more than 250 possible species, Dr. Woodcock selected chimpanzees, our closest genomic relativesto imitate the bard. He enlisted 200,000 – the entire population of chimpanzees currently on Earth – until the end of time. (Optimistically, it did not predict the decline or extinction of the species. Nor did it take into account constraints such as the availability of paper or electricity; the study does not specify not what platform the monkeys could use.)
Monkeys eager to recreate Shakespeare would also need editors, with a strict reinforcement training program that would enable learning – and much of it, since Dr. Woodcock set each monkey’s lifespan at 30 years old. “If it’s cumulative, obviously you can come up with something,” said Richard Dawkins, the evolutionary biologist, who discusses typing monkeys in “The Blind Watchmaker,” his 1986 book on evolution. Unless input was “iterative,” Dr. Dawkins said in an interview, progress would be impossible.
The new document was mocked online because the authors apparently fail to tackle infinity. Even the title of the article, “A Numerical Evaluation of the Finite Monkey Theorem,” appears to be mathematical bait. Isn’t infinity a fundamental condition of the infinite monkey theorem?
That shouldn’t be the case, Dr. Woodcock seems to be saying. “The study we did was entirely a finite calculation on a finite problem,” he wrote in an email. “The main point made was how limited the resources of our universe are. Mathematicians can enjoy the luxury of infinity as a concept, but if we are to derive meaning from results at infinite limits, we need to know whether they have any relevance in our finite universe.
This conclusion dates back to the French mathematician Borel, who took an unlikely turn into politics, eventually fighting against 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 sufficiently low probability never occur.” This is also where Dr. Woodcock arrives. (Mathematicians who believe the infinite monkey theorem to be true cite two related minor theorems known as Borel-Cantelli lemmasdeveloped in the pre-war years.)
The new article offers a subtle commentary on the seemingly unbridled optimism of some supporters of artificial intelligence. Dr. Woodcock and Mr. Falletta note, without really elaborating, that the monkey problem could be “very relevant” to today’s debates about artificial intelligence.
For starters, just as monkey typists will never write “Twelfth Night” without superhuman editors watching over their shoulders, so increasingly powerful artificial intelligences will need increasingly intensive human input and monitoring. “If you live in the real world, you have to limit yourself to the real world,” said Mr. Anderson, who conducted the monkey experiment in 2011.
There is no free lunch, so to speak, said Eric Wernerresearch scientist who runs the Oxford Advanced Research Foundation and has studied various forms of complexity. In a 1994 article about antsDr. Werner outlined a guiding principle that he believes applies both to typing apes and to current models of language learning: “Complex structures can only be generated by more complex structures.” » Without constant conservation, the result will be a procession of incoherent letters or what we now call “Slop AI. »
A monkey will never understand the anguish of Hamlet or the bawdy humor of Falstaff. But the limits of AI Cognition are less clear. “The big question in the industry is when or if AI will understand what it writes,” Mr. Anderson said. “Once this happens, will AI be able to surpass Shakespeare in artistic merit and create something as unique as Shakespeare created?”
And when that day comes, “Will we become the AI apes?” »