Science doesn’t usually tolerate frivolity but the infinite monkey theorem enjoys an exception. The question it poses is thoroughly outlandish: could an infinite number of monkeys, each given an infinite amount of time to peck away at a typewriter 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 pulls in computer science and astrophysics, among other disciplines.
In 1979, The New York Times reported on a Yale University professor who, using a computer program to try to prove this “venerable hypothesis”, managed to produce “startlingly intelligible, if not quite Shakespearean” strings of text. In 2003, British scientists put a computer into a monkey cage at the Paignton Zoo, UK. The outcome was “five pages of text, primarily filled with the letter S,” according to news reports. In 2011, Jesse Anderson, an American programmer, ran a computer simulation with much better results, albeit under conditions that — like the Yale professor’s — mitigated chance.
A new paper by Stephen Woodcock, a mathematician at the University of Technology Sydney, Australia, suggests that those efforts may have been for naught.
It 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 Curious George, let alone King Lear.
The idea for the paper came to Woodcock during a lunchtime discussion with Jay Falletta, a water-usage researcher at the University of Technology Sydney. The two were working on a project about washing machines, which strain Australia’s extremely limited water resources. They were “a little bit bored” by the task, Woodcock acknowledged. (Falletta is a co-author on the new paper.)
If resources for washing clothes are limited, why shouldn’t typing monkeys be similarly constrained? By neglecting to impose a time or monkey limit on the experiment, the infinite monkey theorem essentially contains its own cheat code. Woodcock, on the other hand, opted for a semblance of reality — or as much reality as a scenario featuring monkeys trying to write in iambic pentameter would allow — to say something about the interplay of order and chaos in the real world.
Even if the life span of the universe were extended billions of times, the monkeys would still not accomplish the task, the researchers concluded. Their paper calls the infinite monkey theorem “misleading” in its fundamental assumptions.
It is a fitting conclusion, perhaps, for a moment when human ingenuity seems to be crashing hard against natural constraints.
Low as the chances are of a monkey spelling out “bananas”, they are still “an order of magnitude which is in the realm of our universe”, Woodcock said. Not so with longer material such as the children’s classic Curious George by Margret Rey and H.A. Rey, which contains about 1,800 words.
Like other monkey theorem enthusiasts, Woodcock mentioned a famous episode of The Simpsons, in which crusty plutocrat C. Montgomery Burns tries the experiment, only to fly into a fury when a monkey mistypes 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 blurst of times”) would have been a stunning triumph over randomness. Outside cartoons, such successes are unlikely.
Then there’s the availability of monkeys. Of the more than 250 possible species, Woodcock selected chimpanzees, our closest genomic kin, to mimic the Bard. He enlisted 2,00,000 — the entire population of chimps currently on Earth — until the end of time. (Optimistically, he did not plan for the species’ dwindling or extinction. Nor did he consider constraints like the availability of paper or electricity; the study does not specify which platform the monkeys might use.)
Monkeys intent on re-creating Shakespeare would also need editors, with a strict reinforcement training regimen that allowed for learning — and a lot of it, since Woodcock set each monkey’s life span at 30 years. “If it’s cumulative, obviously, you can get somewhere,” said Richard Dawkins, an evolutionary biologist who discusses the typing monkeys in The Blind Watchmaker, his 1986 book about evolution. Unless the typing were “iterative”, though, Dawkins said in an interview, progress would be impossible.
The new paper has been mocked online because the authors purportedly fail to grapple with infinity. Even the paper’s title, “A numerical evaluation of the Finite Monkeys Theorem,” seems to be a mathematical bait-and-switch. Isn’t infinity a basic condition of the infinite monkey theorem?
It shouldn’t be, Woodcock seems to be saying. “The study we did was wholly a finite calculation on a finite problem,” he wrote in an email. “The main point made was just how constrained our universe’s resources are. Mathematicians can enjoy the luxury of infinity as a concept, but if we are to draw meaning from infinite-limit results, we need to know if they have any relevance in our finite universe.”
NYTNS
