Games of the maths genius: Compilation of geniuses

Off The Shelf

We usually write a date such as March 1, 2014 as 1/3/14. Americans, however, write the month first, and so that becomes 3/1/14. How many dates in a year are ambiguous in this notation? This problem was popularised by Martin Gardner in his Mathematical Games column in the Scientific American. You should be able to work that out in your head.

“If you look over all my columns (they are collected in 15 books), you’ll find that they steadily become more sophisticated mathematically. That was because I was learning math,” said Gardner. Generations of mathematicians grew up on that column. Gardner had no training in maths but did more to popularise it than anybody else. Recreational mathematics, an apparent oxymoron, slid easily into our lexicon.

In his book Fear No Evil, the Soviet dissident Natan Sharansky has written about how the only book he was allowed in prison was a collection of Gardner’s logical puzzles. A study of these helped Sharansky outwit his interrogators.

Years ago when I met Roger Penrose, the physicist and philosopher of science, some of the excitement was caused by the fact that there was now just one degree of separation between Martin Gardner and me. Gardner had been a schoolboy hero, continued to be one as I took fledgling steps towards a career in science, and became an even bigger favourite when I exchanged science in university for the arts.

James Randi, the magician and debunker of pseudo-science frequently had to explain to audiences that Gardner actually existed and was not an amalgamation of Isaac Asimov, Arthur C Clarke, a famous magician and a well-known literary critic. For such was Gardner’s range. He also wrote The Annotated Alice, on Lewis Carroll’s classic as well as learned essays on GK Chesterton, Coleridge, Eliot and Joyce.

“Pick up anything he wrote. You’ll smile and learn something,” says the mathematician Persi Diaconis. Gardner was both hugely amused by the mysteries of the world and hugely amusing about them.
This is Gardner’s Centenary Year (he died in 2010), and for those who ask themselves What Would Martin Gardner Tweet, the answer is on @WWMGT. A recent tweet asks: What letter is in not in the name of any number from 0 through 99, yet is in the name of every number greater than 99 and less than 1 million?

“I wrote a book on relativity mainly to teach myself the theory,” says Gardner in his recently-released autobiography Undiluted Hocus-Pocus, and in those 12 words gives us a glimpse into the mind of one of the 20th century’s giants in philosophy, mathematics, literary analysis, scientific scepticism and magic. Some of us learn by reading, others by writing.

Gardner was 95 when he wrote that book, one of over a 100 he published. Among his fans were the artist Salvador Dali and the novelist Vladimir Nabokov. There is a playful reference to Gardner in one of Nabokov’s novels. Dali was intrigued by Martin’s writings on the 4-dimensional cube, a feature of his own painting Crucifixion.

Yet for all his achievements as a debunker of pseudo-science (Fads and Fallacies in the Name of Science was an early book), sceptic and literary sounding board, Gardner’s autobiography is a strange mix of the banal and the brilliant. This is partly because events that seem hilarious when they occur often lose their sting when recalled out of context, and partly because the attempt here is not to tease —  as some of Gardner’s best writing is — but to explain himself. And that, for an essentially modest man is clearly a difficult task.

Gardner is at his best when he shines the light away from himself, and enlivens discussions on maths and magic, on philosophy and cheating in the name of science. For the true autobiography, there is   The Whys of a Philosophical Scrivener, a “book of essays about what I believe and why”. There is no compulsion here to speak of birth and background, military training and early jobs, just a series on why he is what he is and not something else.

Thus, Gardner tells us why he is not a pragmatist or why he is not an anarchist or indeed why he is not an atheist. This last caused a few eyebrows to be raised when the book appeared — a sceptic who believed in god? But Gardner’s argument was far more subtle and nuanced than that. This ‘essential’ Gardner was given a scathing review by George Groth in the New York Review of Books: “He defends a point of view so anachronistic,” said Groth, “so out of step with current fashion, that were it not for a plethora of contemporary quotations, his book could have been written at the time of Kant.” The last sentence of the review said: “George Groth is one of Martin Gardner’s pseudonyms.” How can you not admire a writer who takes a hatchet to his own book under an assumed name?

The best introduction to Martin Gardner is his collection of essays, The Night is Large.

Here, sieved through Gardner’s exquisite mind are essays on symmetry, quantum mechanics, relativity, string theory, Werner Heisenberg, HG Wells, cultural relativism, artificial languages, the irrelevance of Conan Doyle, Sigmund Freud, William James, George Perec, fractal music, Newcomb’s paradox, free will, Isaiah Berlin, god and much more.

The Whys of a Philosophical Scrivener tells us what Gardner is not. He begins his autobiography by telling us what he is. “I am a mysterian,” he says in the prologue. Mysterians (a list which includes Penrose and Noam Chomsky among others) “share a conviction that no philosopher or scientist living today has the foggiest notion of how consciousness, and its inseparable companion free will, emerge, as they do, from a material brain.”

Go figure, as the Americans say. Which brings me back to the problem we started this column with. Each month has eleven ambiguous dates (a date such as 5/5/14   is not ambiguous), and thus we have 132 in a year.

The author is currently Editor, Wisden India Almanack