Someone once said maths is like love — a simple thing that tends to get complicated. Yes, maths is simple, but only if one understands it. It must be very simple, for example, for Srikar Varadaraj, the 14-year-old who held Viswanathan Anand to a draw in simultaneous chess at the International Congress of Mathematicians (ICM) in Hyderabad last month.
It was evidently complicated for the bureaucrats who got Anand’s citizenship wrong; for them, the details in the world chess champion’s passport just didn’t add up to make him Indian.
But sometimes even the brightest of mathematicians get it wrong, the likes of those who presented papers at the ICM — a 113-year-old event, held in India for the first time, and in a developing country for only the second time. And when these geniuses goof up, the consequences can be devastating, puzzling or plain comical.
Approximating art
At the root of the problem is the mathematician’s obsession with beauty and elegance. But why are numbers — and symbols — beautiful? The eccentric Hungarian mathematician Paul Erdos put it thus: “It’s like asking why is Beethoven’s Ninth Symphony beautiful. If you don’t see why, someone can’t tell you.” Broadly, it means that equations are beautiful, especially if they lead to some blissful truth. But then, some beautiful equations, like some beautiful women, can be deceptive.
Peter Woit, a mathematical physicist at Columbia University and author of the acclaimed Not Even Wrong, says: “The use of sophisticated mathematical techniques that few people understand can sometimes obscure basic problems.”
That is the constrained language of a mathematician, and Woit is a very good one. In layman’s language, elegant but improper use of maths can screw up the world.
A formula for chaos
It sounds straight out of Ripley’s Believe It or Not, but much of the chaos of the global financial crisis can be traced to a single formula — the Gaussian copula. The name sounds bovine, but is far from benign.
The Gaussian copula is a grand theme. It wanted to be in finance what the string theory wants to be in physics — a ‘theory of everything’. It was a formula created to “model default correlations, so that collateralised debt obligations (CDOs) could be accurately priced”, says Felix Salmon, the American financial journalist and analyst who brought the formula to the attention of the wider world in a groundbreaking article in Wired last year (CDOs are a type of sophisticated financial tool to represent different types of debt and credit risk).
If you unscramble it, what Salmon means is that the formula was trying to figure out if different types of bonds were correlated, and whether they were sailing or sinking together.
For Wall Street, the Gaussian copula acted as the proverbial philosophers’ stone. Minting money, traditionally, had never been without sweat and grime. But here at last was a shortcut to reap untold riches from the fuzziness of the financial world. All it required was variables like bonds, stocks or securities to travel from one end of the formula and congeal into hard currency by the time they reached the other.
For a time it worked. Spectacularly. So much that even Moody’s, the credit rating agency, factored the Gaussian copula into its methodology for evaluating CDOs. This happened in 2004. But within four years, the model had taken over, and then taken apart, the financial system.
The idea of the formula was simple: to predict the pattern of risk. The man who published it in 2000, David Li, is considered a genius even now (though, since the financial crisis hit, he has melted into the vast homeland, China). But it did not factor in unpredictable or risky events of great magnitude, like millions of Americans defaulting on home loans. “In the case of the Gaussian copula, I believe what got obscured was certain very large sources of risk,” Woit says.
The beauty myth
“Just because a formula is complex does not mean that it is right, and is a good model,” says Nigel Goldenfeld, a physics professor at the University of Illinois and founder of the investment software firm NumeriX. Indeed, an elegant formula can actually mislead the practitioner by its beauty.
“The elegance means that the practitioner can be deluded, and the complexity... the arcane mathematics means that the practitioner (the trader in the financial context) does not understand what is going on — and therefore takes appalling risks.”
Topping the ranks of the people who get besotted with the beauty of elegant formulas are physicists. Sometimes the beauty of the maths underlying the physics is so overwhelming that it very much overtakes reason. When this happens, physics stops being science, as Woit points out in Not Even Wrong, Lee Smolin illustrates in The Trouble With Physics, and Lawrence Krauss suggests in Hiding In The Mirror.
Take string theory, for example. Smolin, a founding member of the Perimeter Institute for Theoretical Physics, Waterloo, Canada, writes in The Beauty Myth, the second chapter of his book: “The most cherished goal in physics, as in bad romance novels, is unification. To bring together two things previously understood as different and recognise them as aspects of a single entity... is the biggest thrill in science.”
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