It took all of 28 seconds. Hearing that, you have to wonder what went through her mind in that time. What kind of grey-cell-churning happened? What were the thoughts that flitted in and out?
Fascinatingly, it’s likely she herself couldn’t tell you. Much as you can’t explain how you keep your balance on a bicycle. Or the precise order in which you filled your pockets this morning with your wallet, a hanky, a pen and some loose change. And you’re walking down the street with all that in your pockets but suddenly you know, with no need to check, that you’ve forgotten your keys. How?
Those seconds must have gone something like that. In 1980, someone gave the mathematical prodigy Shakuntala Devi two numbers. She multiplied them in 28 seconds flat. You think, well, that’s easy. What’s the big deal in multiplying 12 and 20? Only, the numbers Shakuntala got were slightly larger: 7,686,369,774,870, and 2,465,099,745,779. Try multiplying those. Or even just writing them down. Or even just comprehending exactly how big they are. Were you able to tackle that?
Me? In a matter of seconds I can tell you authoritatively that the answer has 26 digits, the last being zero. Excuse me while I preen. And let’s understand: in the few seconds you and I took to begin work on this multiplication—yes, to even divining that last digit—Shakuntala was halfway to finishing the whole thing. (Answer: 18,947,668,177,995,426,462,773,730. See my earlier column here, “Difficult, but really difficult”).
What do you say about that kind of ability?
Now there are mathematical performers—“mathemagicians”—who have worked out techniques to do large calculations quickly. They build entire stage shows around such techniques. Arthur Benjamin is one of the best of these, mixing wit, charm and remarkable felicity with numbers into his performances. Look him up online and find his TED talk—don’t miss his hilarious “recap”—which ends with a spectacular, crowd-pleasing squaring of a number. He does this in his head, and he tells you exactly how his cells are churning. He takes a minute—twice as long as Shakuntala took for her multiplication—and when he’s done, his audience goes wild. As they should: none of us ordinary pen-pushers could do that much mentally.
Yet let’s put even this feat in perspective: the number Benjamin squares has five—count ‘em, five—digits. Not Shakuntala’s 13. Clearly, Shakuntala Devi’s abilities were of a different magnitude altogether. Every so often, a prodigy like her shows up and amazes folks with mathematical exploits. There’s no easy way to understand them, and they don’t easily understand themselves either. Remarkable people.
Shakuntala Devi died last Sunday. Two things about her life, in particular, interest me, are worth celebrating and, if you think about it, are even linked.
One was her lifelong effort to get people, especially students, familiar with mathematics. It’s one thing to do huge calculations quickly and wow an audience. It’s quite another to make the case that mathematics is not just essential to your life, but in fact adds to your life in measurable, pleasurable ways. That’s a hard sell, because it jars with the experience most of us have: teachers themselves are so frightened of numbers that their greatest skill is in faithfully passing on that fear to their students.
Contrast that to Shakuntala’s list of reasons to take an interest in math, enumerated in her book Mathability: Awaken the Math Genius in Your Child. Here are just three:
1) “It gives you a purpose, an aim, a focus that insures you against restlessness.”
2) “It makes you regard yourself with greater respect and in turn invokes respect from others around you.”
3) “It makes you more aware, more alert, more keen because it is a constant source of inspiration.”
Which of your various mathematics teachers ever cast the subject in such terms? (But celebrate those who did).
But the other thing that interests me about Shakuntala came, oddly enough, out of her marriage.
Her husband turned out to be homosexual and so their marriage crumbled in 1979. It’s a tribute to the lady that her reaction was not a bitter homophobia, but an effort to better understand homosexuality. The result was her book The World of Homosexuals. As she confessed: “My only qualification for writing this book is that I am a human being.” It argued for an entirely different way of considering gays—really, as just human beings: “Nothing less than full and complete acceptance will serve—not tolerance and not sympathy.”
And take these two sentences from inside the book: “Immorality does not consist in being different. It consists in not allowing others to be so.”
What a fine epitaph for the lady, even a reminder of her point above about respect. Go well, Shakuntala Devi. May we all become more aware and alert.
(Thanks to a tribute on orinam.net for some of this material).
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers will explore the joy of mathematics, with occasional forays into other sciences.
To read Dilip D’Souza’s previous columns, go to www.livemint.com/dilipdsouza