A life in numbers

BOOK EXTRACT

Childhood friends Suri and Bal, a management consultant and a journalist with a maths degree, have together written this novel of two generations of a mathematically inclined family. In it, a young Ravi is introduced to the fascination of maths by Bauji, his grandfather. When he later discovers that Bauji went to prison for blasphemy in America because he thought that ultimate truth could be approached through mathematics, he is impelled to reinvestigate the case. There is a host of interesting characters (many historical) and an unusual, if maths laden, approach to storytelling.

Yesterday I found the calculator my grandfather gave me on my 12th birthday. It had fallen behind the bookcase and I saw it when I was rearranging the study. I had not thought about it for years, yet when I held it, it seemed as familiar as ever. The "I" in Texas Instruments was missing, as it had been for all but two days of its life; the buttons still made a confirming clicking sound when pressed; and when I put in some new batteries, the numbers on the LCD shone through with a blazing greenness, more extravagant than the dull grey of the modern calculator. My grandfather had intended this calculator to mark a change in my life "" a new direction. As it turned out, it did mark a change, though not the one he had in mind.

I punched in the number 342 without thinking about it. It was the same number I had entered 25 years ago when the calculator was brand new.

"Want to see some number magic?" my grandfather had asked as he watched me push the buttons more or less randomly. I was sitting in his room completely taken by his birthday present, if not quite sure what to do with it. He put his notebook down, temporarily giving up on the math problem that had resisted solution since morning.

"Yes, Bauji!" I had rushed over to him.

"Enter any three-digit number in your calculator and do not let me see it." That is when I had first entered 342, the same three digits I entered now. "OK. Now enter the same number again, so you have a six-digit number," he had said. I punched in 342 again, so now I had 342342 entered in my calculator. Now, I do not know the number you have in there, Ravi, but I do know that it is evenly divisible by 13."

By "evenly divisible" he meant that there would be no remainder. For example, 9 is evenly divisible by 3 but not by 4.

Bauji's claim seemed fantastic to me. How could he know that my number, randomly chosen and completely unknown to him, would be evenly divisible by 13? But it was! I divided 342342 by 13 and I got 26334 exactly, with no remainder.

"You're right,"I said, amazed.

He wasn't finished, though. "Now, Ravi, I also know that whatever number you got after you divided by 13 is further divisible by 11." He was right once again. 26334 divided by 11 was 2394. Why was this working? "Take the number you got and divide by 7. Not only will it divide evenly, but you will be surprised at what you get." He had begun his pacing and I knew that he was as excited as I was.

I divided 2394 by 7 and I got 342! "Oh! Oh! It's the number I started with! Bauji, how did this happen?"

My grandfather just sat there, grinning at the completeness of my astonishment. "You will just have to figure that one out Ravi," he said, walking out to check the state of his tomato plants, the newest additions to his vegetable garden in the backyard. He seemed to be the only person who could grow tomatoes in New Delhi's dry summer heat.

The first thing I did was to check the divisions by hand. My hypothesis was that Bauji had rigged the new calculator somehow. But no, the numbers worked out exactly the same way when I did the long divisions by hand. Next, I decided to try this with some other three-digit numbers. The same thing worked every time. Whatever the repeated number, I could divide it evenly by 13, 11, and 7, and each time I got back to the number I started with. A few minutes of checking and rechecking convinced me that this property was true of any three-digit number. I tried doing the same thing with four-digit numbers and it did not work any more. Neither did it work for two-digit numbers. What was going on?

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A Certain Ambiguity: A mathematical novel

Author: Gaurav Suri and Hartosh Singh Bal

Publisher: Penguin Viking

Pages: 281

Price: Rs 450