Saturday, February 1, 2003
M I N D  G A M E S


When Abacus was beaten
Aditya Rishi

We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover up all the tracks, to not worry about the blind alleys or describe how you had the wrong idea first, and so on. So there isn't any place to publish, in a dignified manner, what you actually did in order to get to do the work.

— Richard Philips Feynman (1918-1988) in his Nobel Lecture in 1966

MR Processor 'the computer' to Later 'the calculator': "Talk about false pride; I just logged onto my network and found out that abacus, once, lost to Dr Richard Feynman, physicist number genius who led the probe into the exploding of space shuttle Challenger. In the chapter 'Lucky Numbers' in his book 'Surely, You're Joking, Mr Feynman!', Dr Feynman narrates an incident that happened in Brazil:

A Japanese man came into the restaurant; he was trying to sell abacuses. He started to talk to the waiters, and challenged them: He said he could add numbers faster than any of them could do. The waiters didn't want to lose face, so they said, "Yeah, yeah. Why don't you go over and challenge the customer over there?"

 


The man came over. The waiters brought me a paper and pencil. The man asked a waiter to call out some numbers to add. He beat me hollow, because while I was writing the numbers down, he was already adding them as he went along. "Multiplicação!" he said. Somebody wrote down a problem. He beat me again, but not by much, because I'm pretty good at products. The man, then, made a mistake: he proposed we go on to division. What he didn't realize was, the harder the problem, the better chance I had. We did a long division problem. It was a tie.

"Raios cubicos!" he says with a vengeance. Cube roots! He writes down a number: 1729.03. He starts working on it, mumbling and grumbling; Meanwhile I'm just sitting there. I write down 12 on the paper. After a little while, I've got 12.002. The man with the abacus wipes the sweat off his forehead: "Twelve!" he says. "Oh, no!" I say. "More digits!" I add on two more digits. He finally lifts his head to say, "12.01!" The waiter are all excited and happy. They tell the man, "Look! He does it only by thinking, and you need an abacus! He's got more digits!"

The number was 1729.03. I happened to know that a cubic foot contains 1728 cubic inches, so the answer is a tiny bit more than 12. The excess, 1.03 is only one part in nearly 2000, and I had learned in calculus that for small fractions, the cube root's excess is one-third of the number's excess. So all I had to do is find the fraction 1/1728, and multiply by 4 (divide by 3 and multiply by 12). I was lucky that he chose 1729.03." (To be continued; write at The Tribune or adityarishi99@yahoo.co.in)