Alex's Adventures in Numberland - Alex Bellos [59]
Conspicuously absent from proceedings in Leipzig, however, was perhaps the world’s most famous mathlete, the French student Alexis Lemaire, who prefers another yardstick to measure computational power. In 2007 Lemaire, aged 27, made international headlines when, at the Science Museum in London, he took just 70.2 seconds to calculate the thirteenth root of:
85,877,066,894,718,045,602,549,144,850,158,599,202,771,247, 748,960,878,023,151,390,314,284,284,465,842,798,373,290, 242,826,571,823,153,045,030,300,932,591,615,405,929,429,773, 640,895,967,991,430,381,763,526,613,357,308,674,592,650,724, 521,841,103,664,923,661,204,223
Lemaire’s achievement was undoubtedly the more spectacular. The number has 200 digits, which can barely be pronounced in 70.2 seconds. But did his feat mean that, as he claims, he is the greatest lightning calculator of all time? This is a matter of deep controversy in the calculation milieu, mirroring the battle almost 200 years ago between Zerah Colburn and George Bidder, both exceptional at their own type of sum.
The term ‘thirteenth root of a’ refers to the number that when multiplied by itself 13 times equals a. Only a fixed amount of numbers when multiplied by themselves 13 times equal a 200-digit number. (It is a large fixed amount. The answer is limited to about 400 trillion possibilities, all 16 digits long and beginning with 2.) Because 13 is prime and considered unlucky, Lemaire’s calculation was vested with an extra aura of mystery. In fact, 13 brings with it some advantages. For instance when 2 is multiplied by itself 13 times, the answer ends in 2. When 3 is multiplied by itself 13 times the answer ends in 3. The same is true for 4, 5, 6, 7, 8 and 9. In other words, the last digit of the thirteenth root of a number is the same as the last digit of the original number. We get this number for free, without having to do any calculation.
Lemaire has worked out algorithms, which he has not divulged, to calculate the other 14 digits in the final answer. Purists, possibly unfairly, say that his skill is less a feat of calculation and more one of memorizing huge strings of numbers. And they point out that Lemaire cannot find the thirteenth root of any 200-digit number given to him. At the Science Museum in London he was presented with several hundred numbers and allowed to select the one that he would do the calculation for.
Still, Lemaire’s performance was more in keeping with the tradition of the stage calculators of old. Audiences want to feel the ‘wow’, rather than understand the process. By contrast, at the Mental Calculation World Cup, Coto had no choice about the problem to be solved and used no hidden techniques when he multiplied 29,513,736×92,842,033. He simply used his 1-to 9-times tables. The fastest way to multiply eight digits by eight digits is using the Vedic sutra Vertically and Cross-Wise, which breaks the sum into 64 multiplications of single-digit figures. He managed to get the right answer in an average of less than 51 seconds. Knowing what he was doing made it less dazzling, even though it was obviously still a formidable feat.
As I talked with competitors in Leipzig, I discovered that many of them had fallen in love with speed arithmetic thanks to Wim Klein, a Dutch lightning calculator who was a celebrity in the 1970s. Klein was already a veteran of circuses and music halls when, in 1958, he was given a job by Europe’s top physics institute – the European Organization for Nuclear Research (CERN) in Geneva, providing calculations for the physicists. He was probably the last human calculator to have been employed as one. As computers developed, his skills became redundant, and in retirement he returned to showbiz, appearing frequently on TV. (Klein, in fact, was one of the first to promote thirteenth-root calculations.)
A century before Klein another human calculator, Johann Zacharias Dase, was also employed by the scientific establishment to do their sums for them. Dase was born in Hamburg and started performing as a lightning