Mnemonic - Articles
READER'S DIGEST, Nowember 1976
Meet the Human Computer
In the numbers game, this Dutch wizard is unbeatable
By Samuel Schreiner, Jr
On stage in a school auditorium in Lyons, France, stands a diminutive, bespectacled Dutchman named Willem (Wim) Klein. In the audience are 200 scientists and mathematicians who have given Klein a 200-digit number scrawled across eight blackboards. The test: to extract, without pencil, paper or machinery, the twenty-third root of that number in the shortest possible time.
Suddenly, the clock hands above the blackboards being turning. Klein looks at the number, then paces the stage, furiously muttering to himself in Dutch. The audience watches breathlessly as the clock moves on - five minutes ... eight ... ten.
At exactly 10 minutes 30 seconds, Klein takes a piece of chalk and writes a large number on the board. A computer quickly confirmed the answer and the audience loudly applauds the shattering of yet another mental arithmetic record by one of the world's handful of professionals in the field. Klein's feat - in March last year - puts him in the Guinness Book of Records for the second year running, and once more reinforces his claim to the title of "the human computer."*
Far from being limited to such stage stunts, 63-year-old Klein's mathematical dexterity has been put to serious use for 18 years at CERN (European Organization for Nuclear Research) outside Geneva. Among all the people who work at CERN, Wim Klein is unique: he is the only man whose flashing mind can still perform feats impossible tor CERN's humming hanks of computers.
Indeed, before these sophisticated machines were available, Klein was the computer at CERN. Whenever a scientist ran into a mathematical problem that, might take days, weeks, months to work out on paper, he presented it to Wim and got an almost instantaneous answer.
Nowadays, the scientists tend to put problems through computers, but in some ways a human mind like Wim's still has an edge over the machines. "Roughly speaking, the computer does; processes in a serial order, one after the other," explains physicist Jeremy Bernstein. "Wim, on the other hand, can see his combinations in parallel, and be discarding one that does not work while simultaneously trying out another. This accounts in part tor his astonishing speed."
And Wim's speed is indeed astonishing. On one occasion, he asked CERN physicist Henk Wind and myself for three two-digit numbers which he would multiply in his head while Wind raced him with a pocket computer. We gave him 21x16x87. In less than a second, Wim sputtered, "29232." Wind confirmed the answer a bit later. "I just couldn't put the numbers in fast enough," he said, and Wim modestly admitted, "I can beat the operator, but not the computer."
Not surprisingly, Wim's CERN colleagues consider him a natural wonder, a sort of human Matterhorn or Grand Canyon. Wim is inclined to take a less mysterious view of his abilities. He admits, tor example, that be couldn't function without the continuous guttural muttering that makes him sound like a machine gone berserk. "I don't see numbers - I hear them," Wim explains. "Once when I was young, a Dutch psychologist tested me by making me hold water in my mouth while I did a calculation. It slowed me right down."
In fact, nothing in Wim's story, as he tells it, would seem to put his feats out of the reach of a similarly dedicated person. One of two sons of a Jewish doctor, Wim was born in Amsterdam on December 4, 1912. With an average IQ, Wim was an indifferent student until about the age of ten when he arrived at what he now calls his first "blossoming": he encountered the factorization of numbers, breaking them down to the prime numbers of which they are composed. "For example," Wim explains, "21 is three times seven; 22 is two times 11; but 23 cannot be divided, so it is a prime number already."
So fascinated was young Wim by tearing numbers apart in his mind that "instead of playing football I was factorizing numbers up to 20000." As a result, Wim gradually committed to memory the multiplication tables up to 100, the squares up to 1000 and the prime numbers up to 10000. How does he memorize numbers? "I just keep saying them to myself - hammer them into my head - the way you learn a language." He also plays with them. If you stroll through a ear park with Wim, you'll hear him muttering Dutch under his breath while he keeps up a spritely patter in English - he's factorizing car number plates.
Wim's second blossoming came at 14 when a teacher, after explaining the use of logarithm tables, loaned them to him over the weekend. Wim began memorizing them at once, and now knows the whole table tip to 150 - making him one of only two people ever known to have accomplished this (the other was the German mathematician Ruckle).
Far from delighting his parents, Wim's talents alarmed them. When people began asking him to make public appearances, Dr. Klein feared Wim would be diverted from the sober pursuit of medicine. So Wim plodded on with his studies until his father's death in 1937, which was soon followed by the chaos of the war.
Free to abandon medicine after the war, Wim turned to show business. He started where he could - at the bottom. With a guitar player and an accordionist, he would perform mathematical stunts on street corners and in parks. Soon tiring of that, he began lecturing in grammar schools in Holland and Belgium and came to the attention of the Institute of Mathematics in Amsterdam, where he went to work as a calculator. But show business was - and still is - in Klein's blood, and today he appears as frequently as possible on radio and television. "It stimulates me," he says. "I like the challenge of an audience."
One of Wim's most popular stunts is something he calls the magic square. Give him a number and he'll draw a square of 16 blocks, into each of which he writes a different number. When he's finished, you find you can add it up, down and diagonally and get the number you gave him. In my case, it was 111. Into the four blocks across the top, Wim scribbled 18-32-40-21; into the first column on the left 18-38-25-30; and so on. The whole process took a mere two minutes.
We can all learn to use numbers more skilfully. The first essential, says Klein, is not to be afraid of them. Take them apart and make them work for you. "For example, most people know that 6x6 is 36," Wim says, "but if you give them 60x60, they're frightened, although the answer is simply 36 plus two noughts."
To handle numbers easily, he suggests, turn them into workable combinations you probably know already. Most people can handle tens and hundreds in multiplication since they've been taught that ten times anything is the number itself with a nought added: 10x3=30; 10x30=300. One hundred times anything is the number with two noughts added: 100x30=3000. Therefore, to multiply anything by 30, say, multiply by three and add a nought: 30x7=210.
With this in mind, breaking numbers down to the nearest tens and then adding or subtracting what's left over becomes the short way to mental multiplication. Take 21x12. It's 20x12, or 2x12=24 with a nought added to make 240, plus one more 12, making 252. Or another example: 23x97. The-short cut to this one is 23x100 (2300) minus 3x23 (69) for a result of 2231.
Wim notes unhappily that nobody seems interested in teaching such methods to the young. Indeed, he and scientists I talked to at CERN are worried that the combination of "new maths" being taught today and inexpensive pocket calculators will entirely wipe out the art of mental calculation.
The more I talked to Wim Klein, the more convinced I became that he does, indeed, have something to teach us all. For one thing, there is his self-renewing attitude towards life. You could compare him to an athletic champion whose natural endowment of good co-ordination would be meaningless without years of disciplined practice and the nerve to accept challenges. Another lesson we can learn from Wim is a better feeling for numbers. None of us is likely to become a Wim Klein any more than we are likely to become an Arthur Ashe. But by following Klein's methods, we can all learn to play our own level of the mathematical game more skilfully.
*In August this year, in front of 600 mathematicians and scientists Klein beat his own record by extracting the seventy-third root of a 507-digit number in 2 minutes 43 seconds.