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Tatsuya Shimizu,
Mental Math
Imaginary Abacus Calculates Strings of Numbers in Seconds

A boy uses an abacus to calculate at an abacus school just north of Tokyo. An ancient form of Japanese mathematics called anzan uses an imaginary abacus to compute complex series of numbers. (Shizuo Kambayashi/AP Photo)
 
By Ginny Parker
The Associated Press
K Y O T O, Japan, Oct. 30 — The contestants sit hunched over bare tables, some in sweatshirts, some in neckties. A small audience watches quietly, while judges pace the floor in wait for a response.
    
Suddenly, a teenager’s hand shoots up and a shout breaks the silence. “Done!” he calls out, and passes his answer sheet to a moderator.
     Within seconds, Hiroaki Tsuchiya has multiplied — in his head — a list of numbers that would make an accountant’s head spin. How does he do it? On an imaginary abacus, just as merchants, students and others have done throughout Asia for centuries.

Hours of Practice
Today, despite computers and calculators, the technique survives as a strenuous workout for the brain. Teachers say almost anyone can master it if they start young, although it takes hours of practice, mental dexterity and Herculean powers of concentration.
     “If you space out, you lose,” said Tsuchiya, who at age 13 recently became the youngest winner of a Kyoto tournament where Japan’s best mental mathematicians display their amazing feats.
     Tsuchiya, for example, takes only a few moments to solve a problem like 992.587318 divided by 5,647.723. And he has to go to the final digit of the answer: 0.17575000013279688115015555826658.
     Called “anzan,” which translates roughly as “mental calculation,” the technique springs from an age when the easiest way to work with large numbers was to use an abacus, a manual calculator introduced to Japan from China in the 1500s.
     The box-shaped instrument is made of beads that serve as counters, which users push back and forth along metal rods, clicking their way through cube roots, addition and subtraction, long division.

Quick But Not So Easy
But skilled abacus users often find it easier to just imagine the beads rather than physically move them.
     This is anzan, and those who master it can work faster than a clerk on an adding machine.
     “Instead of thinking of the number one, imagine an apple in your pocket. It has shape, it’s concrete.” said Koji Suzuki, a Tokyo abacus instructor. “In anzan, we try to see the beads.”
     That’s obvious at the Kyoto competition.
     When contestants’ race through problems, their fingers skitter across ghost abaci lying on the table. Others bob or rock in their seats, moving unconsciously to the internalized lilt of the sliding beads.
     As with many traditional Japanese arts, students of the abacus move through several ranks of expertise. The top title is given only to those who get perfect scores in four categories: multiplication, division, addition and subtraction, and bookkeeping — in which students calculate numbers written on a stack of paper.

Keeping the Brain Sharp
Instructors say there’s a gain from such mental acrobatics besides money saved on calculator batteries.
     Students who master anzan, they insist, tend to excel not only in math, but other subjects as well.
     “You have to be fast, and you have to be accurate,” said Kazuyuki Takayanagi, another instructor. “Your mind gets foggy if you’re using a calculator all the time.”
     Kimiko Kawano, a scientist at Nippon Medical School who has analyzed the brain activity of anzan experts, says learning the skill doesn’t hasten or improve brain development.
     But the concentration and imaging techniques needed for anzan — which exercises the right side of the brain rather than the analytic left, used for ordinary calculation — can be useful in non-mathematical situations, she added.
     “Students I’ve studied say that other subjects become easier for them,” Kawano said. “If someone makes a conscious effort to apply the techniques, they may be able to learn faster than others.”
     Then again, your average anzan whiz is probably more inclined to study than most.

Two Hours Practice Each Day
Abacus proficiency takes several nights a week of special classes, as Japanese schools have for the most part phased out such instruction, requiring only a few introductory lessons in the third grade.
     And young experts like the contest-winning Tsuchiya, who started working the beads in kindergarten, practice at least two hours a day — ”still not enough,” according to his teacher.
     Today, most young Japanese don’t use an abacus, much less perform calculations in their head. Older store clerks may use the instrument to make change or add up a restaurant tab, but such a scene is increasingly rare.
     “I’ve got an abacus at home, but it’s become just a toy for my toddler to play with,” said Tokyo housewife Ikuko Tsunokake, 26. “With calculators and computers, I have my doubts about its usefulness.”
     Takayanagi, the teacher, says abacus instruction has gone the way of other traditional Japanese pursuits like flower arranging or calligraphy, replaced by piano lessons, baseball games, English classes.
     “People used to need the abacus to get a job,” Takayanagi said. “Now, it’s just a brain exercise.”

Copyright 2000 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.

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