November 18: Quick! Tell me what you get when you divide the number 992.587318, by 5,647.723? Stumped? Need a calculator? Well, thirteen-year-old Hiroaki Tsuchiya of Japan arrived at the answer in no time at a mental mathematics tournament in Kyoto: the right answer – 0.17575000013279688115015555826658. And, he did it without a calculator, too!
Hiroaki is adept at mental arithmetic multiplying, dividing, adding or subtracting large numbers that would make an accountant’s head spin. An Associated Press report that appeared in ‘The Asian Age’ says that Hiroaki is not the only one with such ability. For centuries, merchants, students and thousands of ordinary people throughout Asia have been calculating dizzying rows of numbers, using the same technique that Hiroaki has.
They have been doing it on an imaginary abacus. Experts say it’s possible for anyone to master the abacus if he or she starts young. But it takes hours of practice, a quickness of mind and immense powers of concentration. “If you space out, you lose”, says Hiroaki sagely.
Hiroaki should know. He became the youngest mental mathematician to win the tournament.
What is an abacus? The abacus is a mechanical aid used for counting. Addition, subtraction, division and multiplication can be performed on it.
The abacus is usually constructed out of wood and comes in varying sizes. The frame of the abacus has a series of vertical rods (at one time made of bamboo) on which a number of wooden beads are allowed to slide freely. A horizontal beam separates the frame into two sections, known as the upper deck and the lower deck.
Placing the abacus flat on a table or in one’s lap calculations are performed by manipulating the beads with the fingers of the hand. Each bead in the upper deck has a value of five; each bead in the lower deck has a value of one.
The beads serve as counters, which users push back and forth along metal rods, clicking their way through cube roots, addition and subtraction, and long division.
The abacus probably originated in Babylon, the ancient region occupying south-eastern Mesopotamia between the Tigris and Euphrates rivers (modern southern Iraq from around Baghdad to the Persian Gulf). Many regard it as the ancestor of the modern calculating machine and computer.
By the Middle Ages though, the use of the abacus, generally in the form of a large calculating board, had spread from the Arab world to Europe and to Asia as well. It reached Japan in the 16th century through China. The introduction of the Hindu-Arabic system of numerals, with its place value and zero, gradually replaced the abacus, though it still remains in use in Japan and China.
Skilled abacus users like Hiroaki prefer to imagine the beads rather than physically move them. This technique is called ‘anzan’, which translates roughly as ‘mental calculation’.
“Instead of thinking of the number one, imagine an apple in your pocket. It has shape, it’s concrete,” says a Tokyo abacus instructor, explaining the way in which the experts use the technique. “In anzan, we try to see the beads”, he adds. From the success rate of their calculations, it appears that the technique rarely fails.