The soroban made arithmetic so easy, he found it hard to believe that in his grandfather’s day, merchants still used calculating rods. Of course, not every merchant was as adept as Takuma; he could even divide one number into another.
This magnificent soroban, of course, was not intended for a crass commercial use. Rather, it was for managing the accounts of a great estate. Takuma was proud to be considered worthy to help Shigetsuna-tono with those of New Nippon itself. Unfortunately, there weren’t enough hours in the day to do all of the calculations himself, together with all the other tasks he had been assigned.
“Gombei!”
That was his assistant, who hurried in. He had been engaged in what he thought was brilliant conversation with the daughter of the family who lived next door.
“Sir!”
“I need these calculations done by sunset. Remember, they are for the grand governor, so all the multiplications and divisions must be done twice, and make sure you get the same result each time.”
“Yes sir. Uh, what if a pair of calculations disagree?”
“Then redo them until you get the same number three times in a row!”
* * *
Mathematics was not Gombei’s strong point. Especially when he could hear Shima singing a risque folk song as she went about her chores.
“Oh! my darling boy!” she sang. “Though first we slept a hiro apart, by rolling we came together . . .”
Gombei’s only chaperone was Takuma’s son, Hiraku. He was playing with toys in a corner.
Shima was still singing: “Yes, we slowly came together . . .”
Gombei stuck his head out the door. “Hey, Shima, the acoustics are better in here. Why don’t you come in and keep me company?”
“Perhaps another time, Gombei dear,” said Shima. “Hurry up, and you can take a walk with me.” She paused. “If, that is, you can finish before the hour of the Ape.” That was late afternoon.
Gombei was hurrying, all right. But the saying was, “he who chases two hares will not even catch one.” Trying to do the arithmetic faster just led to more mistakes, and thus more rechecks.
Finally, Shima strode in. “How much longer are you going to be, Gombei?” No “dear” this time.
“I’ll be out as soon as these fucking beads give me the same answer three times in a row for 256 times 3473.”
“Don’t look at me,” said Shima, “I’ve never touched a soroban in my life.”
“It’s 889,008,” said Hiraku, the forgotten boy in the corner.
“Really?” said Gombei. “I got that the first time. But then I got 888,548.”
“Oh. Then you did the last part on the wrong rod,” Hiraku explained. The last part, by the Japanese method, being the multiplication of the leftmost digit of the 256 and the rightmost of the 3473.
“Hiraku, how did you know the correct number?” asked Shima. “You weren’t even looking at the soroban, let alone moving the beads.”
“I just picture the beads in my head.”
* * *
Shima mentioned Hiraku’s mathematical ability to her mother, who told Hiraku’s mother, who told his father. Takuma had not, it turned out, taught Hiraku how to use the soroban. He had apparently learned by watching and listening to the lessons that Takuma had given to the apprentice.
Takuma was shocked and pleased to discover that Hiraku was not only adept at addition, subtraction and even multiplication, but that he had figured out for himself that the soroban could be used to calculate in hexadecimal as well as in decimal. It had this ability because the soroban was copied from the Chinese Suan Pan, and in China there were sixteen liang-ounces to the jin-pound, and sixteen dou of grain to the yu.
The following week, Katakura Shigetsuna invited Takuma to the castle. It was a mark of approval, especially since the invitation included Takuma’s family.
“Your calculations have been of great assistance in the construction of the castle in a timely and accurate manner, Takuma. I am promoting you, effective immediately.”
Takuma thanked him profusely.
“Keep up the good work. Now, who’s the little fellow hiding behind you? And has he any skills yet?”
“My son. He is very skilled in mathematics.”
“Oh?”
Takuma had Hiraku do some mental calculations for the councillor’s entertainment.
“I have a copy of Jinko-ki I can lend you,” Shigetsuna declared. “Why don’t you help Hiraku study it? A talent like his should be nurtured, for the good of the realm.” Jinko meant “small-large,” and ki was a treatise, so the manuscript was a study of numbers, from smallest to largest. It was written by Yoshida Shichibei Koyu in 1627, and it taught, among other things, how to extract square and cube roots using the soroban.