King and Emperor by Harry Harrison. Chapter 19, 20, 21, 22

His voice rose to a strangled yell, he fought rage down again and continued with the thoughts that had buzzed round and round his head like weary bees. “Now, I am not a fool, Solomon. One hundred and twenty is to one hundred as six to five, is it not? So I must make the other things as six to five. Or is it five to six? No, lower the weight thrown. Lower the three hundred pounds as six to five. Or raise the weight throwing as five to six, the ten hundred pounds. Now how many fives are there in ten hundred? How many fives in ten, there are two. So two hundred, and then what do I do with that, I take six of them. Oh, I can find the answer, Solomon, in the end. But it takes me as long as it takes a slow ox to plow a furrow. And I end up doing it with these little stones for markers because I forget what I’m doing!”

Shef yelled with honest fury for a moment and hurled his handful of pebbles scattering into the blue water of the harbor. As if in answer, the fort floating almost a mile away beyond the stone jetties sent a rock at extreme range splashing into the dock. The laboring men averted their eyes, tried not to seem aware of what was happening.

“And all the time,” Shef concluded, “I know that I am doing the whole thing with the simplest numbers. Because really any rock we use will weigh three hundred-pound bags and maybe twenty-seven over. And I will need to raise the range not twenty yards out of a hundred, but seventeen out of ninety-five.”

He squatted by a patch of sand. “I wish I had learned the trick of numbers from some skilled Roman. See,” he drew a V in the sand. “I know that is for five.” He added a stroke to make a VI. “That is for six. Or the other side,” he drew a IV, “that is for four. But how to make all this answer my question, that I do not know. Only the ancient folk of Rome were wise enough for that art.”

Solomon pulled his beard, marveling internally. Fortunate that Moishe had not heard this. Or Elazar. Their remarks about barbarians would have become even more barbed. “I do not think,” he said carefully, “I do not think it is the ancient Romans you should go to for an answer.”

Shef looked up, eye gleaming. “You mean there is an answer?”

“Oh yes. They could have told you in Cordova, if you had asked. But even here, many men know the answer to what you seek. Every merchant, every astronomer. Even Mu’atiyah could have told you.”

“What is the secret then?” Shef was on his feet.

“The secret?” Solomon had been speaking in Anglo-Norse, which he now spoke as familiarly as any man in the fleet. Now he shifted to Arabic. “The secret is al-sifr.”

“Al-sifr? That means empty. That means nothing. How can nothing be the secret, are you mocking me, longbeard…?”

Solomon held up a hand. “There is no mockery. But look, this is not for prying eyes, see how everyone is staring. Come with me to the courtyard. I promise you, by the time men dowse their lamps you will be a greater arithmeticus than any Roman is or ever was. I will show you the devices of al-Khwarizmi the Great.”

Solomon led a silent king towards the shaded court.

Little more than an hour later, Shef looked up from the table of fine white sand on which he and Solomon had been drawing. His one eye was wide with astonishment. Carefully he swept his hand over the sand-tray, obliterating all the markings on it except the column of ten signs which Solomon had showed him to begin with.

“Let’s try it again,” he said.

“Very well. Draw your lines.”

Shef drew five vertical lines down the sand, making four columns. He drew two horizontal ones across the top, three more across the bottom.

“We will try to solve your range problem, only with harder numbers than the ones you told me. Let us say that you have thrown a boulder of two hundred and eighty pounds, and it has reached one hundred and twenty yards, six score in your language. But you need to reach one hundred and forty, seven score. Your throwing weight was eleven hundred and forty pounds. You must increase that in the proportion of seven to six. So, first, we must multiply eleven hundred and forty by seven and then divide by six.”

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