King and Emperor

After a few further moments explanation Shef sent Steffi off to find a gang and practice attaching the cloth.

“Don't light anything, mind,” he warned him. “Just figure out how they have to be rigged to open properly. Go easy with the saltpeter crystals, it'll take time to make more.”

As the squint-eyed ex-slave went off, Shef's mind went back to the counterweight machine no doubt already approaching. His eye fell on the still-bandaged Tolman. The lad had been silent and downcast ever since he came round from his long unconsciousness, not surprising with his two comrades dead. Could another boy be used? No, there was no doubt that Tolman was the most experienced flyer, the most likely to succeed. Yet he would have to be persuaded.

Shef's face took on the reasonable and friendly air that his closest associates had come to dread, the expression that showed he was about to use someone.

“Well, Tolman,” he began. “Like to try a flight over nice soft water this time? Get your nerve back before it goes, eh?”

The boy's lip trembled, he blinked back tears. Dumbly, obediently, he nodded. Shef patted him carefully on his deep-grazed shoulder, led him away, shouting as he went for Cwicca, Osmod, and the most skillful of the kitemen and catapulteers.

As he had been during the long northern winter seven years before, Shef was amazed at the speed with which—sometimes—an idea could become reality. Before the day was out the materials for the new-style siege catapult had been assembled, including the massive beam that would be its throwing arm, stripped without complaint from the keel of a coasting vessel still on the stocks. It helped, of course, that there was no ordinary work to be done. The entire population of Septimania was idle, and when they thought of what a sack by Imperial troops would mean, anxious to assist in any way. Skilled carpenters and smiths abounded for every task: cost was not considered. It helped too that Shef had skilled taskmasters ready and willing to drive men beyond their normal habits—as he watched Cwicca swinging a rope's end at a sweating gang working on the iron rim of one of the six huge cartwheels that would shift the monster when it was done. Shef observed that having been a slave perhaps gave some men a taste for authority.

Like himself? he wondered for an instant. No, he dismissed the thought. He did only what had to be done.

Besides, the critical thing, the thing that no other group in the world had in such abundance, was confidence. Confidence that to every problem, whether it was flying in the sky or launching huge boulders, there was a hard solution, if only one could work out all possible details. Cwicca and Osmod and even Steffi, like their now-missing comrade Udd, had seen kings collapse and armies break before them, all because of machines. They did nothing half-heartedly.

And that was all very well, but this time, this time they might be wrong! Shef plunged back into the problem that had preoccupied him ever since he had set the gangs working. He roved up and down the dock, muttering and counting, telling over the piles of white and black stones he had collected and stowed in every pocket he owned.

Cwicca, rope's end laid aside, nudged one of his mates. “He's getting in a rage,” he muttered. “Someone'll cop it, you see.”

“Us and all,” his mate answered gloomily. “What's biting him?”

“Don't know. Something too clever for the likes of us.”

Solomon the Jew, his translating labors completed, also saw the growing fury on the face of the strange king: the strange king he had grown to like, in spite of the dire fate he had brought to Septimania, for his constant curiosity. A mind more active than that of any Talmudist, he reflected. But in so many fields the mind of a child.

Rather more politely than Cwicca's mate, he moved to put the same question. “Something disturbs you, lord of the North?”

Shef glowered, caught his own fury and mastered it, made himself speak connectedly. Maybe, he thought, maybe saying the problem out loud would assist him. And after all, he had found out long ago, when you could not solve a problem, ask everybody. Someone always knew.

“It's like this,” he said. “At some time or other I will need to know how far this thing will throw. Now, it ought to be easier with a machine of this sort than it is with the hand-pulled machines. For with them all you can say is ‘pull hard,’ or ‘not so hard,’ and ‘not so hard’ cannot be counted. But with this machine I can count everything! I have been thinking it out, what will happen when we try. Suppose I tell Cwicca to take ten hundred-pound bags and put them in the bucket, the bucket that drops the short arm. Now suppose I put a rock that weighs the same as three hundred-pound bags—if I could find one that would be so convenient, hah!—but suppose I did. Then suppose the ten hundred pounds threw the three hundred pounds one hundred paces. And I needed to make it throw one hundred and twenty paces. Then it is obvious, I would need more weight in the bucket. Or less weight to be thrown. And they have something to do with each other. But what?”

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.