King and Emperor

Chapter Twenty-one

The Emperor had had little hope of success from the scaling ladders: he had tried them out because he had plenty of men and one never knew the enemy's weaknesses. The ram had seemed more practicable. Watching from a distance he had made out the unmistakable figure of Brand on the ramparts, once his ally, never his friend. To lose to him had been galling. Now the time had come, he decided, for serious thought, and to help him he had called in the few men of his army he thought might be capable of it. Agilulf, his deputy, an experienced warrior. Georgios the admiral of the Greeks, with the proverbial subtlety of that race. Erkenbert the deacon, on whom he most relied. Once he and they had made their plan he would communicate it to the host of subordinate leaders who made up his army's contingents: none of them, in the Emperor's candid opinion, fit to lead anything more complicated than a charge or an ambush.

“Those in the city are not stupid,” he concluded, “and their defenses are good. Also, we know the one-eye is there, and where he appears, strange things happen. Now, what can we do to puzzle them?”

Georgios replied, speaking slowly in his camp-Latin. “The harbor remains a weak point,” he said. “I will not risk my galleys close in against their mule-stones, but at the same time we have proved that they dare not come out against the floating fort designed by the wise deacon here: I am glad to have seen it and will take careful note of it for my Emperor's uses in the future. Still, the stone jetties are only six feet above the water, and they run many stadia long. There is a chance there for an escalade, if we can get close enough.”

“Many small boats, not a few large ones?” suggested Bruno.

“And, I would suggest, at night.”

“What about the Greek fire? Can you not bring it close up to the jetties and burn all the defenders off as you did the Arab galleys?” asked Agilulf.

The admiral hesitated. He could not lie to Agilulf, who had seen the Greek fire used several times. Yet at the heart of the policy of the Byzantines was the need to keep their one great technical advantage secret. No barbarian—and barbarian included the servants of the Emperor of Rome, as far as the Greeks were concerned—was allowed to get too close to the projectors or the fuel tanks. The operators were the most highly paid men in the fleet, the admiral included, and all had moreover left hostages for their secrecy in Byzantium. Georgios felt that he had learnt much on this trip, including the details of the Roman and Northern catapults. He wanted to give nothing back in return. Yet he must answer.

“The Greek fire has certain limitations,” he temporized. “It needs a large ship to carry it. I cannot put the devices into mere fishing boats. Nor can I take the risk of losing one to enemies who, as the Emperor says, are only too ready to learn new and strange devices. Yet at night, I might risk one galley close in.” With trusted men aboard to burn and destroy the evidence if it might fall into the wrong hands, he did not say.

“We'll try it,” said Bruno decisively. “Night after next, there'll be no more than a thin moon. Now, Erkenbert, where is the War-Wolf?”

“War-Wolf” was the name of the great engine that Erkenbert himself had designed, and that had battered down the gates of castle after castle in the Emperor's triumphant progress to Puigpunyent. It was, in a way, no more than a giant version of the simple traction catapults that Shef had designed and that even now were hurling rocks at every besieger who came within range of the city of Septimania. Yet it did not rely on mere feeble human muscles to give it power. Power came from the giant counterweight, the counterweight that was both its strength and its weakness: enabling massive boulders to be thrown, taking an age to empty and refill, demanding great weight and strength in its supporting timbers—timbers still crawling along the coast road to the siege.

“Two days' travel away still,” Erkenbert replied.

“And where do you mean to use it once it has arrived?”

“We have little choice. It is coming down the coast road from the north. We cannot move it through the hills above the town, and if we were to load it on board ship we would need cranes and a stone jetty out into deep water. So we will have to attack the north gate of the town. It is a strong and stout gate, but only wooden. One boulder from ‘War-Wolf’ will beat it down.”

“If it lands on the right place.”

“Trust me for that,” said Erkenbert definitely. “I am the arithmeticus.”

The Emperor nodded. He knew that no-one in the world was more skilled than the puny deacon in the mind-numbing task of translating weight to distance in the number-system his world had inherited from the Romans.

“Harbor attack the night after next, then,” he concluded. “If that fails, ‘War-Wolf’ breaks down the north gate the next morning.”

“And if that fails?” enquired Georgios, always ready to disconcert his temporary allies.

The Emperor looked at him forbiddingly. “If that fails, we try again. Till the Holy graduale on which our Savior was borne is in my hands, along with the Lance by which he died. But I don't want to fail. Remember, all of you, we are dealing with clever heathens. Be alert for anything new. Expect the unexpected.”

In silence, his advisers speculated on how this paradox might be achieved.

The bastards are too quiet, thought Brand, strolling along the harbor front in search of his master. There he was, still in the courtyard, all of them still reading, gabbling, scritch-scratching away with never a care in the world. He waited till Solomon noticed his looming presence and broke off his reading.

“Sorry to disturb you,” he remarked ironically. “I thought I'd mention the siege.”

“It's going well, isn't it?” asked Shef.

“Well enough. But I think it's time you did something.”

“What?”

“What you're best at. Thinking. It's all gone quiet. But I've seen our friend Bruno through the far-seer. He won't give up. So—they're going to do something. I don't know what. You are the best person in the world for imagining new things. Time for you to do it again.”

Slowly, bringing his mind back from the fascinating problems of the book, Shef realized the truth of what Brand had said. Realized too, with some subconscious calculation, that the breathing space he had counted on, and had been using on what he felt was the most vital if not the most urgent task, the task he alone could do—that that breathing space was over. Besides, he was getting bored with sitting. And the book was nearly done.

“Find Skaldfinn to take my place here,” he ordered. “He can translate from Solomon for Thorvin to write down. Tolman, you come along too.”

He stepped out into the sunlight with the gigantic Brand and the limping kite-boy at his heels, followed by a glower from Svandis. She wanted to listen to the end of the strange book. At the same time she resented the way her lover could turn his attention instantly to something new. Something without her.

“I brought two people to talk to you,” added Brand once they were in the open. “Steffi and a native.”

Shef turned his attention first to the native, as Brand called him, another dark-faced man of clear Arab descent: there were still many non-Jews in the town, traders caught by the unexpected closure of roads.

“You speak Arabic?” he asked.

“Of course.” A slight sneer at the question: Shef's Arabic was no more than serviceable, far removed from the pure tongue of Cordova or Toledo.

“What is your news?”

“The Christian Emperor, your enemy and the enemy of my master the Caliph, has destroyed many walls and forts this summer. He has killed many of the faithful too, all along the sea-coast they once controlled. Do you wish to know how he did it?”

“We will pay gold for it,” Shef replied.

“I would tell you anyway, as a service against the Nazarenes. He has a machine. Only one machine, and it is many times bigger than anything you have here. He uses it for only one thing, and that is to hurl great boulders on to his enemy's gates. Some say that it needs flat ground, that it can shoot only very slowly.”

“Have you ever seen it?”

“No, but I have spoken with men who escaped with their lives when strongholds were taken.”

Bit by bit Shef drew from the Arab what little accurate information he could provide, and began to realize the use of the counterweight. Absently he dismissed the man, thinking already of the problems of a pivot, of retention and release: above all, the central problem of all the traction engines, of how to control range. It depended on weight. There must be some way to tell, if you knew how much was in the counterweight and how much in the launching-sling, what you needed to add or to take out in order to throw a set distance. But a three-element calculation was beyond Shef, or any other man in his realm. Even working out how many water-barrels you needed, or what share of loot went to each ship or each man, was a trial-and-error business with the Northern counting-system. Shef wished in frustration that he too, like Bruno, had in his service an arithmeticus. Even someone who knew what arithmetic might be. As he pounded a fist into his palm he became aware that Steffi was standing on one foot, eying him nervously from his usual wide angle.

“Why did Brand send you here?”

“I was thinking. About the flares we used from the kites. And that time I jumped off the cliff, you remember? I was thinking, how would it be, at night like, if we had some flares ready to light, and threw them from a pull-thrower? We could put some cloth on so they'd open out, see, and come down slowly, with a hole in, like we've learned how to do…”

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.

“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.”

Shef nodded: the words “multiply” and “divide” were strange to him, but he understood the ideas.

“First,” Solomon went on, “write the numbers for eleven hundred and forty in their correct place.”

Shef pondered for a moment. He had soon grasped the idea of a number-system based on position, but it still did not come easily to him.

“Try writing it the Roman way first,” said Solomon gently. “Write it in the sand away from your table. The Romans wrote a thousand by ‘M’.”

Shef wrote a wavering “M” in the sand, followed by a dot. Then a “C” for one hundred. Then the familiar four “X”s for forty. His hand reached out to make the hole sign for al-sifr, nothing, but drew back. The Romans would have left such a number as M.C.XXXX.

“Now enter the Arabic signs at the head of your table,” Solomon prompted. “Eleven hundred and forty at the top, seven at the bottom.”

Shef hesitated again. This was the tricky part. Now. The right-most column was for numbers below ten. In the horizontal line one above the bottom, the line for the multiplier, he wrote the shaky hook of a ‘7’: the multiplier. The topmost horizontal line was for the multiplied, as he could see from his Roman numerals, one thousand, one hundred and forty.

In the left-most column he wrote a ‘1,’ corresponding to the ‘M’. In the next, another one, corresponding to the ‘C.’ In the next, the more complex shape of a ‘4,’ for the four ‘X’s. And finally, in the right-most column, the column for the ten numbers below ten—ten, not nine, as Solomon had proved to him—he drew the al-sifr hole.

Now to do the sum. The first thing, the most vital thing, was that seven noughts were nought. So write in the nought. Deliberately, watched by four pairs of eyes, Shef began to work his way through the calculation on the sand-table, primitive ancestor of the abacus. For long moments he thought of nothing else, lost in a sensation no man of his race had ever before experienced: the fascination of number. In the end, hardly aware of how he had come by it, he stared with surprise and deep satisfaction at the result written in the sand. Seven thousand nine hundred and eighty. He had never seen a number like that before—not because it was too large, not when every part of his realm was counted in hides, thirty thousand for a province, a hundred thousand for what had once been a kingdom. No, because of its exactness. Over a thousand, numbers to him were counted in scores, or tens, or hundreds, or half-hundreds: not sixes and sevens and eights and fours.

“Now you are to divide seven thousand nine hundred and eighty by six,” went on the quiet voice of Solomon. “Make your table for divisions.”

Shef's hand brushed the sand away, began another table. Prompted again and again by Solomon, he worked his way doggedly through.

“And so in the end,” said Solomon finally, “you know that you would need to increase your throwing weight to…”

“Thirteen hundred and thirty pounds,” said Shef.

“So you would add to your original weight…”

“Two hundreds less ten. One hundred and ninety pounds. Exactly.”

“But by the time you'd set up your sand table and done all this,” objected Skaldfinn, “your enemy would have buried you under a hail of boulders. Because he'd have been shooting while you'd been drawing!”

“Not with the new machine,” said Shef flatly. “I could have done all this while they were still taking the weights out to winch the arm back up again. Then I could just tell them to put the same weight back in with a measured one hundred and ninety on top. And besides: I can see this is just like the far-seer.”

“Like the far-seer?” asked Solomon.

“Yes. You remember that fool Mu'atiyah. He could make the far-seer, he had been shown how the glass should be ground, something we might never have realized in a thousand years. But he never thought to go a step further. I swear, by the time we return to our own home my wise men will have learned more of glass and sight than Mu'atiyah, or even his master. Because they will not rest till they have! Now, this calculation you have shown me, this too I might never have learned for myself. But now I have learned it, I see it can be made quicker, much quicker. The sand table—it's not needed, nor the stones in my hand. I use them because I am not practiced. If I were, then I could put my counters on wire and carry it all with me, like a harp. Or I could do it without any columns at all. Ideas are hard to come by, easy to improve. I will improve this one yet. Improve it till—what was his name, Solomon, al-Khwarizmi?—till al-Khwarizmi himself would not recognize it. And I will use it for more than catapults! This is the anvil for a smith-craft on which the Way could beat out the world! Is that not right, Thorvin? Skaldfinn?”

Solomon fell silent, hand going up to his beard as if for comfort. He had forgotten the furious spirit of the Northerners, and of the One King in particular. Was it wise ever to tell them anything? Too late, now, to reconsider.