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.
Chapter Twenty-two
Dimitrios, senior siphonistos to the Greek fleet, listened to the orders of his admiral with doubt tinged with alarm. The orders were, of course, expressed with great care, somewhere between suggestion and persuasion. The siphonistoi were almost a law unto themselves, curators of the ultimate weapon of Byzantium, in their own opinion more important in the last resort even than emperors, let alone admirals. Dimitrios, if he chose, could make a fortune and live like a lord anywhere in the civilized world, Baghdad or Cordova or Rome, simply by selling the information in his head. A wife, a mistress, seven children and two thousand golden hyperpers in the banks of Byzantium stood forfeit to his treachery. But in any case the whole city knew that no siphonistos would ever reach mastery of his trade if there were the slightest doubt about his loyalty to the cause of Church and Empire: loyal
ty from principle, not compulsion.
That loyalty caused Dimitrios's doubt. One of his greatest compulsions was to preserving the secrecy of the fire. Better to lose a battle by destroying one's equipment, he had been told a thousand times, than to risk its capture for a purely temporary victory—all victories, for the beleaguered Empire of the Byzantines, had long been recognized as temporary. Now the admiral wanted him to risk a ship and a projector close inshore, in doubtful battle against Jews and strange heathens. Dimitrios was a brave man, who would take his chance of being sent to the bottom by the strange mule-stones, as the barbarians called them. Risking the fire and the secret were another thing.
“The small boats will go in first,” repeated Georgios cajolingly. “Only if they make a lodgement will we bring up your galley.”
“To do what?”
“If they can detach the booms you may be able to get into the harbor and burn out all the stone-thrower ships at once.”
“They'd sink us as we came in.”
“It will be black night, a thin moon, barely a hundred yards to row to the nearest. After that you can always keep an enemy ship between you and their catapults till you are close enough to pump the fire at them.”
Dimitrios considered. He had indeed been enraged at the sinking of the galley and the butchery of its men in the inconclusive battle at sea weeks before: an act of defiance which had left him for the first time in his career feeling helpless. It would be a delight to avenge that shame by burning every enemy ship to the waterline, as all enemies of Byzantium deserved. To show the devil-worshipers the power of God and his Patriarch. And close range and at night were exactly the right conditions for the use of his weapon.
“What if they don't get the boom open?”
“You could pull along the stone jetty and sweep it of any resistance. That way you would have the jetty between you and the stone-throwers in the harbor. Clear the jetty and pull out to sea again in the darkness.”
Dimitrios thought carefully. There were risks in this, he could see, but perhaps no more than were justifiable. He would take his own precautions, of course, as the admiral certainly knew he would. Men standing by to fire the tanks, boats in waiting to collect himself and his crew if they had to abandon ship. No need to repeat all that.
Seeing him waver, the admiral added a final dose of flattery to win his supposed subordinate over. “Of course we know that the most important thing in our fleet is yourself. You and the skill you have developed. We dare not lose that to any barbarian. I will myself stand by in the rescue boats, to come in for you if there is any sign of mischance.”
Dimitrios smiled, a little mirthlessly. What the admiral said was true. But he had no idea how true. He himself, Dimitrios, knew the entire process of making the Greek fire from ground to nozzle, as the siphonistoi said. He had been beyond the Black Sea to far Tmutorakan, where the colored oils oozed from the ground. He had seen it in the winter, when the oil ran thin and clear, and in the stifling summer, when it came out like sludge from a foul farmyard. He knew how it was collected, he knew how it was stored. He himself had soldered the copper tanks with precious tin, to be sure there was no leak. He had built his own equipment with his own hands, lank and valves, brazier and bellows, pump and nozzle. Again and again, under the guidance of the old masters of the trade, he had fired up, pumped in the air, seen the flame flow. Three times his masters had made him pump on beyond the safe limit, using small and old devices and condemned criminals as pump-hands, so that he could hear the rising shrillness of the niglaros, the valved pressure-whistle, whose valve was opened to test the vapors within. He had looked with interest at the bodies of the condemned, to see what effect the bursting tanks had had upon them. Not one had ever survived, and Dimitrios thought they had chosen ill to take the siphonistos chance instead of sure but less painful death on the execution ground. He was acutely aware of every difficulty in the whole process, how much easier it was to have it go wrong than go right. Without him, he knew, mere knowledge would not be enough. It was his experience that was vital and precious. Good, at least, that the admiral had recognized it.
“With the proper safeguards, I consent,” he said.
The admiral sank back in his chair with relief. While he knew how much less than biddable his corps of siphonistoi were, he would not have relished explaining the fact to the Emperor of the Romans: a man who, he thought, should be given a skilled Byzantine doctor as soon as possible, to ensure that he ate something that disagreed with him.
“Have one ship ready at nightfall,” he said. “Take my own Carbonopsina.”
The Black-Eyed Beauty, thought Dimitrios. Pity that there were none such in this far land of strangers. Only thin Moorish women and the ugly descendants of Goths, with their pale skin and discolored eyes. Ugly as the revolting Germans, their allies, though these insisted that their barbarian enemies were even worse for pallor and bulk and the size of their feet. Certainly all should be swept from the sea, the Inner Sea, the Sea of the Middle of the World become once more a Greek and Christian lake. Dimitrios rose, bowed sketchily, withdrew to make his preparations.
The first sign of the sea-borne assault came only as the patrolling squad of city guardsmen marching along the longer jetty saw faint shapes crowding in out of the blackness. They stood, gaped for an instant to make sure, then began to blow the alarm on their ram's horn trumpets. By then the sixty fishing boats which Bruno had commandeered were bare yards from the stone wall, men in them already swinging their grapnels to pull the boats alongside, others raising the short boarding-ladders which were all they would need for the six-foot climb. The guardsmen bent their bows, the short breast-bows which were all they carried, shot, shot again at the targets pouring towards them. Then, as the first grapnels clinked on stone, they realized they were alone on a long stone causeway, about to be cut off. They ceased shooting and ran for the harbor end of the jetty, cut down as they fled by javelins and arrows flying out of the blackness. Bruno's first wave reached the jetty almost without resistance, divided immediately into two groups, one turning to their left and racing for the seaward end with hammers, saws and chisels, to try to cut the boom and open the entrance for the reinforcements and the fire-ship. The other turned right and poured in an armed mob for the landward end, seeking to reach and hold it till the rest came up and drove either for the open harbor, or—just as disastrously for the defense—to seize a stretch of the main wall and open it for escalade. The rams' horns had done their work, though. While only a score of men at a time marched along the jetties, open as they were to the unpredictable shooting of the catapults on the offshore fort, many more stood to arms or slept by them at the vulnerable points where jetties met shore. The attackers charging along the stone strip, carried on with excitement at their easy landing, met a sudden rain of arrows at close range, with behind them a solid wall of spears and shields. Lightly-armed levies from the South, the men Bruno habitually sent in first as most dispensable, many of them went down even before the puny arrows of the breast-bows, shot at no more than ten yards' range. Those who pressed on found themselves hacking at a disciplined line behind a barricade. Slowly those who survived realized that the pressure of comrades from behind was slackening, had gone. Unsure why, or if they too were to be taken from behind in the darkness, they drew back, at first step by step behind their shields, then as the arrows lashed at their unprotected legs and sides, turning and running back into the protective dark.
Shef had started from sleep at the first horn-blast. He slept naked in the heat, seized tunic and boots, struggled into them in seconds, started for the door. Svandis was there before him, naked also but barring his way. Even in the almost pitch-black of the shuttered room Shef could feel the scowl on her face, hear the lash in her voice.
“Don't run out like a fool! Mail, helmet, weapons! What good will you be if the first stray slingstone cuts you down?”
Shef hesitated, full of counter-arguments, but Svandis carried on. “I am the child of
warriors, even if you are not. Better ready and slow than early and dead. My father could have told you that. Who won the battle where I first saw you? You, or he?”
Well, he did not, Shef thought to say. But it was no use arguing. Quicker to obey than to try to thrust her aside. He turned to the mail-shirt which hung ready from a hook, thrust his arms through the heavy sleeves. Svandis was behind him, pulling the iron round, fastening it behind with the heavy rawhide laces. It was true at any rate that she was the child of warriors. He turned and embraced her, pulling her breasts on to the hard iron rings.
“If we live, when we return home I will make you a queen,” he said.
She slapped his face sharply. “This is no time for love-whispers in the dark. Helmet. Shield. Take your Swedish sword and try to live up to it.”
Shef found himself thrust out into the courtyard, could hear her behind him rummaging for her own clothes. Wherever the fighting was, she would appear, he knew. He began to run, heavy under the weight of thirty pounds of wood and iron, towards the command post where he would find Brand. Across the water came a clangor of metal, war-cries and cries of pain. They had come by sea.
As Shef puffed up, he saw Brand towering in the midst of a squad of Vikings, his gigantic cousin Styrr standing next to him, almost his equal in size. Brand seemed in no great hurry or alarm, was busy counting his men.
“They landed on the jetty,” he remarked. “I never thought that would give them much trouble. They've got to get off it if they're going to be a nuisance, and they'll have to do it fast.”
Shef's ears had picked out different noises from the immediate ones of battle, already dying away: smithy noises, metal on metal, axe on wood.
“What's happening at the far end?”
“They're trying to cut the boom. Now that we don't want. We'll have to clear them off. All right, boys, got your boots laced up? Let's stroll along and shoo these Christians back into the water. You stay at the back,” he added to Shef. “Organize some crossbows, make sure the catapults shoot at the opposition, not us. This would be easier if we could see what was going on.”
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