The Khan heard this and was not amused. 'You're suggesting we pile earth all around Samarqand? Impossible! It would be too ugly! The other khans and emirs would laugh at us. We cannot live like ants in an anthill!'

Khalid turned to Nadir, his face a polite blank.

'Next?' Nadir said.

'Of course. Now see, we have determined that at the distances a gun can cast a ball, it cannot shoot straight. The balls are tumbling through the air, and they can spin off in any direction, and they do.'

'Surely air cannot offer any significant resistance to iron,' Nadir said, sweeping a hand in illustration.

'Only a little resistance, it is true, but consider that the ball passes through more than two li of air. Think of air as a kind of thinned water. It certainly has an effect. We can see this better with light wooden balls of the same size, thrown by hand so you can still see their movement. We will throw into the wind, and you can see how the balls dart this way and that.'

Bahram and Paxtakor palmed the light wooden balls off, and they veered into the wind like bats.

'But this is absurd!' the Khan said. 'Cannonballs are much heavier, they cut through the wind like knives through butter!'

Khalid nodded. 'Very true, great Khan. We only use these wooden balls to exaggerate an effect that must act on any object, be it heavy as lead.'

'Or gold,' Sayyed Abdul Aziz joked.

'Or gold. In that case the cannonballs veer only slightly, but over the great distances they are cast, it becomes significant. And so one can never say exactly what the balls will hit.'

'This must ever be true,' Nadir said.

Khalid waved his stump, oblivious for the moment of how it looked. 'We can reduce the effect quite a great deal. See how the wooden balls fly if they are cast with a spin to them.'

Bahram and Paxtakor threw the balsam balls with a final pull of the fingertips to impart a spin to them. Though some of these balls curved in flight, they went farther and faster than the palmed balls had. Bahram hit an archery target with five throws in a row, which pleased him greatly.

'The spin stabilizes their flight through the wind,' Khalid explained. 'They are still pushed by the wind, of course. That cannot be avoided. But they no longer dart unexpectedly when they are caught on the face by a wind. It is the same effect you get by fletching arrows to spin.'

'So you propose to fletch cannonballs?' the Khan inquired with a guffaw.

'Not exactly, your Highness, but yes, in effect. To try to get the same kind of spin. We have tried two different methods to achieve this. One is to cut grooves into the balls. But this means the balls fly much less far. Another is to cut the grooves into the inside of the gun barrel, making a long spiral down the barrel, only a turn or a bit less down the whole barrel's length. This makes the balls leave the gun with a spin.'

Khalid had his men drag out a smaller cannon. A ball was fired from it, and the ball tracked down by the helpers standing by, then marked with a red flag. It was farther away than the bigger gun's ball, though not by much.

' It is not distance so much as accuracy that would be improved,' Khalid explained. 'The balls would always fly straight. We are working up tables that would enable one to choose the gunpowder by type and weight, and weigh the balls, and thus, with the same cannons, of course, always send the balls precisely where one wanted to.'

'Interesting,' Nadir said.

Sayyed Abdul Aziz Khan called Nadir to his side. 'We're going back to the palace,' said, and led his retinue to the horses.

'But not that interesting,' Nadir said to Khalid. 'Try again.'

Better Gifts for the Khan

'I suppose I should make the Khan a new suit of damasked armour,' Khalid said afterwards. 'Something pretty.'

Iwang grinned. 'Do you know how to do it?'

'Of course. It's watered steel. Not very mysterious. The crucible charge is an iron sponge called a wootz, forged into an iron plate together with wood, which yields its ash into the mix, and some water too. Some crucibles are placed in the furnace, and when they are melted their contents are poured into molten cast iron, at a temperature below that of complete fusion of the two elements. The resulting steel is then etched with a mineral sulphate of one kind or another. You get different patterns and colours depending on which sulphate you use, and what kind of wootz, and what kind of temperatures. This blade here,' he rose and took down a thick curved dagger with an ivory handle, and a blade covered with a dense pattern of crosshatchings in white and dark grey, 'is a good example of the etching called "Mohammed's Ladder". Persian work, reputed to be from the forge of the alchemist Jundi Shapur. They say there is alchemy in it.' He paused, shrugged.

'And you think the Khan…'

'If we systematically played with the composition of the wootz, the structure of the cakes, the temperatures, the etching liquid, then we would certainly find some new patterns. I like some of the swirls I've got with very woody steel.'

The silence stretched out. Khalid was unhappy, that was clear.

Bahram said, 'You could treat it as a series of tests.'

'As always,' Khalid said, irritated. 'But in this case you can only do things in ignorance of their causes. There are too many materials, too many substances and actions, all mixed together. I suppose it is all happening at a level too small to see. The breaks you see after the casting look like crystalline structures when they are broken. It's interesting, what happens, but there's no way to tell why, or predict it ahead of time. This is the thing about a useful demonstration, you see. It tells you something distinct. It answers a question.'

' We can try to ask questions that steelwork can answer,' Bahram suggested.

Khalid nodded, still dissatisfied. But he glanced at Iwang to see what he thought of this.

Iwang thought it was a good idea in theory, but in practice he too had a hard time coming up with questions to ask about the process. They knew how hot to make the furnace, what ores and wood and water to introduce, how long to mix it, how hard it would turn out. All questions on the matter of practice were long since answered, ever since damasking had been done in Damascus. More basic questions of cause, which yet could be answered, were hard to formulate. Bahram himself tried mightily, without a single idea coming to him. And good ideas were his strength, or so they always told him.

While Khalid worked on this problem, Iwang was getting terrifically absorbed in his mathematical labours, to the exclusion even of his glassblowing and silversmithing, which he left mostly to his new apprentices, huge gaunt Tibetan youths who had appeared without explanation some time before. He pored over his Hindu books and old Tibetan scrolls, marking up his chalk slates and then adding to the notes he saved on paper: inked diagrams, patterns of Hindu numerals, Chinese or Tibetan or Sanskrit symbols or letters; a private alphabet for a private language, or so Bahram thought. A rather useless enterprise, disturbing to contemplate, as the paper sheets seemed to radiate a palpable power, magical or perhaps just mad. All those foreign ideas, arranged in hexagonal patterns of number and ideogram; to Bahram the shop in the bazaar began to seem the dim cave of a magus, fingering the hems of reality…

Iwang himself brushed all these cobwebs aside. Out in the sun of Khalid's compound he sat down with Khalid, and Zahhar and Tazi from Sher Dor, and with Bahram shading them and looking over their shoulders, he outlined a mathematics of motion, what he called the speed of the speed.

'Everything is moving,' he said. 'That is karma. The Earth revolves around the Sun, the Sun travels through the stars, the stars too travel. But for the sake of study here, for demonstrations, we postulate a realm of non movement. Perhaps some such motionless void contains the universe, but it doesn't matter; for our purposes these are purely mathematical dimensions, which can be marked by vertical and horizontal, thusly, or by length, breadth and height, if you want the three dimensions of the world. But start with two dimensions, for simplicity's sake. And moving objects, say a cannonball, can be measured against these two dimensions. How high or low, how left or right. Placed as if on a map. Then again, the horizontal dimension can mark time passed, and the vertical, movement in a single direction. That will make for curved lines, representing the passage of objects through the air. Then, lines drawn tangent to the curve indicate the speed of the speed. So you measure what you can, mark those measurements, and it's like passing through rooms of a house. Each room has a different volume, like flasks, depending on how wide and how tall. That is to say, how far, in how much time. Quantities of movement, do you see? A bushel of movement, a dram.'