'Look at this string,' Thomas said, excited. 'Pythagorei – see it? Surely there is meaning here at last.'

'Good, good,' Bacon said. 'You can imagine the variants I explored before I hit on this correct route through the maze. Now all we have to do is find the breaks between the words…'

But Thomas was ahead of him, splitting the line with bold slashes.

And there, for Saladin, the magic happened, a readable sentence emerging from a clamour of nonsense. He was the first to read it aloud: '"By Pythagoras's number take saltpetre, charcoal, sulphur."'

'Almost there,' said Bacon. 'Almost there.'

'But what does it mean?'Joan said.

'Well, Pythagoras's number is obvious. It is six.'

'It is?'

'Six is the perfect number,' said Saladin.

Thomas raised his eyebrows at him. 'And why is it perfect?'

'Because if you take the numbers that divide into it evenly…' Saladin took the chalk now, and wrote out, 1,2,3. 'If you add them up you get six again.' 1+2+3=6.

Bacon smiled. 'Once again you surprise us.'

Saladin felt sheepish. 'Another lucky number for the villagers.'

'In fact there are many perfect numbers,' Bacon said. 'Pythagoras did indeed study them. Twenty-eight is the next one. You see, it is divisible by-'

'Never mind,' Joan said hastily. 'So now we have this: "By one, two, three take saltpetre, charcoal, sulphur."'

'Or,' Bacon said, 'three, two, one. In fact those proportions aren't quite correct, but near enough the range that a little trial and error gives you the right product. The value of experimentation,' he said, smiling.

Saladin was mystified again. 'What product?'

'Why, it's obvious – black powder. Haven't you heard of it? The Chinese have studied it for centuries, we're told. They call it the "fire drug". It's said they found it looking for an elixir of life! I had been hoping to obtain samples via the trade routes opened up by the Mongol empire, in order to verify its properties for myself. Now I can begin to experiment with its very manufacture.'

'The manufacture of what?' Joan demanded. 'What does this stuff do, you infuriating monk?'

He didn't seem insulted. 'Well, if you set fire to it-'

'Yes?'

'It explodes.'

They sat around the low table, heaped with Bacon's papers and covered with chalk scribbles.

'Explodes,' Joan said.

'Somebody,' Bacon said, 'your Weaver of the tapestry of time, Thomas, wants you to make explosions. Incendium Dei indeed. I wonder why.'

Joan glanced at Thomas. 'Have you told him of the engines?'

Thomas closed his eyes. 'No. Because I did not have your permission. And because, frankly, I was frightened where it might lead, if he knew.'

Bacon's eyes were wide. 'What engines? You must tell me.'

Thomas glanced at Joan. 'You see what I mean?'

Joan said, 'Well, we are committed. And perhaps this strange monk of yours can help us.' She described succinctly the legend of Sihtric and his machines of war, the plans now believed lost beneath the floor of the great mosque of Seville, in faraway al-Andalus.

'But you must retrieve this Codex,' Bacon said. 'You must!'

'Why?'

'Can't you see? Combine these engines of war, engines that roll and swim and even fly, with the black powder, with the Fire of God, and no man could stand before you. Think of it – a miniature Vesuvius loaded on each arrow!…'

Saladin's experience of explosions was limited. But once he had seen a forge blow itself apart. He tried to imagine such energies harnessed, launched, and used against the flesh of enemies.

'He's right,' he said reluctantly. 'You told us, Thomas, that Sihtric was dissatisfied with the engines he made. Perhaps this black powder will provide the potency they always lacked.'

Thomas looked pale. 'If it can be made to work – but what a horrible vision of destruction! What man is this Weaver to scatter the seeds of such carnage in our age?'

Roger Bacon seemed to care nothing for that. Saladin saw he was fired only by his curiosity, by the scent of fresh knowledge in his nostrils. 'You must retrieve these designs,' he said rapidly. 'And you must bring them to me. What you need to make all this work is a dominus experimentorum. Such as myself, or an assistant. I can see it now. A scheme of work designed around two elevating principles. First, the verification of the designs, and the physical principles on which they have been based, perhaps principles hitherto unknown to mankind and therefore an everlasting gift to scholarship. Second, the use to which the new understanding may be put, which is the protection of Christendom, and thereby the spiritual welfare of all mankind and the greater glory of God.'

Thomas said, 'You would think, brother, from what you say, that you were being asked to make cathedrals, not weapons.'

'There is no sin in using the power of the mind to build weapons to fight a just war. Why, your Weaver must be a Christian, or he would not have put these engines into the hands of Christians. How can this not be God's work?'

'I know very little about the Weaver, and you know less,' Thomas said sternly. 'You must ensure you discuss this work with your confessor, brother. Fully and regularly.'

'Yes, yes.' Bacon leaned towards Joan, eyes bright, like the cat's into which he had spent long hours staring, Saladin thought. 'Bring me your plans, lady. By God's bones, there is no other way – indeed it must be divine providence that brought you to me.

'Give me your plans,' said Roger Bacon, 'and I will build the Engines of God for you.'

The guard brought the two of them to Ibrahim's office: the accuser, a middle-aged man, and the accused, a scared-looking girl with a baby in her arms.

Ibn Shaprut sat silently at Ibrahim's side, plucking at his shabby robes. The doctor was a big man who had been a lot bigger before this dreadful summer of siege. Now his grimy, much-patched clothes didn't fit him properly, and Ibrahim sometimes thought his very skin hung loose, drained of fat. However Ibrahim was glad of his steady company and hard-headed advice.

It was an August afternoon in Seville, a city under siege and hot as a furnace. Distantly the muezzins called for prayer. Ibrahim was too busy for prayers. He tried to concentrate on the case.

The accuser was a man called Ali Gurdu. Aged about fifty, his face round as the moon, he looked sleek and prosperous in the middle of a famine that even reached inside the emir's palace, though in August's heat sweat stained his turban a grimy yellow. This man looked suspiciously at Ibn Shaprut. 'Who's he? A lawyer, a magistrate?'

'I'm a doctor,' said Ibn Shaprut.

'What's a doctor got to do with it? This is a case of theft, pure and simple.'

'I rely on his judgement,' said Ibrahim, 'so you will be respectful, Ali Gurdu.'

Ibn Shaprut was watching the girl. 'Your baby is very quiet.'

She smiled thinly. 'He's clever. He's learned not to waste energy crying.' Her voice was scratchy, like an old woman's. Her robe was filthy and torn, her eyes huge in a shrunken face, and the baby in her arms was wrapped in rags. She was called Obona. Ibrahim had had to confirm her age, which was sixteen; he had learned that hunger made you look young, even giving some a kind of ethereal beauty, before it turned you very old indeed.