‘I’ll be the one to ask,’ Joan said heavily. ‘What is a “simple cyclic displacement”?’
Bacon reached for a bit of chalk and scribbled on the tabletop. ‘You write out your alphabet. A, B, C, D. And you write it out again with the letters shifted through three spaces, say. D, E, F, G. You have the word you wish to encode, say “CAESAR”. And you exchange the true letters for the shifted ones. So C becomes F, A is D, E is H ...’
‘I understand,’ said Joan.
‘Now, history tells us there have been ciphers a good deal more sophisticated than that. Polybius himself described a bilateral substitution system, which means... never mind! Happily for your weary brains, I soon concluded we aren’t dealing with anything much more complex than Caesar’s substitutions.’
‘Why do you believe that?’ Saladin asked.
‘This is a message in the Latin alphabet, not Arabic or Persian or Greek. So it is surely a Latin message. The Moors of Spain are developing extremely advanced cryptographic systems, I’m told. But a thousand years after the Caesars, we Latin scholars still lag behind the rest in our ciphers as in everything else. One point on which I kept an open mind was which alphabet we are using here.’
‘The Latin one,’ said Saladin.
‘Ah, but which Latin? Caesar used twenty-three letters. We use twenty-five, for we have added U and J. I thought it most likely the classic alphabet was the one employed.
‘So I began my analysis. A common technique in breaking ciphers is to study the distribution of letters. The most common symbol is likely to correspond to a common letter in plain language - E perhaps, or S, or T. But this fragment is too short to enable such a count. I experimented with scytales of various dimensions, to no avail. And I tried all the possible cyclic permutations, with no luck either. With all the permutations exhausted, I racked my brains for a new way forward.’
Joan murmured, ‘And in the end, after much heroic struggle, you found a way, did you?’
Bacon blithely ignored her sarcasm. ‘A simple variant on cyclic substitution is to use a key.’
‘A key?’ Saladin asked.
‘Caesar, for instance, could have used his own name.’ He wrote it out: CAESAR. ‘We must eliminate repetitions.’ He crossed out the second A. ‘Now we use this five-letter key as the foundation of our cipher.’ He wrote out a twenty-three Latin letter alphabet with a code beneath it:
‘You see? A substitution with the shift depending on the key word, and with those letters removed. So the word CAESAR now encodes as—’ He wrote it out:
ECRQCP
‘It’s a poor sort of code,’ Saladin observed. ‘The last few letters are transcribed without change.’
‘You’re a practical man, I can see that,’ Bacon said. ‘That’s true. But there are easy variants. The simplest is to put the key word at the end of the alphabet, not the beginning, and to proceed backwards.’ He scribbled quickly,
‘Now all the letters save one have a different symbol.’
‘This is all very well,’ Joan said, ‘but we don’t have a key, do we?’
‘Oh, but we do,’ Bacon said. ‘You gave it to me - or rather, to Thomas.’
‘I did? What key?’
‘It was in the letter you received. From your cousin in Spain. The phrase she was particularly interested in, that appeared to be left incomplete on the scrap of parchment you held.’
‘Incendium Dei,’ Saladin said, wide-eyed.
Joan stared at Bacon. ‘Can it really be as simple as that?’
Bacon grinned. He now had a full hold on their attention, Saladin thought, and he knew it. ‘Shall we try it?’ He wiped the table clean of chalk with his sleeve, and began to scribble again. The three of them bent over to see. ‘We begin with the key,’ Bacon said. He wrote,
INCENDIVM DEI
‘The U replaced by V as you see. Next we eliminate duplicates.’
INCEDVM
‘There is our key. So we construct our code. I tried out a forward substitution, but succeeded with a backward...’ He scribbled rapidly.
‘Now we reconstruct our message. That first B becomes a P, the M becomes R ...’
BMQVK XESEF EBZKM BMHSM BGNSD DYEED OSMEM HPTVZ
HESZS ZHVH
PRGSL CVEVO VPALR PRMER PNYET TBVVT IERVR MHDSA
MVEAE AMSM
Saladin stared at the new string, unreasonably disappointed. ‘It’s still nonsense.’
Bacon smiled, a magician with another trick to show. ‘A simple transposition would be too easy. Our puzzle involves numbers as well as letters. Look at the “sentence” again. Nine “words” of five letters, and one of four. What sentence is as regular as that? What we have here is a simple string of letters, of length - how many, Thomas?’
‘I’m not one of your Parisian students,’ Thomas growled.
‘Just answer,’ Joan murmured.
‘Forty-nine, then.’
‘Good. What’s significant about the number forty-nine?’
‘Seven sevens,’ said Saladin immediately.
‘Very good!’ said Bacon.
Thomas looked surprised. Saladin said, ‘Some of the villagers think it’s a lucky number. Seven times seven. That’s how I know.’
‘Seven squared,’ Bacon said. ‘That is surely a clue. So now, if we write out the decoded message again, not in these arbitrary blocks of five or four, but in a grid of seven by seven...’
‘It still means nothing to me,’ Joan said.
But Thomas was tracing the letters with a chalky fingertip. ‘But if you read, not across, but down - else why put them in a grid at all? P - E - R ... Give me that chalk, Roger.’ He wrote out the letters, column by column, as a single line.
PERNVMERVPYTHAGOREIDESVMTESALPETRAMCARBVM
SVLPVRVM
‘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.
PER / NVMERV / PYTHAGOREI / DESVMTE / SALPETRAM /
CARBVM / SVLPVRVM
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. N
ow 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.’
XXII
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.’
XXIII
AD 1248
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.
‘You brought him here today,’ said Ibn Shaprut. ‘You have no family who could have taken him?’
‘My parents fled to Granada before the Christian armies came to the walls.’
‘Without you?’
‘They were ashamed of me. My grandmother stayed, though, and helped me. But she died in the spring.’
‘Now you’re alone,’ said Ibrahim.
‘Yes, sir.’
Ali Gurdu clenched a podgy fist. ‘You’ll be offering her a sugared apricot next. Enough of these questions! She’s a thief! That’s what this is all about, never mind her baby and her grandmother. She stole from me!’
Ibrahim glanced at his notes. Ali Gurdu described himself as a food merchant. He was steadily selling off a hoard of dried fruit and salted meat and rice. That wasn’t quite against the law, even at the exorbitant prices he no doubt charged. But Ibrahim thought there was a stink about the man that was more than just a layer of greasy sweat.
‘She came to you as a customer,’ he said. ‘She bought a bit of salted meat.’
‘What meat was that?’ Ibn Shaprut asked the girl.
She shrugged. ‘Rat, I think. Or cat. What else is there?’
The flesh of a rat, which had no doubt gorged itself on the bodies in the communal graves. ‘So you took your bit of rat—’
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