‘That could explain the absence of any mummies,’ I mused. ‘But when we explored the pyramid we confirmed that its descending corridor dead-ends. It doesn’t rise again in the opposite direction like this medallion. There is no descending V.’
‘That is true of the corridors we know,’ Astiza said, suddenly excited. ‘But what side of the pyramid is the entrance on?’
‘The north.’
‘And what constellation does the medallion display?’
‘Alpha Draconis, the polestar when the pyramids were built. So?’
‘Hold the medallion out as if the constellation were in the sky.’
I did so. The circular disc was held against the northern sky, light shining through the tiny perforations and making the pattern of Draconis, the dragon. When I did so, the medallion’s arms were perpendicular to north.
‘If that medallion were a map, which sides of the pyramid would the shafts be on?’ Astiza asked.
‘East and west!’
‘Meaning perhaps there are entrances not yet discovered on the east or west flanks of the pyramids,’ she reasoned.
‘But why haven’t they been found? People have climbed all over the pyramids.’
Astiza frowned. ‘I don’t know.’
‘And why the connections to Aquarius, the rising Nile, and this time of year?
‘I don’t know that, either.’
And then we saw a scrap of white, like snow, in the desert.
It was a curious tableau. French officers, aides, savants, and servants were arranged in a semicircle for a picnic in the desert, their horses and donkeys picketed behind. The party faced the pyramids. Camp field tables had been put end to end and covered with white linen. Felucca sails had been rigged as canopies, with captured Mameluke lances as tent poles and French cavalry sabres thrust into the sand as pegs. French crystal and golden Egyptian goblets had been laid out with heavy European silver and china. Bottles of wine were open and half-empty. There were lavish heaps of fruit, bread, cheese and meat. Candles were ready for lighting. Seated on folding stools were Bonaparte and several of his generals and scientists, all of them chatting amiably. I also spotted my mathematician friend, Monge.
Dressed as we were in Arab robes, an aide-de-camp came to shoo us away like any other curious Bedouins. Then he noticed my complexion and Astiza’s beauty, only partly covered under the tattered cloak that she’d drawn around her as best she could. He gaped more at her than me, of course, and while he was doing so I addressed him in French.
‘I’m Ethan Gage, the American savant. I’m here to report that my investigations are nearing completion.’
‘Investigations?’
‘Of the secrets of the pyramid.’
He went to murmur my message and Bonaparte stood, peering like a leopard. ‘It’s Gage, popping up like the very devil,’ he muttered to the others. ‘And his woman.’
He beckoned us forward and the soldiers looked greedily at Astiza, who kept her gaze over their heads and walked with as much decorum as our costumes would allow. The men restrained from rude comment because there was something different about us, I think, some subtle signs of partnership and propriety that signalled we were a couple, and that she was to be respected and left alone. So their gaze reluctantly turned from her to me.
‘What are you doing in that dress-up?’ Bonaparte demanded. ‘And didn’t you desert my command?’ He turned to Kleber. ‘I thought he deserted.’
‘Damned rascal broke out of jail and eluded a pursuing patrol, if I recall,’ the general said. ‘Disappeared into the desert.’
Thankfully, word did not appear to have reached them of the events at Dendara. ‘To the contrary, I’ve been much at risk in your service,’ I said blithely. ‘My companion here was held for ransom by Silano and the Arab, Achmed bin Sadr: her life for the medallion we’ve discussed. It was her courage and my own determination that got us free to resume our studies. I’ve come looking for Doctor Monge to consult on a mathematical question that I hope will shed light on the pyramids.’
Bonaparte looked at me with disbelief. ‘Do you think me an idiot? You said the medallion was lost.’
‘I said so only to keep it from Count Silano, who does not have your interests, or those of France, at heart.’
‘So you lied.’
‘I dissembled to protect the truth from those who would misuse it. Please listen, General. I’m not jailed, not captured, and not fleeing. I came looking for you because I think I’m near a major discovery. All I need now is the help of the other savants.’
He looked from me to Astiza, half-angry and half-amused. Her presence gave me a curious immunity. ‘I don’t know whether to reward you or shoot you, Ethan Gage. There’s something baffling about you, something that goes beyond your crude American habits and rustic education.’
‘I just try the best I can, sir.’
‘The best you can!’ He looked to the others, because I’d given him a subject to pontificate on. ‘It is never enough to do your best, you must be the best. Is this not true? I do what’s necessary to exert my will!’
I bowed. ‘And I am a gambler, General. My will is irrelevant if the cards don’t go my way. Whose fortune doesn’t vary? Isn’t it true you were a hero at Toulon, then imprisoned briefly after the fall of Robespierre, and then a hero again when your cannon saved the Directory?’
He scowled a moment, then shrugged as if to concede the point, and finally smiled. If Napoleon didn’t suffer fools, he did enjoy the stimulation of argument. ‘True enough, American. True enough. Will and luck. In one day I went from a cheap Parisian hotel, in debt for my uniform, to having my own house, coach, and team. In one day of fortune!’ He addressed the others. ‘Do you know what happened to Josephine? She was imprisoned too, destined for the guillotine. In the morning the jailer took her pillow away, saying she wouldn’t need it because by nightfall she wouldn’t have a head! Yet just hours later word came that Robespierre was dead, assassinated, that the Terror had ended, and that instead of being executed, she was free. Choice and destiny: What a game we play!’
‘Destiny seems to have trapped us in Egypt,’ a half-drunken Kleber said. ‘And war is not a game.’
‘On the contrary, Kleber, it is the ultimate game, with death or glory the stakes. Refuse to play and you only guarantee defeat. Right, Gage?’
‘Not every game must be played, General.’ How strange this man was, who mixed political clarity with emotional restlessness, and the grandest dreams with the meanest cynicism, daring us to call him on it. A game? Is that what he’d say to the dead?
‘No? Life itself is war, and all of us are defeated in the end, by death. So we do what we can to make ourselves immortal. The pharaoh chose that pyramid. I choose … fame.’
‘And some men choose home and family,’ Astiza said quietly. ‘They live through their children.’
‘Yes, that’s enough for them. But not for me, or the men who follow me. We want the immortality of history.’ Bonaparte took a swallow of wine. ‘What a philosopher you’ve made me at this meal! Consider your woman, there, Gage. Fortune is a woman. Grasp her today, or you will not have her tomorrow.’ He smiled dangerously, his grey eyes dancing. ‘A beautiful woman,’ he told his companions, ‘who tried to shoot me.’
‘It turns out, General, that she was trying to shoot me.’
He laughed. ‘And now you’re a pair! But of course! Fortune also turns enemies into allies, and strangers into confidants!’ Then he abruptly sobered. ‘But I’ll not have you running around the desert in Egyptian dress until this matter with Silano is sorted out. I don’t understand what’s going on between you and the count, but I don’t like it. It’s important we all stay on the same side. We’re discussing the next stage of our invasion, the conquest of Syria.’
‘Syria? But Desaix is still pursuing Murad Bey in Upper Egypt.’
‘Mere skirmishing. We have the means to push north and east as well. The world awaits me, even if the Egyptians can’t
seem to grasp how I could remake their lives.’ His smile was tight, his disappointment obvious. His promise of Western technology and government had not won the population over. The reformer I’d seen in the great cabin of L’Orient was changing, his dreams of enlightenment dashed by the seeming obtuseness of the people he’d come to save. Napoleon’s last innocence had evaporated in the desert heat. He waved aside a fly. ‘Meanwhile, I want this pyramid mystery resolved.’
‘Which I can best do without the count’s interference, General.’
‘Which you will do with the count’s cooperation. Right, Monge?’
The mathematician looked puzzled. ‘I suppose it depends on what Monsieur Gage thinks he has figured out.’
And then there was a rumble, like distant thunder.
We turned toward Cairo, its minarets lacy across the Nile. Then another echo, and another. It was the report of cannon.
‘What’s that?’ Napoleon asked no one in particular.
A column of smoke began rising into the clear sky. The gunfire went on, a low mutter, and then more smoke appeared. ‘Something’s happening in the city,’ Kleber said.
‘Obviously.’ Bonaparte turned to his aides. ‘Get this mess packed away. Where’s my horse?’
‘I think it may be an uprising,’ Kleber added uneasily. ‘There’s been street rumour, and mullahs calling from their towers. We didn’t take it seriously.’
‘No. The Egyptians have not taken me seriously.’
The little party had lost all focus on me. Camels lurched upright, horses whinnied in excitement, and men ran to their mounts. As sabres were pulled from the sand, the awnings began to droop. The Egyptians were rising in Cairo.
‘What about him?’ the aide-de-camp said, pointing at me.
‘Leave him for now,’ Bonaparte said. ‘Monge! You and the savants take Gage and the girl with you. Get back to the institute, close the doors, and let no one in. I’ll send a company of infantry to protect you. The rest of you, follow me!’ And he set off on a gallop across the sands toward the boats that had transported them across the river.
As the soldiers and servants hurriedly packed away the last awnings and tables, Astiza quietly kept a candle. Then they scurried off too, following the trail of officers. In minutes we were left alone with Monge, except for the footprints of the vanished banquet. A whirlwind had passed, once more leaving us all breathless.
‘My dear Ethan,’ Monge finally said as we watched the exodus toward the Nile, ‘you do have a way of arriving with trouble.’
‘I’ve been trying since Paris to stay out of it, Dr Monge, with little success.’ The sound of revolt was an unmelodic rattle echoing across the river.
‘Come, then. We scientists will keep our heads down during this latest emergency.’
‘I can’t go back to Cairo with you, Gaspard. My business is with this pyramid. Look, I’ve got the medallion and am on the brink of understanding, I think.’ At my gesture, Astiza brought out the pendant. Monge started at the new design and its seeming Masonic symbolism.
‘As you can see,’ I went on, ‘we’ve found another piece. This trinket is a kind of map, I think, to hidden places in the Great Pyramid, the one you said embodied pi. The key is this triangle of scratches on the central disc. In a tomb to the south I realised they must represent Egyptian numbers. I think they’re a mathematical clue, but of what?’
‘Scratches? Let me see it again.’ He took the piece from Astiza and studied it under a hand lens.
‘Imagine each bunch of scratches as a digit,’ I said.
He counted silently as his lips moved, then looked surprised. ‘But of course! Why didn’t I see this before? Now this is an odd pattern, but appropriate given where we are. Oh dear, what a disappointment.’ He looked at me with pity, and my heart began to sink. ‘Gage, have you ever heard of Pascal’s triangle?’
‘No, sir.’
‘Named for Blaise Pascal, who wrote a treatise on this particular progression of numbers just one hundred and fifty years ago. He said many wise things, not the least of which was the more he’d seen of men, the better he liked his dog. See, it’s a pyramidal kind of progression.’ Borrowing a dragoon’s sabre, he began scratching in the sand and drew a number pattern that looked like this:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
‘There! You see the pattern?’
I must have looked like a goat trying to read Thucydides. Groaning inwardly, I remembered Jomard and his Fibonacci numbers.
‘Except for the ones,’ Monge said patiently, ‘you’ll notice that every number is the sum of the two numbers to each side above it. See that first 2? Above it are two 1s. And the 3 there: above it are a 1 and a 2. The 6? Above it are two 3s. That’s Pascal’s triangle. That’s just the beginning of the patterns you can detect, but the point is that the triangle can be extended downward indefinitely. Now, look at the scratches on your medallion.’
I
I I
I II I
I III III I
‘It’s the start of the same triangle!’ I exclaimed. ‘But what does that mean?’
Monge passed the medallion back. ‘It means the pendant can’t possibly be ancient Egyptian. I’m sorry, Ethan, but if this is Pascal’s triangle, your entire quest has been futile.’
‘What?’
‘No ancient mathematicians knew this pattern. It must undoubtedly be a modern fraud.’
I felt as if I’d been hit by a blow to the stomach. A fraud? Was this one of the tricks of the old conjurer Cagliostro? Had this long journey – Talma’s and Enoch’s death – been for nothing? ‘But it looks like a pyramid!’
‘Or a pyramid looks like a triangle. What better way to pass on a crude piece of old jewellery than by linking it to the pyramids of Egypt? Yet it was probably some scholar’s toy or good-luck piece, with pi and the legs of a compass. Perhaps it was a joke. Who knows? I merely suspect, my friend, that you’ve been duped by some kind of charlatan. The soldier you won it from, perhaps.’ He put his hand on my shoulder. ‘There’s no embarrassment. All of us know that you’re not really a savant.’
I was reeling. ‘I was sure we were so close …’
‘I like you, Ethan, and don’t want to see you come to any harm. So let me give you some advice. Don’t go back to Cairo. God knows what’s happening there.’ The sounds of firing kept getting louder. ‘Bonaparte suspects your uselessness, and frustration is making him impatient. Take a boat to Alexandria with Astiza and take ship for America. The British will let you through if you explain yourself, as you do so well. Go home, Ethan Gage.’ He shook my hand. ‘Go home.’
I stood in shock, barely comprehending that all my exertions had been for nothing. I’d been certain the medallion pointed a way into the pyramid, and now the greatest mathematician in France had told me I’d been bilked! Monge smiled at me sadly. And then, gathering up his few belongings, he mounted the donkey that had borne him here and slowly began riding back to the capital and his institute, gunfire growling in the distance.
He turned. ‘I wish I could do the same!’
* * *
Astiza was looking after Monge in frustration, her face dark and contemptuous. When he was out of earshot she exploded. ‘That man is a fool!’
I was startled. ‘Astiza, he has one of the finest minds in all of France.’
‘Who apparently believes that learning begins and ends with his pompous opinions and his own European ancestors. Could he build this pyramid? Of course not. And yet he insists that the people who built it knew far less of numbers than him, or this Pascal.’
‘He didn’t put it that way.’
‘Look at those patterns in the sand! Don’t they look like the pyramid before you?’
‘Yes.’
‘And yet they have nothing to do with why we are here? I don’t believe it.’
‘But what’s the connection?’
She looked from sand to pyramid, p
yramid to sand. ‘It is obvious, I think. These numbers correspond to the blocks of the pyramid. A single one at the top, missing now. Then two on this face, then three, and so on. Row after row, block after block. If you follow this pattern, each block will have a number. This Monge is blind.’
Could she be right? I felt a rising excitement. ‘Let’s complete a few more rows.’
The pattern soon became more apparent. Not only did the numbers grow rapidly bigger near the pyramid’s apothem, the imaginary line that bisected the pyramid’s face, but to either side of this centre point they would pair outward. The next line, for example, read 1, 5, 10, 10, 5, 1. Then 1, 6, 15, 20, 15, 6, 1. And so on, each row getting broader and its numbers bigger. By the thirteenth row from the top, the centre number was 924.
‘What number are we looking for?’ I asked.
‘I don’t know.’
‘Then what good is this?’
‘It will make sense when we see it.’
On we figured. As the sun sank toward the western horizon the pyramid shadows lengthened. Astiza touched my arm and pointed to the south. There was a plume of dust that way, marking the approach of a sizable party. I felt uneasy. If Silano and Bin Sadr had survived, that was the direction they’d be coming from. To the northeast we could begin to see the glow of fires in Cairo and hear the now-steady roar of French artillery. A full-scale battle had broken out in the supposedly pacified capital. Napoleon’s grip was more fragile than it seemed. I saw a round bag begin to lift into the air. It was Conte’s balloon, no doubt being used by observers to direct the fight.
‘We’d better hurry,’ I muttered.
I began sketching numbers faster, but each row added to the sequence was two numbers longer than the one before, and more complicated. What if we made a mistake? Astiza helped fill in the numbers with the necessary arithmetic, murmuring as she added in her quick mind. On and on our pyramid grew, number by number, block by block, as if we were duplicating its construction on the sand. Soon my back ached, my eyes began to blur. Numbers, numbers, numbers. Was it all a hoax, as Monge had implied? Had the ancient Egyptians known such puzzles? Why would they invent something so obscure and then leave a clue to find it? Finally, some one hundred and fifty rows of blocks from the top, we came to a stone that had the same digits as what the mathematician had told me was the Egyptian value for pi: 3160.
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