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 gray 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 rumor, 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 sabers 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 realized 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 saber, he began scratching in the sand and drew a number pattern that looked like this:
“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 a2. 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.”
“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 jewelry 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, pyramid 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 center 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 center 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.
I stopped, stunned. Of course! The medallion was a map to a certain point on the pyramid! Face north. Imagine a shaft and door on the west or east faces. Remember pi. Look for a block valued pi under this ancient number game. Time it to Aquarius as the Egyptian used the sign, for the rising of the Nile, and…enter.
If I was right.
The western face of the pyramid glowed pink as we began to climb it. It was late in the afternoon, the sun low and fat, like Conte’s balloon. Our horses were tied below, and the sounds of gunfire in Cairo were muffled by the bulk of the monument between us and the city. As before, our climb was an awkward scramble, the blocks high, steep, and eroded. I counted as we climbed, trying to find the row and block that corresponded to pi, the eternal number codified into the dimensions of the pyramid.
“What if the numbers refer to the facing stones, now gone?” I said.
“They would match these inner ones, I hope. Or close to it. This medallion would be directing us to a stone that led to the core.”
We had just reached the fifty-third row, panting, when Astiza pointed. “Ethan, look!”
Rounding the corner of the adjacent pyramid was a party of galloping horsemen. One of them spied us, and they began to shout. Even in the dying light I had no trouble making out the bandaged figures of Bin Sadr and Silano, lashing at lathered horses. If this didn’t work we were dead—or worse than dead, if Bin Sadr had his way.
“We’d better find that stone.”
We counted. There were thousands of blocks on this western face, of course, and when we came to the supposed candidate, it looked no different than its brothers around it. Here was a rock eroded by millennia of time, weighing several tons, and firmly wedged by the colossal weight above it. I pushed, heaved, and kicked, to no effect.
A bullet pinged off the stonework.
“Stop! Think!” Astiza urged. “There has to be a special way or any
fool could have stumbled upon this.” She held up the medallion. “It must have something to do with this.”
More shots pattered around us.
“We’re like targets on a wall up here,” I muttered.
She looked out. “No. He needs us alive to tell him what we’ve discovered. Bin Sadr will enjoy making us talk.”
Indeed, Silano was shouting at those who had fired and shoving their muskets down, instead pushing them toward the base of the pyramid.
“Great.” I fumbled with the medallion. Suddenly I realized the second pyramid was shadowing our own, its long triangle reaching across the sands and climbing the layers of stone to where we were standing, pointing at us. Its capstone was intact, its point more perfect, and its apex seemed to shadow a block a few to the right and several courses lower than where we were standing. Each day, as the sun marched along the horizon, the shadow would touch a different stone, and this was the date I’d surmised from the calendar. Was our count of the blocks off slightly? I bounded down to just above the shadow and held the medallion up to the sun. Light shone through the tiny perforated holes, making a star pattern of Draconis on the sandstone.
“There!” Astiza pointed. A faint tracery of holes, or rather chisel points, near the base of the stone, mimicking the constellation pattern on the medallion. And beneath it, the joint between our stone and the one below was slightly wider than the usual. I crouched and blew the dust away from this tiniest of cracks. There was the subtlest of Masonic signs chiseled into the stone as well.
I could hear Arabs shouting to each other as they started to climb. “Gage, give it up!” Silano called. “You’re too late!”
I could feel a shallow breath of wind, air coming from some hollowness on the other side. “It’s here,” I whispered. I slammed the stone with my palm. “Move, damn you!”
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