Ethan Gage Collection # 1 (39 page)

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.

M
y 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!”

A
stiza 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 sup
posedly 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.

T
he 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!”

Then I recalled what others had named the medallion since I'd won it. A key. I tried sliding the disc into the crack but it was slightly convex and its swell wouldn't fit.