As remarkable as it had been to fight in sight of these famed structures, they’d been too distant from Imbaba to impress us with their size. It had been their geometric purity, set against the stark desert, which caught the eye. Now, as we laboured up a trail from the great river, their immensity became apparent. The pyramids first peeked above the brow of the slope like perfect deltas, their design as harmonious as it was simple. The volume of their mass against the sky lifted the eye to their apex, beckoning us to heaven. Then, as they came into fuller view, their titanic dimensions were at last apparent, stone mountains ordained by mathematics. How had primitive Egypt built something so vast? And why? The very air seemed crystalline around them, and their majesty carried a strange aura, like the curious smell and prickling I sometimes feel when demonstrating electricity. It was very quiet here after the clamour of Cairo.
Adding to the pyramid’s daunting effect was their famed guardian who stared due east. The gigantic stone head called the Sphinx, as remarkable as we’d imagined from written descriptions, guarded the slope a short distance below the pyramids. Its neck was a dune of sand, its leonine body buried beneath the desert. The statue’s nose had been damaged years ago by Mameluke cannon practice, but its serene gaze, full African lips, and pharaoh’s headdress created a visage so eternal as if to deny the toll of time. Its eroded and damaged features made it seem older than the pyramids beyond, and made me wonder if it had perhaps been built before them. Was there something sacred about this site? What kind of people had made such a colossus, and why? Was it a sentinel? A guardian? A god? Or mere vanity to one man, tyrant and master? I couldn’t help but think of Napoleon. Would our republican revolutionary, liberator and common man, ever be tempted to commission a head like this?
Beyond were dunes strewn with scraps of rubble, broken walls, and the crumbled tips of smaller pyramids. The trio of major pyramids that dominated Giza made a diagonal line, northeast to southwest. The Great Pyramid of Khufu, called Cheops by the Greeks, was the closest to Cairo. A second, slightly smaller one beyond had been attributed by the Greeks to the pharaoh Khafre, or Khephren, and a third even smaller one to the southwest had been built by a Menkaure.
‘One of the interesting things about the Great Pyramid is that it is aligned precisely with the cardinal directions and not just magnetic north,’ Jomard told us as we rested a moment. ‘It is so precise that its priests and engineers must have had a sophisticated knowledge of astronomy and surveying. Also, notice how you can judge the direction you face by the way the pyramids relate to each other. The pattern of shadow works as a kind of compass. You could use the relation of their apexes and shadows to orient a surveying tool.’
‘You think they are a kind of geodetic landmark?’ I asked.
‘That’s one theory. The others depend on measurement. Come.’ He and Ashraf strode ahead, carrying reels of measuring tape. Talma and I, hot and winded from the climb, lagged a little behind.
‘Not a scrap of green,’ Talma muttered. ‘A place of the dead, all right.’
‘But what tombs, eh, Antoine?’ I looked back at the head of the Sphinx, the river below us, the pyramids above.
‘Yes, and you without your magic key to get inside.’
‘I don’t think I need the medallion for that. Jomard said they were opened centuries ago by Arab treasure hunters. I suppose we’ll go in ourselves, eventually.’
‘Still, doesn’t it bother you not to have the medallion?’
I shrugged. ‘It’s cooler not to carry it, frankly.’
He looked at the brown triangles above us, dissatisfied. ‘Why do you trust the woman more than me?’ The hurt in his voice surprised me.
‘But I don’t.’
‘When I’ve asked you where the necklace is, you’ve been coy. But she persuades you to give it to an old Egyptian we barely know.’
‘Loan it, for study. I didn’t give it to her, I loaned it to him. I trust Enoch. He’s a savant, like us.’
‘I don’t trust her.’
‘Antoine, you’re jealous.’
‘Yes, and why? Not just because she’s a woman, and you run after females like a dog after a bone. No, because she’s not telling us everything she knows. She has her own agenda, and it’s not necessarily ours.’
‘How do you know that?’
‘Because she’s a woman.’
‘A priestess, she said, trying to help us.’
‘A witch.’
‘Trusting Egyptians is the only way we’re going to solve the mystery, Antoine.’
‘Why? They haven’t solved it in five thousand years. Then we come along with some trinket and suddenly we have more friends than we know what to do with? It’s all too convenient for me.’
‘You’re too suspicious.’
‘You’re too naive.’
And with that we went on, neither satisfied.
As I trudged up the slippery sand toward the largest pyramid, sweating in the heat, I felt increasingly small. Even when I turned away the monument’s bulk seemed omnipresent, looming over us. Everywhere around us was the sand-strewn wreckage of time. We threaded past rubble that must once have been the walls of causeways and courtyards. The great desert rolled beyond. Dark birds wheeled in the brassy air. At last we stopped before the highest and greatest of all structures on earth, dunes undulating along its base. The blocks it was built from looked like the bricks of giants, massive and heavy.
‘And here, perhaps, is a map of the world,’ Jomard announced.
With his sharp features, the French savant reminded me of some of the carved stone falcons I had seen in Enoch’s house: Horus. He was looking up at the triangular face of the pyramid with happy awe.
‘A map of the world?’ Talma asked sceptically.
‘So said Diodorus and other ancient scholars. Or, rather, a map of its northern hemisphere.’
The journalist, flushed and cranky from the heat, sat down on an upended block. ‘I thought the world was round.’
‘It is.’
‘I know you savants are cleverer than I, Jomard, but unless I’m hallucinating, I believe the structure before me comes to a rather noticeable point.’
‘An astute observation, Monsieur Talma. You have the makings of a savant yourself, perhaps. The idea is that the apex represents the Pole, the base the equator, and each side a quarter of the northern half-sphere. As if you had sliced an orange first in half, horizontally, and then into four vertical pieces.’
‘None of them flat triangles,’ Talma said, fanning himself. ‘Why not just build a mound, like a loaf, if you want to model half our planet?
‘My maps of Egypt and the world are flat, and yet they represent something round,’ the savant replied. ‘Our question is, did the Egyptians, in an abstract way, design the pyramid with a precise angle and area to mathematically mirror our globe? The ancients tell us its dimensions correspond to a fraction of the 360 degrees in which we divide the earth. This is a sacred number that came from the Egyptians and Babylonians, based on the days of the year. So did they, in fact, choose proportions to demonstrate how to accurately translate a curved earth to a flat plane, like the face of a pyramid? Herodotus tells us that the area of the face of the pyramid is equal to the square of its height. It just so happens that such a proportion is an ideal way to calculate the surface area of a circle, like our planet, from a square, and translate the points of one to the other.’
‘Why would they do so?’ the journalist asked.
‘To boast, perhaps, that they knew how.’
‘But, Jomard,’ I objected, ‘People believed the world was flat until Columbus.’
‘Not so, my American friend. The moon is round. The sun is round. It occurred to the ancients that the earth, too, is round, and the Greeks used careful measurements to calculate the circumference. My idea is that the Egyptians preceded them.’
‘How could they know how big our planet is?’
‘It is child’s play if you understand basic geometry and astronomy, measuring fixed points against the shadow of the sun or the declination of the stars.’