Napoleon’s Pyramids

CHAPTER ELEVEN

I began with one of the expedition’s astronomers, Nicholas-Antoine Nouet. While most of the French had cursed the desert for its enervating heat and scuttling vermin, Nouet had been delighted, saying the dry air made it unusually easy to chart the heavens. ‘It’s an astronomer’s paradise, Gage! A country without clouds!’ I found him crouched at the new institute, coat off and sleeves rolled up, sorting through a stack of calibrated rods used to measure the position of the stars against the horizon.

‘Nouet,’ I addressed, ‘is the sky constant?’

He looked up with irritation since I’d broken his chain of thought. ‘Constant?’

‘I mean, do the stars move?’

‘Well.’ He straightened, looking outside to the shaded garden that the scientists had expropriated. ‘The earth rotates, which is why the stars seem to rise and set like the sun. They make a wheel around our northern axis, the polestar.’

‘But the stars themselves don’t move?’

‘That is still under debate.’

‘So thousands of years ago,’ I pressed, ‘when the pyramids were built, the sky would have looked like it does now?’

‘Ah, now I see what you’re driving at. The answer is yes – and no. The constellations would basically be unchanged, but the earth’s axis wobbles on a twenty-six-thousand-year cycle.’

‘Doctor Monge told me about that, on L’Orient. He said the position of the zodiac, relative to the rising sun on a particular date, changes. Would anything else?’

‘One difference over many millennia would be the polestar. Because the earth’s axis wobbles, it pointed to a different North Star thousands of years ago.’

‘Is there any chance that star might have been Draco?’

‘Why, yes, I believe so. Why do you ask?’

‘You’ve heard I have an artifact of the past. My preliminary investigations here in Cairo suggest it may represent the constellation of Draconis, the dragon. If Draco was the polestar…’

‘It tells you to orient your artifact north, perhaps.’

‘Precisely. But why?’

‘Monsieur, it is your fragment of antiquity, not mine.’

‘Monge showed me something else in the hold of L’Orient. It was a circular device with signs of the zodiac. He thought it was some kind of calendar, perhaps to predict future dates.’

‘That wouldn’t be unusual among ancient cultures. Ancient priests exhibited great power if they could predict how the heavens would look in advance. They could forecast the rising of the Nile and optimum dates for sowing and reaping. The power of nations and the rise and fall of kings hinged on such knowledge. To them, religion and science were one. Do you have this device? Perhaps I could help decipher it.’

‘We left it aboard L’Orient with the Maltese treasure.’

‘Bah! So it could be melted down and spent by the next batch of rascals to seize control of the Directory? Why are such treasures on a warship that might go into battle? These are tools we need here in Egypt! Get Bonaparte to let you fetch it, Gage. These things are usually simple, once you puzzle them out.’

I needed something more substantial before going to our general. Enoch was still ensconced with the medallion in his library when I learnt, two days later, that the geographer Jomard whom I’d met in the hold of L’Orient was going to cross the Nile to Giza and make the first preliminary measurements of the pyramids. I volunteered my services and those of Ashraf as guide. Talma came too while Astiza, now subject to the customs of Cairo, stayed behind to help Enoch.

The four of us enjoyed the morning breeze as we ferried across. The river ran close to the mammoth structures, along a sand-and-limestone bluff that led up to the plateau where they were built. We beached and began climbing.

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.’

‘Ah, yes,’ said Talma. ‘As a babe I did it before my naps.’

Jomard refused to be goaded. ‘Anyone who has seen the shadow the earth casts on the moon or watched a ship disappear below the horizon would suspect our planet is a sphere. We know the Greek Eratosthenes used the differing length of shadows cast by the noon sun at the summer solstice at two different points in Egypt to get within 320 kilometres of the correct answer in 250 B.C. This pyramid was nearly three thousand years old when he made his measurement. Yet what was to prevent its ancient builders from doing the same, or measuring relative star height at points north and south along the Nile to again calculate the angles and, by implication, the size of our planet? If you travel along the river the height of stars above the horizon changes by several degrees, and Egyptian mariners would surely have noticed that. Tycho Brahe did such star measurements with his naked eye to sufficient accuracy to calculate the size of the earth, so why not the ancients? We attribute the birth of knowledge to the Greeks, but they attributed it to the Egyptians.’

I knew Jomard had read more of the ancient texts than any of us, so I regarded the great mass before me with new curiosity. Its outer sheathing of smooth limestone had been robbed centuries ago to build Muslim palaces and mosques in Cairo, so only the core blocks remained. Yet each piece of that was colossal, set in endless rows. I began to count the tiers of masonry and gave up after a hundred. ‘But the Egyptians had no ships to circle the globe, so why would they care what size the planet was?’ I objected. ‘And build a mountain to contain a calculation? It makes no sense.’

‘As baffling as building St Peter’s to a being none but saints and lunatics can claim to see,’ Jomard retorted. ‘What makes no sense to one man is life’s purpose to another. Can we even explain ourselves? For example, what is the point of your Freemasonry, Talma?’

‘Well…’ He had to think a moment. ‘To live harmoniously and rationally, instead of killing each other over religion and politics, I think.’

‘And here we are, a few miles from the offal of a battlefield produced by an army filled with Masons. Who is to say who is the lunatic? Who knows why the Egyptians would do such a thing?’

‘I thought this was the tomb of the pharaoh,’ Talma said.

‘A tomb with no occupant. When Arab treasure hunters broke in centuries ago and tunnelled around granite plugs meant to seal the entrance forever, they found not a sign that any king, queen, or commoner had ever been laid to rest here. The sarcophagus was lidless and empty. There was no writing, and not a scrap of treasure or worldly goods to commemorate who it was built for. The greatest structure on the face of the earth, taller than the highest cathedrals, and empty as a peasant’s cupboard! It is one thing to be a megalomaniac, harnessing tens of thousands of men to build your final resting place. It is quite another to do so and not rest there.’

I looked as Ashraf, who had not followed our French. ‘What’s the pyramid for?’ I asked in English.

He shrugged, less in awe of the monument than we were. Of course, he’d lived in Cairo all his life. ‘To hold up the sky.’

I sighed and turned back to Jomard. ‘So you think it’s a map?’

‘That is one hypothesis. Another is that its dimensions signify the divine. For thousands of years, architects and engineers have recognised that some proportions and shapes are more pleasing than others. They correspond to each other in interesting mathematical ways. Some feel such sublime relationships reveal fundamental and universal truths. When our own ancestors built the great Gothic cathedrals, they tried to use their dimensions and geometric proportions to express religious ideas and ideals, to in effect make the building itself holy by its very design. “What is God?” Saint Bernard once asked. “He is length, width, height, and depth.”’

I remembered Astiza’s excitement over Pythagoras.

‘So?’ Talma challenged.

‘So this pyramid may have been, to the ancients who built it, not a picture of the world, but a picture of God.’

I stared uneasily at the vast structure, the hair prickling on my neck. It was utterly silent, and yet from nowhere I sensed a low, background hum, like the sound of a seashell pressed to the ear. Was God a number, a dimension? There was something godlike in the perfect simplicity before me.

‘Unfortunately,’ Jomard went on, ‘all these ideas are difficult to verify until measurements are made to confirm whether height and perimeter match in scale the dimensions of our earth. That will be impossible to do until we excavate enough to find the pyramid’s true base and corners. I’ll need a small army of Arab workmen.’

‘I suppose we can go back then,’ Talma said hopefully.

‘No,’ said Jomard. ‘We can at least begin to measure its height from the lowest course of stone we can see. Gage, you will help with the tape. Talma, you must take the utmost care to write down each stone height we give you.’

My friend looked dubiously upward. ‘All that way?’

‘The sun is declining. By the time we reach the top, it will be cooler.’

Ashraf chose to remain below, clearly believing such a climb was something only sun-addled Europeans would do. And indeed, it wasn’t easy. The pyramid seemed far steeper once we began to mount it.

‘An optical illusion makes it appear squatter than it is, when viewed head on,’ Jomard explained.

‘You didn’t tell us that before we started up,’ Talma grumbled.

It took the three of us more than half an hour of careful ascent to get halfway. It was like climbing titanic children’s blocks, a giant’s staircase, with each step averaging two and a half feet in height. There was a real possibility of a nasty fall. We carefully measured each course of interior stone as we climbed, Talma keeping a running tally.

‘Look at the size of these monsters,’ the journalist said. ‘They must weigh several tons. Why not build with smaller pieces?’

‘Some engineering reason, perhaps?’ I suggested.

‘There’s no architectural requirement for stones this big,’ Jomard said. ‘Yet the Egyptians cut these behemoths, floated them on the Nile, dragged them up that hill, and somehow hoisted them this high. Gage, you’re our expert on electricity. Could they have used such a mysterious force to move these rocks?’

‘If so, they had mastery of something we barely understand. I can devise a machine to give you a tingle, Jomard, but not to do any useful work.’ Once again I felt inadequate to the mission I’d given myself. I looked around for something tangible to contribute. ‘Here’s something. Some of these stones have shells in them.’ I pointed.

The French savant followed my finger. ‘Indeed!’ he said with surprise. He bent to inspect the limestone I’d pointed to. ‘Not shells, but the fossils of shells, as if these blocks originated from beneath the sea. It’s a curiosity that has been noticed in mountain ranges in Europe, and has generated new debate about the age of the earth. Some say sea creatures were carried up there by the Great Flood, but others contend that our world is far older than biblical reckoning, and what today are mountains were once beneath the ocean.’

‘If that is true, the pyramids may be older than the Bible as well,’ I suggested.

‘Yes. Changing the scale of time changes everything.’ He was running his eye along the limestone, admiring the impressions of shells. ‘Look, there! We even have a nautilus!’

Talma and I peered over his shoulder. Imbedded in a pyramid block was the cross section of a spiral nautilus shell, one of the most beautiful shapes in nature. From its small corkscrew beginning its chambers grew larger, in pleasing and delicate proportion, as the sea creature grew in an elegant outward spiral. ‘And what does that make you think of?’ Jomard asked.

‘Seafood,’ Talma said. ‘I’m hungry.’

Jomard ignored that, staring at the spiral in the rock, transfixed for a reason I didn’t understand. Long minutes ticked by and I dared look out from our perch. A hawk was gliding by at our same elevation. It made me dizzy.

‘Jomard?’ Talma finally prompted. ‘You don’t have to watch the fossil. It’s not going to run away.’

As if in reply, the savant suddenly took a rock hammer from his survey bag and tapped at the block’s edges. There was already a crack near the fossil and he worked with this, succeeding in splitting the nautilus specimen loose and cupping it in his hand. ‘Could it be?’ he murmured, turning the elegant creature to see its pattern in light and shadow. He seemed to have forgotten our mission, and us.

‘We’ve still a way to go to the top,’ I warned, ‘and the day is getting late.’

‘Yes, yes.’ He blinked as if waking from a dream. ‘Let me think about this up there.’ He put the shell in his satchel. ‘Gage, hold the tape. Talma, ready your pencil!’

The summit took another half hour of careful climbing. It was more than 450 feet high, our measuring showed, but we could produce no more than a rough approximation. I looked down. The few French soldiers and Bedouins we could see looked like ants. Fortunately the pyramid’s capstone was gone, so there was a space about the size of a bed on which to stand.

I did feel closer to heaven. There were no competing hills, just flat desert, the winding silver thread of the Nile, and the collar of green on each of its shores. Cairo across the river shimmered with a thousand minarets, and we could hear the wail of the faithful being called to prayer. The battlefield of Imbaba was a dusty arena, dotted with pits where the dead were being tossed. Far to the north, the Mediterranean was invisible over the horizon.

Jomard took out his stone nautilus again. ‘There is clarity up here, don’t you think? This temple focuses it.’ Plopping down, he began to jot some figures.

‘And not much else,’ Talma said, sitting himself in exaggerated resignation. ‘Did I mention that I’m hungry?’

But Jomard was lost again in some world of his own, so finally we were quiet for a while, having become accustomed to such meditation by the savants. I felt I could see our planet’s curve, and then scolded myself that it was illusion at this modest height. There did seem a kind of benign focus at the structure’s summit, however, and I actually enjoyed our quiet isolation. Had any other American been up here?

Finally Jomard abruptly rose, picked up a limestone fragment as big as his fist, and hurled it as far as he could. We watched the parabola of its fall, wondering if he could throw far enough to clear the pyramid’s base. He couldn’t, and the stone bounced off the pyramid’s stone blocks below, shattering. Its pieces rattled down.

He looked down the slope for a moment, as if considering his aim. Then he turned to us. ‘But of course! It’s so obvious. And your eye, Gage, has been the key!’

I perked up. ‘It has?’

‘What a marvel we are standing on! What a culmination of thought, philosophy, and calculation! It was the nautilus that let me see it!’

Talma was rolling his eyes.

‘Let you see what?’

‘Now, has either of you heard of the Fibonacci sequence of numbers?’

Our silence was answer enough.

‘It was brought to Europe about 1200 by Leonardo of Pisa, also known as Fibonacci, after he had studied in Egypt. Its real origin goes much further back than that, to times unknown. Look.’ He showed us his paper. On it was written a series of numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. ‘Do you see the pattern?’

‘I think I tried that one in the lottery,’ Talma said. ‘It lost.’

‘No, see how it works?’ the savant insisted. ‘Each number is the sum of the two before it. The next in the sequence, adding 34 and the 55, would be 89.’

‘Fascinating,’ Talma said.

‘Now the amazing thing about this series is that with geometry, you can represent this sequence not as numbers but as a geometric pattern. You do so by drawing squares.’ He drew two small squares side by side and put a number 1 inside each. ‘See, here we have the first two numbers of the sequence. Now we draw a third square alongside the first two, making it as long as they are combined, and label it number 2. Then a square with sides as long as a number 1 square and number 2 square combined, and label it 3. See?’ He was sketching quickly. ‘The side of the new square is the sum of the two squares before it, just as the number in a Fibonacci sequence is the sum of the two numbers before. The squares rapidly get bigger in area.’

Soon he had a picture like this:

‘What does that number at the top, the 1.6 something, mean?’ I asked.

‘It’s the proportion of the length of the side of each of the squares to the smaller one before it,’ Jomard replied. ‘Notice that the lines of the square labelled 3 have a proportional length with the lines of the squares 2 as, say, the proportion between square 8 and square 13.’

‘I don’t understand.’

‘See how the line at the top of square 3 is divided into two unequal lengths by its junction with squares 1 and 2?’ Jomard said patiently. ‘That proportion between the length of the short line and the long line is repeated again and again, no matter how big you draw this diagram. The longer line is not 1.5 times the length of the shorter, but 1.618, or what the Greeks and Italians called the golden number, or golden section.’

Both Talma and I straightened slightly. ‘You mean there’s gold here?’

‘No, you cretins.’ He shook his head in mock disgust. ‘Only that the proportions seem perfect when applied to architecture, or to monuments like this pyramid. There’s something about that ratio which is instinctively pleasing to the eye. Cathedrals were built to reflect such divine numbers. Renaissance painters divided their canvases into rectangles and triangles echoing the golden section to achieve harmonious composition. Greek and Roman architects used it in temples and palaces. Now, we must confirm my guess with measurements more precise than those we’ve made today, but my hunch is that this pyramid is sloped precisely to represent this golden number, 1.618.’

‘What has the nautilus to do with anything?’

‘I’m coming to that. First, imagine a line descending under our feet from the tip of this colossus to its base, straight down to the desert bedrock.’

‘I can confirm it is a long line, after that hard climb up,’ Talma said.

‘More than four hundred and fifty feet,’ Jomard agreed. ‘Now imagine a line from the centre of the pyramid to its outside edge.’

‘That would be half the width of its base,’ I ventured, feeling the same two steps behind that I’d always felt with Benjamin Franklin.

‘Precisely!’ Jomard cried. ‘You have an instinct for mathematics, Gage! Now, imagine a line running from that outside edge up the slope of the pyramid to where we are here, completing a right triangle. My theory is that if our line at the pyramid’s base is set as one, such a line up to the peak here would be 1.618 – the same harmonious proportion as shown by the squares I’ve drawn!’ He looked triumphant.

We looked blank.

‘Don’t you see? This pyramid was built to conform to the Fibonacci numbers, the Fibonacci squares, the golden number that artists have always found harmonious. It doesn’t just feel right to us, it is right!’

Talma looked across to the other two large pyramids that were our neighbours. ‘So are they all like that?’

Jomard shook his head. ‘No. This one is special, I suspect. It is a book, trying to tell us something. It is unique for a reason I don’t yet understand.’

‘I’m sorry, Jomard,’ the journalist said. ‘I’m happy for you that you are excited, but the fact that imaginary lines equal 1.6, or whatever you said, seems an even sillier reason to build a pyramid than calling something pointed a hemisphere or building a tomb you won’t be buried in. It seems perfectly possible to me that if any of this is true, your ancient Egyptians were at least as crazy as they were clever.’

‘Ah, but that is where you are wrong, my friend,’ the savant happily replied. ‘I don’t blame your scepticism, however, because I didn’t see what has been staring us in the face all day until sharp-eyed Gage here helped me find the fossil nautilus. You see, the Fibonacci sequence, translated into Fibonacci geometry, yields one of the most beautiful designs in all nature. Let’s draw an arc through these squares, from one corner to another, and then connect the arcs.’ He flipped his drawing. ‘Then we get a picture like this:’

‘There! What does that look like?’

‘The nautilus,’ I ventured. The man was damned clever, even though I still didn’t get where he was heading.

‘Precisely! Imagine if I expanded this picture by adding additional squares: 21, 34, and so on. This spiral would continue to grow, round and round, bigger and bigger, looking ever more like our nautilus. And this spiral pattern is something we see again and again. When you take the Fibonacci sequence and apply it to geometry, and then apply that geometry to nature, you see this sublime number pattern, this perfect spiral, being used by God himself. You will find the spiral in the seed head of a flower or the seeds of a pinecone. The petals on many flowers are Fibonacci numbers. A lily has 3, a buttercup 5, a delphinium 8, corn marigolds 13, some asters have 21, and some daisies 34. Not all plants follow the pattern, but many do because it is the most efficient way to push growing seeds or petals out from a common centre. It is also very beautiful. So, now we see just how marvellous this pyramid is!’ He nodded to himself, satisfied with his own explanation.

‘It’s a flower?’ Talma ventured, relieving me of the burden of being dense.

‘No.’ He looked solemn. ‘What we have climbed is not just a map of the world, Monsieur Journalist. It’s not even just a portrait of God. It is in fact a symbol for all creation, the life force itself, a mathematical representation of how the universe works. This mass of stone incorporates not just the divine, but the very secret of existence. It has encoded, within its dimensions, the fundamental truths of our world. The Fibonacci numbers are nature at its most efficient and beautiful, a peek at divine intelligence. And this pyramid embodies them, and by doing so embodies the mind of God himself.’ He smiled wistfully. ‘Here it was, all life’s truth in the dimensions of this first great building, and everything since has been a long forgetting.’

Talma gaped as if our companion had gone mad. I sat back, not knowing what to think. Could the pyramid really exist to enshrine numbers? It seemed alien to our way of thinking, but perhaps the ancient Egyptians looked at the world differently. So was my medallion some kind of mathematical clue or symbol as well? Was it in any way connected to Jomard’s strange theories? Or was the savant reading something into this heap of stone that its builders never intended?

Somewhere in that direction was L’Orient, with a calendar that might hold more keys to the puzzle, and that seemed the next thing I could examine. I went to touch the medallion hidden against my breast and suddenly felt disquiet that it wasn’t there. Maybe Talma was right: I was too naive. Was I right to trust Enoch? And with Jomard’s right triangle in mind I imagined the medallion’s arms as dowsing rods, pointing to something far below my feet.

I looked back down the dizzying way we’d come. Ashraf was walking to follow the line of the pyramid’s shadow, his gaze toward the sand instead of up to the sky.