Pyramid Quest (22 page)

For the sake of cosmic symmetry, the Egyptians duplicated this triplicate system at the boundary of Upper and Lower Egypt. They created three lines, each 6° north of the corresponding southern boundary limits: 30° 6’, 30°, and 29° 51’. Significantly, the band between 30° 6’ and 29° 51’ fell within the jurisdiction of none of the local districts, or nomes, of either Upper or Lower Egypt. The boundary zone was something like the United States’ District of Columbia or Mexico’s Distrito Federal, a national capital over which no single town, city, or state had political sway.

Hieroglyphics represented the boundary district as a rectangle that either stood empty or enclosed water or fish. This is an image or icon found all over the world for the Square of Pegasus, a sky region of four stars that form a square. The stars are associated with water and fish because they are part of the constellation Pisces (which means “fish” in Latin). In ancient times, the Square of Pegasus represented the starting point for mapping the sky. The Egyptian “fishpond” district stood for the same point in mapping the earth, and it centered the Two Lands.

It is no accident that the Great Pyramid sat in this district’s center at 30°—or as close to it as the ancient Egyptians could measure. The structure occupied a balance point between Upper and Lower Egypt, exactly on the meridian, its corners defining the limits of the Nile Delta and thus the eastern and western boundaries of Egypt—all at a point exactly one-third of the way between the equator and the pole. Any one of these correspondences could have happened by accident, but so many happening in one spot is no coincidence.

You could come away from all this thinking that the Old Kingdom Egyptians were a narcissistic bunch. After all, they saw their land as the starting point of earth mapping, in the same way that the Square of Pegasus performed that function in the sky, and established their own prime meridian as the center of the ancient world. Yet the Egyptians saw beyond their own country. According to Stecchini, they incorporated into the Great Pyramid a model of the Northern Hemisphere.

The model begins in the Great Pyramid’s perimeter. Based on the lengths for the sides measured by J. H. Cole in his 1925 survey, the perimeter of the monument is 921.455 meters. That value is almost exactly our current measurement for ½ minute of latitude at the equator: 921.463 meters. And if the Old Kingdom Egyptians knew what ½ minute of latitude was at the equator—1,758 royal cubits, to use their unit of measure—they did indeed know the circumference of the earth.

They understood more as well, particularly that the earth isn’t a sphere but an oblate spheroid. A radius drawn from the center of the planet to the equator is longer—6,378,758 meters, by one reckoning—than a radius drawn from the center to one of the poles: 6,355,858 meters, by the same reckoning, or a difference of 22,900 meters. The clue lies in the height of the Great Pyramid, which—it generally agreed—was intended to be 280 cubits. That was a cos mically pleasing number to the Egyptians, because 280 is divisible by 7. But, Stecchini argues, the Great Pyramid didn’t actually reach this height, topping out a bit short at approximately 279.5 cubits. By taking that half-cubit off the predicted and pleasing height, the Egyptians were indicating the slight flattening of the earth at the poles. They knew, too, that a degree of latitude at the equator was longer than a degree of latitude at the pole due to the polar flattening of the earth (see the appendices, section entitled “Latitude and Polar Flattening Expressed in the Shape of the Great Pyramid”).

Since elementary school, we have all seen what is called the Mercator projection, a map that takes the nearly spherical form of the earth and converts it to a flat rectangle. The Egyptians were doing something of the same with the Great Pyramid. They projected the dimensions of the Northern Hemisphere onto four triangles, where the apex represented the pole and the perimeter the equator. The scale was 1:43,200, a number chosen because it represented the length of one-half day (1 day = 24 hours = 1,440 minutes = 86,400 seconds; 86,400 seconds / 2 = 43,200).

In the middle of the third millennium B.C., the ancient Egyptians were demonstrating knowledge about the shape of the planet that wasn’t predicted until the seventeenth century A.D. by Isaac Newton—and not demonstrated experimentally until the eighteenth century.

By the time of the Old Kingdom, it is clear that the Egyptians had amassed a detailed knowledge of the earth and were sufficiently sophisticated to incorporate this knowledge into the Great Pyramid. From their point of view, this knowledge wasn’t recent, either. The geodetic reform that accompanied the unification of the Two Lands, when the seven-based royal cubit supplanted the geographical cubit, points to a body of earth-based knowledge that originated well before Menes pulled the unruly nomes into one political entity. The astronomical sophistication of ancient Egypt reaches back at least to the stargazers of Nabta Playa. The geodetic knowledge is probably every bit as old.

The Great Pyramid stands as a reminder of the extent and the antiquity of this knowledge, both of earth and sky, and it passes on to us at least the outlines of their knowledge. It’s enough to make one wonder: Was there anything else they were trying to tell us?

A CODE FOR THE BREAKING

GOD’S NUMBERS

PRACTICALLY FROM THE TIME NAPOLEON’S INVASION RESTORED ancient Egypt to the western intellectual landscape, various writers and scholars have looked to the pyramids of Giza, and particularly the Great Pyramid, as a source of wisdom. We have seen already how the monument embodies a remarkable level of astronomical and geodetic science. Yet some writers have taken this line of thought even further and proposed that the Great Pyramid provides answers to those ultimate questions about the universe usually assigned to theology and religion. To them, the Great Pyramid is more than an ancient marvel. It is a modern revelation.

John Greaves (1602-1652) would never have been one to say that religious interests brought him to explore the Great Pyramid in 1638 and 1639. An Anglican at a time when holy wars between Catholic and Protestant drenched much of Europe in blood, Greaves had no compunction about visiting the Vatican in the course of his research into ancient measures. Even though the archbishop of Canterbury was one of Greaves’s major sponsors, his stated purpose in going to Egypt was secular. He wanted to standardize the weights and measures of all nations, ancient and modern, once and for all.

Greaves was one of the few scholars in Europe who had the credentials to accomplish the task he set for himself. A 36-year-old professor of geometry at Gresham College in London, Greaves was a master of the ancient astronomical literature in Latin, Greek, Hebrew, Arabic, and Persian. As a mathematician, Greaves understood the implications of the uncertain standards of measure for the world he lived in. As an antiquarian, he thought of Egypt as a place that had escaped the ravages of time and preserved the original measures the modern world needed. Seeking to define those original measures and pass them down for all posterity, Greaves resolved to “have recourse to such monuments of Antiquity, as have escaped the injury, and calamity of time” and to establish the standard for metrology on “the most lasting monuments of the Ancients.”
¹
Listing the monuments that “have stood unimpaired for many hundred years, and are likely to continue many more,” Greaves put the Great Pyramid at the top, less because of its alleged astronomical and astrological connections than its mountainous, timeless stolidity.
²
Greaves entered the Great Pyramid as if he were passing into metrology’s inner sanctum.

What he sought there was elucidation of the English foot, which would then shed light on all units of measurement, ancient and modern. Along the way to Egypt, Greaves researched the Roman
pes,
or foot, and determined that it was just slightly shorter than the English foot. If the English foot were divided into 2,000 parts, the Roman foot was as long as 1,944 of them. It was also important that the Roman foot was
of the Greek foot used in building the Parthenon, that most perfect example of Athenian architecture.

To measure the Great Pyramid, Greaves had taken with him a 10-foot measuring rod, further divided into 10,000 equal parts, that was based on the foot standard preserved in Guild Hall in England. He used it to measure the pyramid’s base, which was so obscured by drifted sand and accumulated rubble that he came up well short, at only 693 feet, despite the accuracy of his instrument. Inside the pyramid, Greaves paid particular attention to the King’s Chamber, whose workmanship awed him. “The structure of it hath been the labour of an exquisite hand,” he wrote later.
³
Greaves meticulously and assiduously measured the King’s Chamber and its peculiar coffer, climbed the pyramid to estimate its height, and counted the exterior courses of limestone.

On his return to England, Greaves recorded his measurements, observations, and musings in
Pyramidographia: Or, a Description of the Pyramids in Ægypt
(1646).
Pyramidographia
is a fascinating mix of learned treatise and travel story that stands out even today for its scholarly quality. It also established a key idea that has influenced thinking and writing about the Great Pyramid ever since: that ancient Egypt had somehow extricated itself from the ordinary passage of time. Even for a scholar as nonsectarian and heterodox as Greaves, the Great Pyramid represented a kind of eternity, a zone of timelessness where the usual laws of decay and corruption held little power.

Isaac Newton (1643-1727), that giant of science known for gravity, calculus, and the clockwork universe, seized upon Greaves’s work for his own purposes. His study of Greaves’s data led him to believe that two different cubits were used during antiquity: a “sacred” cubit, utilized by the Israelites, and a “profane” cubit, utilized by non-Israelite nations. Even though Newton came close to Stecchini’s insight about different types of cubits, namely geographical and royal, Newton’s interest was less in ancient measure per se than it was in establishing once and for all the circumference of the earth, a number he hoped was encoded in the Great Pyramid. Newton needed this value for his theory of gravitation. Since Newton connected the power of gravity in part to the mass of the object exerting it, he needed to know the circumference of the earth to determine its gravitational pull. He hoped that by establishing the size of the cubit he could calculate the exact length of the classical stadium, which, according to some classical authors, was related to a geographical degree. With that number, Newton planned to compute the earth’s circumference to the degree of accuracy he needed.

Newton was stopped by the same obstacle that had prevented Greaves from getting an accurate measurement of the Great Pyramid’s base and perimeter: accumulated sand and rubble. Until the monument was properly cleared, there was no telling exactly where the bottommost course of masonry lay, and measurement was little better than speculation. When Newton didn’t find what he wanted in the ancient data, namely the value of a geographical degree that would give the size of the earth, he had to rely on the work of a French surveyor who in 1671 produced a highly accurate measurement of 1° as 69.1 miles. Newton used that value to complete his computations of the earth’s circumference and gravitational pull and to publish his work on gravity.

Despite his lack of success, Newton had furthered the idea that the Great Pyramid’s dimensions offered a timeless key for unraveling the deepest mysteries of the universe. It fell to another astronomer to take this idea in a direction Greaves and Newton never had in mind.

Charles Piazzi Smyth (1819-1900) was born to a career in science and exploration. His father, William Henry Smyth (1788-1865), achieved renown as naval vice-admiral and surveyor of coastal Sicily, Sardinia, and North Africa. Born in Naples during his father’s long professional sojourn in Italy, Charles took his middle name from his godfather, Giuseppe Piazzi (1746- 1826), the Roman Catholic cleric and astronomer who discovered Ceres, the first and largest asteroid, in the belt between Mars and Jupiter. Charles Piazzi Smyth was also the uncle of Robert Baden-Powell, famed British military officer and founder of the Boy Scouts and the Girl Guides.