Pyramid Quest (21 page)

But once the Egyptians knew that the earth is a sphere and where they stood on it, they were likely to ask another question: How big is the earth?

In theory, the answer isn’t that difficult to determine. First, you set up astronomical observatories at different latitudes. Ideally, the observatories are directly north and south of each other, but, with the proper mathematical analysis, the determination works even if they’re not. Next, select a suitable star and measure its highest point in the sky from each observatory. Alternatively, measure the angle of the sun at its noontime high point at a definite mark in its annual cycle, such as solstice or equinox. Simple geometry reveals that the difference between measurements depends on the latitudinal difference between the two observatories in degrees. Repeat these measurements again and again for a variety of stars or a succession of solstices or equinoxes to ensure reliable data. The third step is measuring the geographical distance between the two observatories on the ground. From this, one can determine the geographical distance equivalent to a change in 1 degree of latitude. Finally, multiply the distance per degree by 360—the number of degrees in a circle. The result is the circumference of the earth through the poles.

Conventional scientific history credits the first measurement of the earth’s circumference to the Greek-speaking astronomer Eratosthenes in about 250 B.C., well over two millennia after the Fourth Dynasty and the great age of pyramid building. Eratosthenes made his measurements in Egypt, using the angles of the sun at summer solstice in the cities of Alexandria, on the Mediterranean, and Syene, on the Nile in Upper Egypt. His result was 250,000 stadia, a somewhat problematical outcome, since no one is now certain just how far a stadion is. Most classicists assume that 1 stadion (a Greek term; in Latin it is
stadium
) equals
mile, which makes Eratosthenes’ calculation of the earth’s circumference equal to 25,000 miles. That’s within approximately 200 miles of our current measurement, or an error of less than 1 percent.

Given what we know of Egyptian astronomy and mathematics, there is no doubting that the elites of the Predynastic through Old Kingdom periods had the wherewithal to measure the earth’s circumference. But saying that the Egyptians could have done it is hardly the same as proving that they did. Academic Egyptologists have long rejected the notion that the Egyptians were anything but flat-earthers who could handle little more than simple arithmetic, despite the evident architectural achievements they left us. But there is another, maverick tradition that says the Egyptians knew and they proved their knowledge in the Great Pyramid. This line of thinking began in modern times with an insightful and unconventional Frenchman named Edmé-François Jomard (1777-1862). Jomard was only in his early twenties when he accompanied Napoleon’s army as one of the
savants
who turned the military invasion of Egypt into a major event of Western intellectual history—resulting in the immense, multivolume, multiau thored work
Description de l’Égypte.

One of the tasks that fell to Jomard during Napoleon’s occupation was measuring the exterior dimensions of the Great Pyramid. That was a difficult task; mounds of debris had built up along the monument’s sides. Still, Jomard and his colleagues made their measurement and came up with a length of 230.902 meters, or 757.5 feet, to a side. Next Jomard climbed the pyramid, then measured down each step. His result was 144 meters, or 481 feet, for the pyramid’s height. With basic trigonometry, Jomard calculated the Great Pyramid’s slope at just over 51°—51° 19’ 14”, to be exact. A further calculation told Jomard that the apothem, the distance from the center of the pyramid’s apex to the midpoint of any one of its sides, was 184.722 meters. Of necessity, Jomard was guessing a bit. Since the outer casing of the pyramid had been removed, he had to estimate the thickness of that last layer of limestone and work the number into his calculation.

Jomard’s result of 184.722 meters (606 feet) rang a bell in the young Frenchman’s classically trained mind. He knew that the historians Diodorus Siculus (c. 80-20 B.C.) and Strabo (c. 63? B.C.-A.D. 24?) said that the Great Pyramid’s apothem equaled 1 stadion (stadium), or about 600 feet, which was a basic unit of land measure in the ancient world. The Greeks of Alexandria—the community that had given rise to Hipparchus, the putative discoverer of precession, and to Eratosthenes—made the stadium equal to approximately 185.5 meters (608.6 feet), a number tantalizingly close to Jomard’s own measurement for the pyramid’s apothem. Was this coincidence, or was it the product of the pyramid builders’ intention?

Some of Jomard’s colleagues corroborated his understanding of the pyramid’s geodetic utility. When the surveyors among Napoleon’s
savants
realized that the monument was oriented correctly to the four cardinal directions, they used the north-south meridian running through the Great Pyramid’s apex as the base line for their measurements of the country. This led to a fascinating discovery: the meridian through the apex divided Lower Egypt neatly in two, while diagonals drawn from the pyramid’s corners completely enclosed the Nile Delta.

But other colleagues of Jomard torpedoed his ideas. When they remeasured the base of the pyramid, they found it to be 2 meters longer than Jomard had. They also made a new measurement of the height. Their result was higher than Jomard’s, which made his angle of incline too low and his apothem too short. The exactness Jomard had claimed fuzzed into sloppy approximation.

Jomard, though, didn’t give up easily. He argued that the Descending Passage was an observatory for watching circumpolar stars—an idea that we now know makes good sense—and that the coffer in the King’s Chamber was not a sarcophagus but a monument of measure: something of an Old Kingdom Bureau of Standards.

Still, modern Egyptologists have largely dismissed Jomard’s ideas on the Egyptians’ knowledge of the earth as so much wishful thinking. It was only in the second half of the twentieth century that a line of curiously esoteric research revealed that Jomard was onto something after all.

The late Livio Catullo Stecchini had the kind of career even academics consider academic. The son of a law professor at the University of Catania in Italy, Stecchini studied Latin and Greek in secondary school, then pursued philosophy in Germany at the University of Freiburg, where the great existentialist philosopher Martin Heidegger (1889-1976) was teaching. Stecchini, though, was less intrigued by the philosophical nature of being than by the study of ancient measurement, a subject that had first drawn his interest back in high school. Forced to leave Germany by Hitler’s attacks on the autonomy of the universities, Stecchini returned to Italy, earned a doctorate in Roman law, and held an academic position at the University of Rome. World War II brought Stecchini to the United States, where he became a candidate for a second doctorate at Harvard, this time in ancient history. While his professors were enamored of the Greeks for their literary and philosophical greatness, Stecchini was drawn more to the utilitarian and practical aspects of their lives. He wrote his dissertation on the origin of money in Greece. The thesis was accepted, and Stecchini got his degree, but the Harvard faculty felt he should lop all the numbers out of his manuscript before he published it, as the classicists of the time had no particular interest in what seemed nothing more than a bunch of extraneous arithmetic.

Stecchini, though, loved numbers, particularly old units of measure, and he continued his research into measurement in the ancient world. He progressed from the study of Greek monetary weights to the operation of Greek mints to the dimensions of Greek temples to ancient geography and geodesy. All the while, his fellow classicists told Stecchini that numbers didn’t count as evidence in ancient studies. Stecchini went off on his own, ignoring their advice, working in what he called “splendid isolation.”
²

In fact, Stecchini’s painstaking and solitary research demonstrates that numbers do matter. And in the case of the Great Pyramid, they matter a great deal.

The French surveyor
savants,
Stecchini showed, had detected only the beginning of the ancient Egyptians’ proclivity toward precise measurement of the land they inhabited. They were right in discovering that the meridian running through the Great Pyramid’s apex neatly divided the Nile Delta into two. In fact, this line served as the prime meridian for the entire country. The Egyptians extended it from Behdet, a Predynastic capital close to where the Nile empties into the Mediterranean at 31° 30’ north latitude, to the Great Cataract of the Nile, which lies directly south on the same line of longitude. The southern boundary of the country was set at 24° 00’ north, near the point where the Nile crossed the Tropic of Cancer, which then lay at 23° 51’ north latitude (it has since moved slightly), close to the First Cataract of the Nile at Aswan. The eastern and western boundaries of the country extended north-south from the edges of the Nile Delta along lines parallel to the prime meridian. The result was a country shaped like a long, thin rectangle and defined by right angles.

Geodetic knowledge in Egypt was so advanced that the country’s prime meridian became the baseline not only for cities and temples within the country but also for the rest of the eastern Mediterranean. It served the same earth-orienting purpose in the ancient world as the 0° longitude line running through Greenwich, England, in our own times. Mount Gerizim, an early Hebrew holy site that continues to be the ritual center of the Samaritan sect, lies exactly 4° east of the Egyptian prime meridian. Delphi, one of the two oracular centers of classical Greece and the geodetic cen-ter of the ancient Hellenes, is 7° north of Behdet along the same line of longitude as the Egyptian prime meridian, while Mecca, the sacred center of Islam (but dating back well before the time of Muslim culture), is both 10° east of Egypt’s western boundary and 10° south of Behdet. In a very real way, Egypt anchored the ancient world.

The location of Giza and the Great Pyramid relative to the Nile Delta and to the earth as a whole. (
From Smyth, 1880, plate II.
)

The geodetic system of ancient Egypt evidenced the unification of the two lands. In the Predynastic Period, the Egyptians measured the distance between their northern boundary (set at Behdet, 31° 30’ north latitude) and their southern (set at 24° 00’ north latitude) as 1.8 million geographical cubits. Therefore, one geographical cubit equaled approximately 1.5 modern feet, or, more precisely, about 461.7 millimeters. The cubit, represented by a hieroglyphic picture of a forearm (transliterated as “mh”)
³
, was not a basic unit of length only in ancient Egypt. The term
cubit
that we use is derived from the Latin
cubitum
(elbow). Each cubit was made up of 6 palms (also known as hands), which were further subdivided into 4 fingers (also known as digits). When the country was unified, a second geodetic system came into use, one that measured the distance from the base of the Nile Delta (31° 06’ north latitude) to the southern boundary of Egypt (24° 00’ north latitude) as 1.5 million cubits. In the new, longer measure, a single cubit, or “royal cubit,” was 524.1483 millimeters (or about 20.6 modern inches, or about 1.72 modern feet). This longer royal cubit was commonly divided into 7 hands, still with 4 fingers to each hand.

The royal cubit is significant because it is the measure used to lay out the Great Pyramid. It is also a base-seven unit, important because the number 7 was sacred to the Egyptians as a cosmic number, one that joined earth and sky. For example, it was a matter of no small importance to the people of the Old Kingdom that Upper Egypt extended 6° of longitude up the Nile, and Lower Egypt another 1°, a total of 7° that mirrored the sacred dimension. The sacred order of the sky replicated itself on the Two Lands in a visible demonstration of
ma’at.

The Egyptians also incorporated an aspect of the sky into the way they defined the boundary between Upper and Lower Egypt, an issue that helps explain the location of the Great Pyramid. In the Old Kingdom, the southern frontier of Egypt was seen as not one boundary but a composite of three lines. The southernmost was the Tropic of Cancer at 23° 51’. When the sun reached its noontime zenith on the summer solstice, it stood at 24° 6’,
^d
which is also the latitude of the lower edge of the First Cataract. That was the northernmost of the three lines. In between lay 24°, the latitude of the upper edge of the First Cataract.