Plotting the Pyramids Owen Gingerich

news and views Plotting the pyramids Owen Gingerich There is no evidence in ancient texts that Egyptians used astronomical knowledge in building the pyramids. But analysis of the night sky in 2500 BC could help explain how the pyramid builders knew the direction of true north. he Egyptian pyramids at Giza — one of 2467 BC, an Egyptian astronomer could wait the seven wonders of the ancient world while the heavens slowly pivoted around the T— are roughly 4,500 years old. Their unmarked pole until a plumb line exactly construction can be dated, at best, to within intersected both stars, one above the invisi- 100 years by existing methods. In this issue ble pole and the other below it (Fig. 1). The (Nature 408, 320–324; 2000), Egyptologist sight line to the horizon point directly below Kate Spence proposes a more accurate way to the plumb line would then point straight to date these monuments using subtle devia- north. tions in the alignment of their bases from true Big Dipper So far Spence’s suggestion is as specula- north.At first glance, this idea seems as likely tive as it is ingenious.But she then introduces as sharpening razor blades by placing them Mizar a second, hitherto unrecognized, mystery. under small pyramids (one of the claims The great pyramid of Khufu is the most made for ‘pyramid power’ in the 1970s). But Celestial Pole accurately aligned to north, deviating just on closer inspection, Spence has come up Kochab slightly to the west.The pyramid of Menkau- with an ingenious solution to a long-standing re, the second pharaoh after Khufu, errs by Little mystery: how were the great pyramids so Dipper about 13 arcminutes in the other direction, accurately aligned in relation to north? whereas the three earlier pyramids of Snofru, Since the nineteenth century it has been N Khufu’s predecessor,are oriented more west- known that the western and eastern sides of ward as they get older. Other pyramids, built the Khufu (Cheops) pyramid deviate from between 2600 and 2300 BC, confirm this true north by an average of three arcminutes. Figure 1 The night sky in ancient Egypt. Kate trend, and their orientations form a straight This corresponds to one-tenth the diameter Spence argues on page 320 of this issue that line when plotted against time. of the full moon and is not far from the 1–2 Egyptian pyramid builders used the vertical How can this puzzle be explained? Because arcminute precision achieved several millen- alignment of two bright stars in the of the Earth’s precession, the celestial north nia later by Tycho Brahe, the greatest of the constellations of the Big and Little Dipper to pole was exactly aligned between Kochab and pre-telescopic observers. align their pyramids north–south. In around Mizar only in the year 2467 BC, and the errors Such an accurate alignment is possible 2500 BC, the star Mizar in the Big Dipper and in the orientations of earlier and later pyra- only by some astronomical procedure, but Kochab in the Little Dipper were located on mids faithfully track the slow drift of Kochab the surviving Egyptian texts seem silent on opposite sides of the north celestial pole — the and Mizar with respect to true north.Because the method used. One way to define north fixed point in the sky around which all the stars the error in the Kochab–Mizar alignment can would be to compare the rising and setting rotate. In 2467 BC an invisible line linking these readily be calculated for any date, the error in positions of the Sun in the east and the west two stars, when they are vertically aligned, each pyramid’s orientation corresponds to a and bisect the angle between them. Such a would pass precisely through the north pole. A specific year.Although each alignment is sub- procedure would have to be carried out near plumb line intersecting these stars would then ject to individual measurement errors, the the time of a solstice, when the Sun seems point straight to north on the horizon. A similar collection of several data points makes the temporarily to stand still in its seasonal observation made before or after this date would method more robust.So it is not preposterous march higher or lower in the sky. But prob- include a systematic error caused by the to believe that Spence can calculate dates for lems with observing objects near the horizon alignment being offset slightly from true north pyramid construction to within five years or (because of interference from the Earth’s (as is the case here). Such astronomical errors so,considerably better than the 100-year error atmosphere), and with having a perfectly show up in the orientations of the ancient currently accepted for their chronologies. level view both east and west,make this tech- pyramids of Giza. A modern astronomer noticing the drift nique unreliable. of the two stars could easily come up with a An alternative method would involve stars in a 26,000-year cycle. simple observational solution to the prob- building some sort of scaffolding to provide This is where Spence’s idea comes in. lem. After 2467 BC, with Kochab directly a sight line for alignment with the north pole Although there was no pole star available for above Mizar, the alignment missed the pole star — except there was no suitable pole star accurately pinpointing north in ancient to the left. But 12 hours later, with Mizar when the pyramids were built. Directly Egypt, there was a pair of fairly bright stars, directly above Kochab, the offset would above their terrestrial counterparts, the one either side of the ancient celestial pole, move equally to the right. These two posi- celestial poles are points in the night sky which in 2467 BC lay precisely along a straight tions could be bisected to give true north. (If around which the stars appear to rotate. line including the pole. One is Kochab in the the 12-hour wait moved the observation into Today,the north celestial pole points close to bowl of the Little Dipper, the other Mizar in daylight, it would mean waiting several the star Polaris — currently designated the the middle of the handle of the Big Dipper months to observe the opposite configura- pole star. Because the Earth’s axis of rotation (to use the popular American names for Ursa tion at night.) is not fixed, but swings in a stately conical Minor and the main stars of Ursa Major). Spence’s interpretation requires that the motion known as precession, the positions Kochab and Mizar are technically known as determinations of north take place at just of the celestial poles drift slowly among the b-Ursae Minoris and z-Ursae Majoris. In one of the two vertical alignments of Kochab NATURE | VOL 408 | 16 NOVEMBER 2000 | www.nature.com © 2000 Macmillan Magazines Ltd 297 news and views and Mizar, generally with Mizar above. Two Egyptian astronomy, and even the constella- species are emerging2. This is allopatric pyramids that do not conform to this pattern tions recorded on the ceilings of tombs speciation, and Mayr’s view became the — the second great pyramid at Giza (Khafre) remain for the most part unknown and orthodoxy for many years. There is now and the later pyramid of Sahure — can easily unmatched with the actual starry sky.One of growing evidence, however, that sympatric be explained if the north alignment was done the few identified constellations is the Egypt- speciation can happen in the right circum- with Kochab above Mizar, producing an ian adze, the sculptor’s mythically powerful stances3. The study by Wilson et al. breaks error to the west instead of the east. tool for making magical images; the adze new ground by providing the first example Spence argues that there was an elaborate matches the modern Big Dipper. A pair of of replicated sympatric speciation: one ‘fixing the north’ ceremony that took place such images are depicted in the wall mural of species splitting in two several times inde- early in a new pharaoh’s reign, rather than a Tutankhamon’s tomb — probably the Big pendently. If confirmed, these natural repli- systematic sequence of observations over and Little Dippers — and elsewhere there is a cates would offer a unique opportunity to months or years. It is an interesting idea, but text about two sharp claws chasing each identify the factors that trigger sympatric one that needs to be tested. Can Egyptolo- other around the pole. Could this be an echo speciation. gists find references to such a ceremony in of Kochab and Mizar making their align- The cichlid fishes are particularly attrac- the ancient texts? This evidence would seem ment rounds? Be on the lookout, Egyptolo- tive for speciation studies. The 700 species to be crucial for the ultimate acceptance of gists,for any such obscure hints. ■ are remarkable for their diverse colours, Spence’s ingenious hypothesis, but sadly Owen Gingerich is at the Harvard-Smithsonian shapes and sizes, and behaviours (which there is no documentation relating to the Center for Astrophysics, Cambridge, Massachusetts include complex courtship and parental construction of the ancient pyramids. 02138, USA. care). Cichlids can speciate rapidly: the 300 In general, little is known about early e-mail: [email protected] species in Lake Victoria, east Africa, may have descended from a single ancestral cichlid in only the past 12,400 years4. Further, Speciation these fish may be prone to sympatric speciation. A remarkable case involves cichlids from isolated crater lakes in Cameroon5.

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