## Simultaneous Transit

The method, proposed by Kate Spence, is called simultaneous transit and consists of observing two circumpolar stars, Kochab (beta-Ursa Minor) and Mizar (zeta-Ursa Major), keeping track of their relative positions. North is identified as the direction on the ground corresponding to the segment joining the two stars when it is perpendicular to the horizon. Because of precession, this direction shifts slowly around the north, and in fact it passed from left of the pole to right of the pole (i.e., from east to west) at around 2500 BC. Inspired by this fact, Spence plotted the deviation from true north of the segment as a function of time, obtaining a straight line. Then the

Figure 18.3: The segment used for the orientation of the pyramids according to Spence.
Figure 18.4: Orientation errors of the fourth dynasty pyramids in Spence's chronology. Notice the point P1, proposed by Spence to explain the anomalous orientation of Giza 2 maintaining the same date, and the point P2 proposed by the author with a slightly earlier date. See text for full details.

points corresponding to the orientation errors were positioned on the line, and finally the dates of construction were "read" on the time axis (in the case of Khafre an ad hoc assumption has to be introduced; see below), thus suggesting a very accurate chronology for the pyramids of the fourth dynasty.

This procedure, though it might seem foolproof, is completely different from the standard way with which experimental data are treated in physics, and for this reason it is also quite difficult to explain (Spence's article is written in a rather cryptic, Sibylline fashion). Usually one possesses given data chosen by the experimenter, such as the time at which a measure of the radioactivity of a substance is done, and experimental data, such as the quantity of a substance present at any given time. Putting the intervals of time on the x-axis and the measurements taken on the y-axis, the curve joining all the points thus obtained corresponds to the physical law underlying the phenomenon and thus provides information about it. Spence, however, did not have access to absolute data on the x-axis. Indeed, we do not know the precise dates of the reigns of the pharaohs of the fourth dynasty (there does not exist an absolute chronology of the Old Kingdom, since the first dating anchored to the Sothic cycle goes back to the Middle Kingdom only). Therefore, Spence is hypothesizing a certain law, and then reasonably adapting the measuring times accordingly. The result is what Spence calls a recalibration of the dates, which leads to the dating of Khufu, for example (or to be precise, the orientation ceremony of Khufu's pyramid), at 2467 BC.

It is evident that this work does not fit in too well with rigorous scientific method, because if you can adapt the points on the x-axis, you can then force a set of experimental data to follow one law rather than another (in particular, a straight line with a more or less marked gradient). No referee, that is, the person responsible for assessing the validity of a scientific paper for an international journal, would ever accept any work of experimental physics using this data procedure. Nevertheless, as we have learned, there may be occasions when insisting too slavishly on scientific rigor at all costs may be counterproductive, and Spence's conjecture is quite appealing. Spence's suggested chronology fits well with the astronomical dating of the shafts of the Great Pyramid; however, it post-dates the chronology habitually acknowledged by many Egyptologists by about 80 years, since they usually place Khufu's reign in the first half of the 26th century BC. To reconcile the simultaneous transit with this earlier dating, Juan Belmonte (2001a) noted that the orientation might have come about via the same method, but using two different stars, Megrez (delta-Ursa Major) and Phecda (gamma-Ursa Major), which both transit on the same side in relation to the pole. The graph of the simultaneous transit corresponding to these two stars turns out to match the earlier chronology fairly well.

In both cases, everything works well only if one resorts to a somewhat curious working hypothesis. As one can see immediately, in fact, the value of the error corresponding to Khafre's pyramid is situated correctly on the calibration line only if it has the opposite sign. To explain this fact, and therefore the fact that Khafre's pyramid deviates to the same direction as Khufu's, Spence has come up with a clever ruse: she assumes that, for some unknown reason, the orientation ceremony of the second pyramid took place in the summer, rather than in the winter. In winter, the segment between Kochab and Mizar is located to the right of the pole at night; hence, in summer, it is seen to the left, and for this reason the error, which should be toward the west, is actually toward the east. A similar trick has to be applied to Belmonte's method; it must be admitted that in the case of Khafre the orientation was effected with the two stars at their lower culmination, that is, under the pole, while all the other pyramids were oriented using the upper culmination.

Although I do find the simultaneous transit methods extremely convincing, I do not find convincing the explanations given for the "anomaly" of orientation of the Khafre pyramid. The reason is that the orientation of a pyramid must have been an operation—or a ceremony—of great importance, as we know happened with the temples. Therefore, it is likely that it would take place on the same day of the year (maybe at the heliacal rising of Sirius?) and not on a random day. So why was the ceremony for Khafre, and only him, held in the opposite season? The situation grows even more paradoxical with Belmonte's theory, since it is perhaps more natural and simpler to carry out observations on a configuration where the two stars he proposes are low on the horizon, and thus under the pole, something, however, that would have happened only in the case of Khafre. On the other hand, the simultaneous transit method is the only one ever proposed that is able to take into account the effect of precession on the distribution of the orientation errors. Not wishing to forsake this method, and at the same time hoping to solve the dilemma of the anomaly point without an ad hoc hypothesis, I proposed another solution a few years ago (Magli 2003, 2005a). Before discussing it, though, we have to return to a matter that was left standing.