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Orientation of the Parthenon

Penrose assumed a priori that the Parthenon must have had corners with right angles. We cannot be too harsh on him for this error, because to assume the existence of regularities that do not occur is one of the pitfalls of the scientific mind.1 Penrose’s error may be understandable, but the fact that the only man who investigated the Parthenon in a truly scientific spirit fumbled on the problem of the squareness of the angles had most unfortunate consequences. Since he did not investigate the problem of the angles of Greek temples nobody has touched upon it since. There are no data about the angular measurements of the corners of Greek temples. This is the result of ill-will against scientific thought by archaeologists, because in the surveying of Greek temples they have often resorted to the assistance of professional surveyors and these, if left to their own initiative, would have measured the angles as a matter of routine. Even Balanos, who had the assistnace of technicians of the Greek geodetic service, did not ask them to test the angles of the Parthenon. If the angles of Greek temples were to be measured, we would have a simple set of data to ascertain in precise quantitative terms what was the limit of accuracy that the Greek builders aimed at and which was the limit of precision they were able to achieve. This would put an end to the prevailing contention that the Greeks were pre-scientific and did not care about accuracy and were not able to achieve precise measurements.2

Penrose made a slip in the matter of the calculation of the angles and of the orientation of the Parthenon. Thereby he opened his flank for an attack by those who are hawkeyed for any opportunity to discredit those who ascribe scientific thinking to the Greeks. In a paper entitled ”Archaeology and Astronomy,” Dinsmoor attacked as ”grotesque” the notion that ”people observing lunar calendars” could have paid attention to the heliacal rising of stars,3 ignoring all the abundant Egyptian and Mesopotamian material that reveal a deep concern with the exact dates and orientation of celestial bodies and of Venus in particular. His main contention (p. 105) was that ”No ancient people possessed such a calendar as would bring any designated moment in the same relationship with the sun or stars in recurring years.” Accordingly the establishment of the regularity of motions of heavenly bodies by observations conducted year after year would have been impossible. Having in this way thrown an entire library of ancinet astronomical texts into the wastebasket, Dinsmoor felt justified in charging Penrose with “blind devotion to astronomy.” (p. 96) Actually Dinsmoor, in the first line of his paper, averred “to know nothing about astronomy.” Instead of asking whether such ignorance is justifiable in an expert on ancient Greek culture, he begged the question by arguing: “It is possible that my primitive state of mind may place me closer to the ancients.” (p. 96) There is no need to follow the rest of the arguments because the conclusion is already implied in the premise: let us use bad reckonings and bad astronomy and thereby we shall have proved that the ancients were bad reckoners and bad astronomers.

What concerns me here is that Dinsmoor used the orientation of the Great Pyramid of Gizah to prove two points: that the ancients could obtain only crude astronomical data and that they could establish right angles with only modest precision (pp. 106-107). He granted that there are numerous Egyptian texts which indicate that Egyptian temples and important buildings were oriented by the polar stars, but he disregarded them as being ”astrological” in meaning. (p. 105). Unfortunately today it has become common among scholars of the ancient world to dismiss outright, without submitting any proof, as “astrological” all texts that contain astronomical data obnoxious to them. Having made short thrift of the textual evidence to the contrary, Dinsmoor asserted that the pyramids were intended to be oriented to the east as indicated by the equinoctial point. Accordingly the builders of the Second and Third Pyramids would have made an error of 5½ and 14 minutes respectively. Then he pointed out that the Great Pyramid has sides with orientations of 0°1’ 57” and 0°2’ 28” north of east and 0°5’30” west of north. According to his argument this proves an error in observing the east compunded by errors in calculating the right angles. Hence, he concluded that the Egyptian astronomers did not use any astronomical calculations, based on past records (which according to him their primitive calendar prevented them from keeping), but on rough observations which could not extend beyond the period of a year. According to him the Egyptian astronomers observed the sun ”towards the time of the solstices,” since they did not know for sure the exact time of the solstices; then, having obtained two points roughly corresponding with north and south, bisected the distance to obtain the direction of the east. His argument was that if the Egyptians were so roughshod in matters of orientation, this would be even more true in the case of the Greeks. Damning the Egyptian astronomers with faint praise, he admires the precision obtained in setting the angles of the Great Pyramid, in spite of their alleged methods. Hence, we must expect much less precision in the orientation of Greek temples in the setting of their angles. Le us leave ut at this time the problem of the orientation of the Parthenon (according to Dinsmoor the Athenians set it without any calculation by looking at the position of the sun as it rose behind the mountains on the day of the foundation of the temple) and let us concentrate on the simpler and more fundamental problem of the precision of angular measurements. It is obvious that people who cannot proceed to precise angular measurements cannot have an astronomical science. Why settle the question of the Greek angular measurements by interpreting or misinterpreting the data provided by the Egyptian pyramids? Why waste time arguing whether Egyptian texts contain astronomical data or are sheer astrology? Dinsmoor boasted of having spent decades in measuring Greek temples. Hic Rhodus, hic salta. Since he claims that the Greeks could not measure angles except in the crudest way, he should have proved it by tests of the angles of Greek temples.

Although I believe that there is a strong possibility that Greek temples were oriented astronomically and I am convinced that this possibility must be thoroughly investigated, I must state that nobody has yet proved that they were so oriented (except for the gross fact that they usually faced east). Certainly Dinsmoor has not produced an iota of evidence to the effect that the Parthenon was so oriented.

Penrose assumed that the orientation of the Parthenon was established by the point of the heliacal rising of some heavenly body on a day particularly sacred to Athena. In his numerous publications on the subject, Penrose could not arrive at any definite conclusion, because he considered too wide a range of possibilities—the heliacal rising of a star or planet, and even the point of the rising of the sun on given dates. In my opinion, since Athena is the planet Venus, one should start by presuming that a temple of Athena would be oriented according to the heliacal rising of Venus. By this restriction the problem of whether the Parthenon was oriented astronomically or not becomes sufficiently delimited to permit a solution. But it would be unconscionable to ask the reader to accept as a fact this educated guess of mine, although the contention of Dinsmoor that the Parthenon was oriented according to the rising of the sun is not supported by any more evidence. I do not intend to pursue this matter in this chapter, since here I am concerned only with the question of the accuracy of angles.

Incidentally, Dinsmoor tried to prove that the substructure was laid out in 488 B.C. also by its orientation to the horizon. It would have been oriented to the point of the rising of the sun on the foundation day. But, since Dinsmoor introduces this argument also in order to support his cherished theory that hte Greeks did not have a scientific conception of the apparent movements of the sun and were incapable of any accurate observation and measurement, he feels justified in submitting only rough calculations such that they cannot be in any way employed to single out the year 488 B.C. rather than any other. Dinsmoor resorts to his favorite device of denying that the Greeks were capable of scientific thought and of exact measurements in order to justify the distorted and arbitrary use of scientific arguments and quantitative data.

References

  1. Galileo, even though he tried to free science from Aristotelian metaphysics, held on, against Kepler’s better understanding, to the notion that the orbits of the planets must be circular.

  2. According to my statistical tabulations the Greek mints aimed at an accuracy of 1/8 of an English grain in the weighing of coins; it can be presumed, even there are no data for a statistical tabulation, that an even greater accuracy was aimed at in preparing reference weights. As I have explained, since the standards of weight were obtained by constructing cubes of the units of length, a precision of 1/8 of an English grain or better in the weights implies a corresponding precision in linear measurements and the drawing of right angles.
  3. Proceedings of the American Philological Society, LXXX, 1939, p. 95, first page of abstract.

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