On the Invariance of the Tropical Zodiac -- Part IV

by Robert Hand

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The difference between the Ptolemaic positions and those of the Anonymous is exactly the 2 degrees that one would get using the erroneous value for precession of Ptolemy's. Only Regulus is different in the Anonymous but the corrected Ptolemy position gives exactly the sidereal position. The coinciding of the positions given by the Anonymous with the sidereal positions is a coincidence! And other authors that are sometimes cited as siderealists are from the same general period, Hephaistio of Thebes, and Firmicus Maternus. On page 10 of The Zodiac: A Historical Survey by Robert Powell the author cites a passage from Neugebauer's HAMA as evidence for the Anonymous being a siderealist. Unfortunately the passage in question is one in which Neugebauer is dating this author and another one named Cleomedes to the 4th century by showing that their values for star positions are derived from correcting Ptolemy's positions using his precessional constant! One wonders how much of the evidence for the sidereal zodiac among the Greeks comes from similarly questionable research.

When did the confusion of the zodiacs clearly end? There is no simple answer to this question. However, it is clear that the kind of confusion that we are documenting here survived among the Hindus. The following is from Varahamahira's Brihat Jataka, chapter 1, sloka 19.

"The measures of the first six signs are represented by the numbers 20, 24, 28, 32, 36, and 40 respectively. The same figures taken in inverse order give the measures of the second six signs."

These are our old friends the System A rising times for Babylon again; and again, just as in Valens, they are identified with the signs of the zodiac, not a separate set of 30 degree divisions having no fixed relation to the signs of the zodiac. And again they are symmetrical with respect to 0 degree Aries, something that can only happen in a tropical zodiac. Was this eminent figure of the Hindu tradition a tropicalist? Apparently so. In another early Hindu work, the Yavana Jataka, we also find symmetrical rising times, indicating a tropical zodiac although these rising times at least are recomputed for India.

We now have to deal with a fundamental question: which zodiac would have seemed the more reasonable to the ancients? This is not a trivial question because it has been argued by moderns that a sidereal zodiac would seem on the face of it to be more rational. After all while the stars to do have a small motion relative to each other, their proper motions', most of their apparent motion is in fact due to the backwards motion of the vernal point with respect to the fixed stars. It is obviously more rational from a modern point of view to consider the one point as being in motion rather than the many points. Also modern astronomy regards the solar system from the point of view of the Sun rather than the Earth, and it is therefore more reasonable to regard the stars as more or less stationary than it is to so regard one single Earth-related point, the vernal point.

But these are the criteria of moderns. Would they have been the criteria of the ancients? Certainly it would have been easier for them to measure positions with regard to fixed stars and we have abundant evidence of the practice. But we also know that various persons among the ancients were in fact quite capable of locating the cardinal tropical points as is evidenced by the number of allignments to the rising positions of the these points all over Europe.

The problem is that most of the ancients regarded the Earth as being completely stationary. There were exceptions such as some Pythagoreans, Aristarchos (who actually posited a heliocentric theory), and at least one Hindu, Aryabhata. The most common view was that there were eight spheres surrounding the earth. The eighth sphere held the fixed stars and also rotated about the stationary earth once very twenty-four hours, what was later called the Primum Mobile. The other seven are the spheres of the seven planets. Here is the description of the creation of these spheres from the Timaeus of Plato.

"And thus the whole mixture out of which he cut these portions was all exhausted by him. This entire compound he divided lengthways into two parts, which he joined to one another at the centre like the letter X, and bent them into a circular form, connecting them with themselves and each other at the point opposite to their original meeting-point; and, comprehending them in a uniform revolution upon the same axis, he made the one the outer and the other the inner circle. Now the motion of the outer circle he called the motion of the same, and the motion of the inner circle the motion of the other or diverse. The motion of the same he carried round by the side to the right, and the motion of the diverse diagonally to the left. And he gave dominion to the motion of the same and like, for that he left single and undivided; but the inner motion he divided in six places and made seven unequal circles having their intervals in ratios of two-and three, three of each, and bade the orbits proceed in a direction opposite to one another; and three [Sun, Mercury, Venus] he made to move with equal swiftness, and the remaining four [Moon, Saturn, Mars, Jupiter] to move with unequal swiftness to the three and to one another, but in due proportion."

The equatorial motion of the eighth sphere is designated the circle of the same or invariant, while the other seven circles, those of the planets, are derived from the circle "of the other or diverse." Then when precession became a clearly understood doctrine, the eighth sphere was divided into a ninth sphere which became the primum mobile, and a new eighth sphere which held the fixed stars which were perceived as moving with respect to the sphere of the primum mobile. This fact clearly demonstrates that the fixed stars were conceived as being in motion with respect to the primum mobile; components of the primum mobile are the vernal point, the celestial equator, the other equinox, and the solstices.

Nor is this all. We have already shown that the rising times in the tropical zodiac, a critical feature of the ancient system, is nearly invariant over time while the rising times of the constellations are not. And those who measured the positions of the Sun at dawn along the horizon would have noticed that the Sun always rose at the same position along the horizon at the same time of year and that the maximum northerly and southerly positions along the horizon were virtually invariant. And even in Babylonia we know that the first constellation of the stellar zodiac was the one which rose at dawn in the spring. Clearly even they, insofar as they knew that the stars and vernal point were moving with respect to each other, would have regarded the stars as being in motion, not the vernal point.

From what we have seen it is clear that the Babylonians had two divisions of thirty degrees, one corresponding to the constellations which they may or may not have known were moving with respect to the vernal point, and another which was fixed with respect to the vernal point with the vernal point at 0 degrees. The Greeks did not invent the tropical zodiac as often charged. All they did was to give the names of the constellations to the tropical signs. We actually have no way of knowing at this point what the ancients regarded as the astrologically effective set of divisions, or even if they did regard only one set as being effective. Later generations right up to modern times in the West regarded both sets as being effective, but the later medieval and renaissance astrologers did not regard the constellations as being equal. They regarded them as asterisms of unequal extent.

To conclude: I do not assert that the ancients were tropicalists, nor do I assert that they were siderealists. I assert that whatever they may have known about precession they tended not to make the distinction, and when they did, they would have been just as likely to give precedence to the tropical as the sidereal for divinatory purposes. After all the pictorial constellations were only physical plane images which roughly corresponded to the ideal, mathematical reality which would have been represented by the tropical system. But fundamentally I believe we have to regard the tropical-sidereal controversy as yet another example of a historical pseudo-problem created by anachronistically projecting a modern problem with modern points of view back onto the ancients. It was not a problem with which the ancients were seriously concerned. Given the limits of their computational accuracy, both systems would have given them the same results. This is a question that we have to solve for ourselves. An appeal to history will not work.

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