ONCE AGAIN HIPPARCHUS AND THE DISCOVERY OF THE PRECESSION:
RESPONSE TO MICHAEL SCHÜTZ
California Institute of Integral Studies
(Forthcoming in Electronic Journal of Mithraic Studies)
In his article "Hipparch und die Entdeckung der Präzession: Bemerkungen zu David Ulansey, Die Ursprünge des Mithraskults," Michael Schütz criticizes three arguments that I make (or, in the case of the first, that he mistakenly believes I make) in my book The Origins of the Mithraic Mysteries.
The first has to do with Hipparchus's astrological interests. Mr. Schütz claims that I argue that the fact that Hipparchus wrote a commentary on the Phaenomena of Aratos proves that Hipparchus was interested in astrology ("beweise sein 'astrologishes Interesse,'" p. 1). In fact, I make no such argument. Rather, the evidence I use in my book to demonstrate Hipparchus's astrological interests is entirely independent of Hipparchus's Aratos commentary, in which, as Schütz rightly points out, there is no trace ("nicht die Spur," p. 3) of astrological interest. I do, it is true, introduce my discussion of Hipparchus's astrological sympathies with a sentence in which I mention that he wrote a commentary on Aratos, but I do this only to show that Hipparchus took an interest in what I there call "astral mythology"-- a fact which I imply is in harmony with Hipparchus's astrological interests, but which I do not use to prove those interests as Schutz claims.
But the important point is that Mr. Schütz's discussion of Hipparchus's commentary on Aratos is actually an irrelevant side-issue, for the real question is whether or not Hipparchus was in fact interested in astrology. And here Schütz does not bother to inform his readers that the universal consensus of historians of astronomy is that Hipparchus was indeed interested in astrology. In my book I cite Otto Neugebauer:
Hipparchus is often quoted in the astrological literature.... It was F. Boll who first emphasized that the ancient reports connecting Hipparchus with astrology have to be taken seriously in view of the time of origin of astrological doctrine in the second century B.C.
and D.R. Dicks:
It would seem that Hipparchus' contemporary fame rested largely on his astrological work, helped no doubt by his foresight in writing a commentary on the most popular didactic poem of his time [Aratos' Phaenomena].
An even more emphatic conclusion was expressed recently by G.J. Toomer, author of both the definitive biography of Hipparchus and the definitive translation of Ptolemy's Almagest (our main source for our knowledge of Hipparchus):
[It is] my conviction that astrology had no importance in the Greek world until after Hipparchus, and that his role, both directly as an advocate of astrology, and indirectly as a developer of astronomical methods which became an essential part of it, was pivotal.
Thus, irrespective of Schütz's quibbles about the nature of Aratos' Phaenomena or Hipparchus's commentary on it, the only important fact is beyond dispute: namely, that Hipparchus was indeed interested in astrology.
Mr. Schütz's next criticism is that I am wrong in arguing that Hipparchus's discovery of the precession of the equinoxes could have catalyzed the creation of a new religion, since in Schütz's opinion ancient cosmology was such that Hipparchus's discovery would not have caused any significant surprise (in spite of the fact that it consisted in the discovery of a previously unknown motion of the entire universe!) However, Schütz's opinion on how Hipparchus's discovery might have been viewed at the time of the origins of Mithraism is based on nothing more than his own speculations, for he provides no evidence whatsoever about how people actually did respond to Hipparchus's discovery before the time of Ptolemy.
The reason Schütz does not provide any evidence other than his own speculations in support of his opinion is that no such evidence exists. This is due to the fact that almost no significant astronomical writings survive from the time period between Hipparchus and Ptolemy. The loss of these writings, as I explain in Appendix IV to the German edition of my book, was caused by the tremendous success of Ptolemy's Almagest, which made all earlier astronomical writings appear obsolete and not worth preserving. Otto Neugebauer describes this effect as follows:
The eminence of [Ptolemy's] works, in particular the Almagest, had been evident already to Ptolemy's contemparies. This caused an almost total obliteration of the prehistory of the Ptolemaic astronomy.
And G.J. Toomer says,
The history of astronomy in the 300 years between Hipparchus and Ptolemy is very obscure, because the unchallenged position of the Almagest in later antiquity resulted in the loss of all earlier works on similar topics.
Under these circumstances, there unfortunately does not exist any evidence that would allow us to know with dependability what the response was to Hipparchus's discovery before the time of Ptolemy-- unless, as I say in Appendix IV, my interpretation of the Mithraic mysteries is correct, in which case we now know significantly more than we did previously about the impact of Hipparchus's work. Perhaps there was a variety of responses, ranging from the simple acceptance that Schütz imagines to the profound reaction that the Mithraic evidence appears to express. We just do not know.
However, the crucial point is that all that is needed for my theory to be correct is that one small group of people saw deep implications in Hipparchus's discovery of a previously unknown motion of the entire universe. This kind of situation is, in fact, identical with what we find in the origins of Christianity. For as far as we can determine, immediately after Jesus was crucified no one in the Roman empire outside of one tiny circle of people saw any special significance in this execution by the Romans of a minor Jewish prophet. But of course that tiny circle of people-- whose existence would be entirely unknown to us today if not for the writing of the New Testament-- saw tremendous significance in the event, and their response catalyzed the birth of a new religion that has now persisted for 2000 years. That is exactly the kind of scenario that I imagine led to the origins of Mithraism, and in my book I provide abundant evidence for the sorts of intellectual and religious developments that could easily have predisposed a small group of people to see profound significance in Hipparchus's discovery.
Mr. Schütz's final criticism involves my statement in my book that Hipparchus saw the precession as being either a movement of the entire sphere of the fixed stars or as a movement of the great cosmic axis around which the sphere of the fixed stars rotates (Schütz does admit that these two formulations are mathematically equivalent, p. 9). Schütz claims that Hipparchus could not have seen the precession as a movement of the cosmic axis, since this would have had unacceptable consequences for geography, and Hipparchus was an accomplished geographer (p. 9).
However, here again Schütz is relying on nothing more than his own personal opinion-- and in this case we possess decisive evidence that his opinion is entirely incorrect. This evidence consists in the direct testimony of Hipparchus himself, as recorded by Ptolemy in two places in the Almagest.
The first of these two pieces of direct evidence preserved by Ptolemy consists of the very title of Hipparchus's main work on the precession, On the Change in Position of the Solstitial and Equinoctial Points. This title can only be understood as referring to a movement of the locations of the solstices and equinoxes (and thus of the cosmic axis and celestial equator, which define the positions of the solstices and equinoxes) with respect to the sphere of the fixed stars. This is confirmed by the second piece of direct evidence: an explicit quotation by Ptolemy from Hipparchus's work On the Length of the Year, where Hipparchus states that the equinoxes move at least 1 degree per century backwards through the zodiac.
The title of Hipparchus's work On the Change in Position of the Solstitial and Equinoctial Points, and the direct quotation from his other work On the Length of the Year, are universally understood by modern historians of astronomy as indicating that Hipparchus sometimes described the precession not as a movement of the sphere of the fixed stars and the zodiac, but rather as a movement of the equinoxes and solstices-- and of the cosmic axis and celestial equator which define the locations of the equinoxes and solstices-- with respect to the sphere of the fixed stars and the zodiac: exactly the understanding which Schütz (on the basis of nothing but his own opinion) denies Hipparchus could have held.
It should be noted that in those few random fragments of direct evidence for Hipparchus's work that Ptolemy preserved, Hipparchus does not happen to mention the cosmic axis specifically. However, as will be pointed out by the preeminent scholars of ancient astronomy whom I will be citing (Noel Swerdlow, G.J Toomer, and B.L. van der Waerden), it is a mathematical necessity that if Hipparchus described the precession as a movement of the solstices and equinoxes with respect to the fixed stars, then he must also have understood the cosmic axis and celestial equator as also being in motion, since these are what define the positions of the solstices and equinoxes.
Thus Noel Swerdlow, one of the foremost contemporary historians of ancient astronomy and one of the few modern specialists on Hipparchus, sums up the current scholarly consensus on Hipparchus's understanding of the precession as follows:
He described it either as an eastward motion of the sphere of the fixed stars about the axis of the ecliptic, thereby shifting the stars in the direction of increasing longitude with respect to the equinoxes, or as a westward motion of the axis of the diurnal rotation in a circle about the axis of the ecliptic, shifting the equinoxes in the direction of decreasing longitude with respect to the fixed stars.
Of course, what Swerdlow says here is exactly the opposite of what Schütz claims is the case.
With regard to the first of our two pieces of evidence-- the title of Hipparchus's work On the Change in Position of the Solstitial and Equinoctial Points-- G.J. Toomer (who, as I mentioned earlier, is the author of both the definitive biography of Hipparchus and the definitive translation of Ptolemy's Almagest) affirms the understanding of this title as indicating that Hipparchus was here interpreting the precession as a motion of the equinoxes with respect to the sphere of the fixed stars, rather than vice versa:
Note that the motion which in modern terminology is 'precession of the equinoxes' (i.e. a motion in the direction of decreasing longitudes of the tropical points with respect to the fixed stars) is described by Ptolemy as a motion of the fixed stars with respect to the tropical points in the direction of increasing longitudes. This accords with his taking the tropical points as the primary reference points. Hipparchus, however, seems at times to have adopted the modern convention, to judge from the title of his work 'On the displacement of the solsticial and equinoctial points.'
Although Toomer does not mention the cosmic axis here, in personal correspondence (which he has given me permission to cite here) he has informed me that he is in agreement with Swerdlow's formulation in the quote above, where Swerdlow says that Hipparchus sometimes described the precession "as a westward motion of the axis of the diurnal rotation...." Specifically, Toomer informs me that he agrees with Swerdlow that (1) the evidence in Ptolemy shows that Hipparchus sometimes understood the precession as being a motion of the equinoxes with respect to the fixed stars, and (2) that although Hipparchus does not explicitly mention the axis, a mathematically necessary consequence of (1) is that Hipparchus sometimes understood the axis of diurnal rotation as being in motion.
Regarding the second piece of direct evidence-- Ptolemy's quotation from Hipparchus's On the Length of the Year-- Swerdlow, in his authoritative article "Hipparchus's Determination of the Length of the Tropical Year and the Rate of Precession," says,
Finally, it should be noted that in the quotation from On the Length of the Year in which Hipparchus estimates the rate of precession [Almagest VII,2], he describes it as a westward motion of the tropics and equinoxes rather than, as Ptolemy does, an eastward motion of the sphere of the fixed stars.
Toomer agrees fully with Swerdlow's interpretation of the quote from Hipparchus, saying:
Hippparchus reverted to the topic [of the precession] in a later work, "On the Length of the Year." Here he came to more definite conclusions. He determined that the tropical and equinoctial points move at least 1/100° backward through the signs of the ecliptic.
Otto Neugebauer as well interprets the quotation from "On the Length of the Year" as meaning that Hipparchus was here describing the precession as a movement of the equinoxes with respect to the fixed stars:
In the work "On the length of the year" Hipparchus came to the conclusion that the equinoctial points move at least 1° per century in a direction opposite to the order of the zodiacal signs.
We see, therefore, that Noel Swerdlow, G.J. Toomer, and Otto Neugebauer are all in agreement that the evidence shows that Hipparchus described the precession either as a movement of the sphere of the fixed stars or as a movement of the equinoxes and solstices. In addition, as we have seen, Swerdlow and Toomer explicitly point out that a mathematically necessary consequence of this is that Hipparchus sometimes understood the precession as a movement of the cosmic axis (which defines the locations of the equinoxes and solstices) with respect to the sphere of the fixed stars.
I should mention that it was the great historian of ancient astronomy and mathematics, B.L. van der Waerden, who first pointed out to me the presence of these two understandings of the precession (movement of the cosmic sphere or movement of the cosmic axis) in Hipparchus's work. It was on van der Waerden's advice that I included both of these understandings in my book. In a letter to me (Nov. 1-4, 1986) he wrote:
I am inclined to believe that the discovery [by Hipparchus] that made the greatest impression was not the discovery of a motion of the fixed stars, but the discovery of a motion of the poles with respect to the fixed stars. (Emphasis in original.)
Thus, contrary to Mr. Schütz's unsupported personal opinion that Hipparchus could not have understood the precession of the equinoxes as being a motion of the cosmic axis, the reality-- expressed by Hipparchus himself and explicitly affirmed by the greatest modern specialists on Hipparchus and ancient astronomy, including Noel Swerdlow, G.J. Toomer, and B.L. van der Waerden-- is that Hipparchus did sometimes describe it in precisely this way.
Finally, I should emphasize that even if Mr. Schütz were correct, and Hipparchus had described the precession only as a movement of the sphere of the fixed stars and not of the cosmic axis, this would not effect the argument of my book in the least. For Hipparchus's description of the precession as a newly discovered movement of the sphere of the fixed stars-- that is, a newly discovered movement of the entire cosmos!-- is obviously astonishing enough that it could easily have catalyzed far-reaching cosmological speculations like those that my research has revealed as being encoded in the iconography of the Mithraic mysteries.
1. Schutz's article is in the Electronic Journal of Mithraic Studies, vol. 1 (2000), available on the World Wide Web at http://www2.uhu.es/ejms/archives.htm. My book is David Ulansey, The Origins of the Mithraic Mysteries: Cosmology and Salvation in the Ancient World (New York and Oxford: Oxford University Press, revised paperback, 1991), translated into German as Die Ursprünge des Mithraskults (Stuttgart: Konrad Theiss Verlag, 1998).
2. Origins, p. 76 (= Ursprünge, p. 68). Schütz (p. 3) disputes my description of Aratos's Phaenomena as being a work of "astral mythology," but there can be no question that astral mythology is an essential element of Aratos's poem. For example, of the first 135 lines of the poem, 45 are devoted explicitly to constellation myths (31-35: catasterism of the bears; 71-73: catasterism of the crown; 98-135: catasterism of the virgin). Schütz claims that the Phaenomena is rather a "compendium of technical astronomy" (p. 3), but there is not a single celestial measurement in the entire text! Indeed, Aratos does not even mention the planets-- the explanation of whose movements was the main concern of ancient astronomy-- except for six lines (454-61) where he explains that he is not competent to talk about them. (See the discussion by Douglas Kidd, Aratus: Phaenomena [Cambridge: Cambridge University Press, 1997] p. 343.) Certainly Aratos gives an accurate poetic description of the celestial sphere and of the risings and settings of the stars, but if one needs to characterize his work as being any one thing, it is perhaps neither mythological nor scientific, but fundamentally poetic. It is, as Douglas Kidd points out in his recent edition of Aratos, solidly in the same tradition as Homer's descriptions of the constellations, Hesiod's descriptions of the risings and settings of the stars, and Sappho's famous use of the setting of the Pleiades to suggest a certain time of night. As Kidd says, "The astronomy of the Phaenomena is limited to what was required for estimating the time of year or month or night, for the purpose of predicting weather conditions." (Kidd, Aratus, p. 13.)
3. Origins, p. 80 (=Ursprünge, p. 71).
4. Origins, p. 76 (=Ursprünge, p. 68).
5. "Hipparchus and Babylonian Astronomy," in E. Leichty, M.deJ. Ellis, and P. Gerardi, eds., A Scientific Humanist: Studies in Memory of Abraham Sachs, Occasional Publications of the Samuel Noah Kramer Fund, 9 (Philadelphia, 1988), p. 362. Toomer's biography of Hipparchus (entitled "Hipparchus") is in Charles Coulston Gillispie, ed., Dictionary of Scientific Biography (New York: Scribner's, 1978), Vol. XV, Suppl. I, pp. 207-224. His translation of the Almagest is entitled Ptolemy's Almagest (New York, Heidelberg, Berlin: Springer Verlag, 1984).
6. In fact, it should be emphasized that even if Hipparchus had not been involved with astrology at all this would not affect the basic argument of my book whatsoever, since it seems to have been the speculations about the precession by the Stoics of Tarsus, rather than by Hipparchus himself, that led to the origins of Mithraism. See Origins, pp. 80-81 (=Ursprünge, p. 72).
7. Ursprünge, p. 122. English translations of the appendices to the German edition of my book can be found on the World Wide Web at http://www.well.com/user/davidu/appendices.html.
8. Otto Neugebauer, A History of Ancient Mathematical Astronomy (New York, Heidelberg, Berlin: Springer-Verlag, 1975) vol. 1, p. 5.
9. G.J. Toomer, "Astronomy," Oxford Classical Dictionary
(Oxford and New York: Oxford University Press, 1996) p. 197.
10. Ursprünge, p. 122. For English translation of this appendix, see above, n. 7.
11. Origins, pp. 78-9 (= Ursprünge, p. 70).
12. Almagest VII.2 [H12]. Toomer, Almagest, p. 327.
13. "For if the solstices and equinoxes were moving, from that cause, not less than 1/100th of a degree in advance [i.e., in the reverse order] of the signs, in the 300 years they should have moved not less than 3 degrees." Almagest VII.2 [H16]. Toomer, Almagest, p. 328.
14. Noel Swerdlow, "On the Cosmical Mysteries of Mithras," Classical Philology 86.1 (January, 1991) p. 54. Emphasis mine.
15. Toomer, Almagest, p. 321, n. 2. Emphasis mine.
16. Electronic mail, Jan. 15, Jan. 17, and July 1, 2002. I am grateful to Prof. Toomer for giving me permission to cite his personal correspondence. He has read the summary I have given here of his position and approved it for publication.
17. Noel Swerdlow, "Hipparchus's Determination of the Length of the Tropical Year and the Rate of Precession," Archive for History of Exact Sciences, vol. 21, #4 (August 29, 1980) p. 304. Emphasis mine.
18. G.J. Toomer, "Hipparchus" (see above, n. 4), p. 218. Emphasis mine.
19. Neugebauer, History, vol. 1, p. 293. Emphasis mine.
20. See the note on this in my Origins, pp. 134-135, n. 49 (=Ursprünge, p. 71 n. 49).
21. Thus in my Princeton dissertation (Mithras and Perseus: Mithraic Astronomy and the Anatolian Perseus-Cult, 1984) which was the foundation of my book, I based my argument entirely on Hipparchus's interpretation of the precession as a movement of the sphere of the fixed stars, since I had not yet learned from Prof. van der Waerden of the scholarly consensus that Hipparchus had actually described the precession in two different ways at different times. In my book I added the second of these ways (the precession as movement of the cosmic axis) for the sake of completeness and accuracy, but it is entirely unnecessary for the basic argument of the book (although it does provide some interesting additional support for my theory.)
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