An objection to my theory has been raised having to do with the question of exactly how Hipparchus understood the nature of his discovery of the precession of the equinoxes. In a review of my book published in Classical Philology, Noel Swerdlow argues that Hipparchus was extremely uncertain about the nature of the precession-- so much so that nobody would have been inspired enough by Hipparchus's presentation of his discovery to do anything like found a new religion.[1] Swerdlow, a historian of astronomy, bases his criticism on his own research into the details of Hipparchus's discovery of the precession, published in his article "Hipparchus's Determination of the Length of the Tropical Year and the Rate of Precession."[2]

In his review of my book, Swerdlow puts his case thus:

"...Hipparchus's treatment of the precession was not at all straightforward and was hardly such as would have suggested the need for a new cosmic deity.... All that is known of Hipparchus's study of what we now call the precession is contained in [Ptolemy's] Almagest 3.1 and 7.1-3, and it is evident from Ptolemy's account that it was highly technical, highly tentative, and did not necessarily indicate anything like a motion of the entire sphere of the fixed stars with respect to the equinoxes."[3]

However, when it comes to presenting his evidence for this claim, Swerdlow seriously misrepresents the facts of the matter. His essential argument is that Hipparchus suggested several possible explanations of precession, and that the one which is the basis of the argument in my book-- i.e., that the precession was a continuous movement of the entire cosmic structure-- was merely one among many suggestions, all of them of more or less equal importance. Hipparchus, says Swerdlow,
...offered various hypotheses, all quite tentative. He considered the possibility that only zodiacal stars, or perhaps bright zodiacal stars like Spica, move with respect to the equinoxes (as though they were very slow, distant planets). Ptolemy calls this Hipparchus's "first hypothesis." He also considered the possibility that the fixed stars were not fixed at all, but had independent motions, and he left many descriptions of stellar alignments that could later be checked to see if any changes had occurred. Ptolemy used them to show that none could be detected. Hipparchus may also have proposed that the sphere of the fixed stars might oscillate back and forth over a short arc of eight degrees, a theory doubtless related to the Babylonian location of the equinoxes at the eighth degree of Aries and Libra. This is the so-called "trepidation of the equinoxes" described by Theon of Alexandria (late 4th cent.) in his shorter commentary on Ptolemy's Handy Tables." Finally, one of his suggestions was a motion of the sphere of the fixed stars through not less than one degree per century with respect to the equinoxes-- the very motion later confirmed by Ptolemy; but it is evident from Ptolemy's account that this too was highly tentative, something that "Hipparchus too seems to have suspected" in his book On the Length of the Year.[4]

Swerdlow here is obviously intending his readers to imagine that the four hypotheses about the precession that he attributes to Hipparchus were of equal weight, and that Hipparchus was unable to choose between them. This is a misrepresentation of the facts. For example, Swerdlow gives the same weight to the "trepidation" hypothesis that he does to the other three. However, the fact is that there does not exist a single ancient source connecting Hipparchus with the trepidation theory. Recall Swerdlow's statement that "All that is known of Hipparchus's study of what we now call the precession is contained in [Ptolemy's] Almagest...." As Swerdlow is well aware, Ptolemy never attributes anything like the trepidation theory to Hipparchus.

The only justification for Swerdlow's linking Hipparchus with the trepidation theory-- the earliest source for which is a fourth century work containing no reference whatsoever to Hipparchus-- is the speculation of the modern historian of astronomy Otto Neugebauer. Neugebauer, based on some similarities that he saw between Theon's comments and Hipparchus's work as described by Ptolemy, suggested a connection which he summarized thus: "I even think one should keep the possibility in mind that [Hipparchus] is connected with, if not responsible for, the theory of trepidation of the vernal point with an 8° amplitude...."[5] As his cautious language shows, Neugebauer was well aware that his proposal was only a speculation.

Indeed, Swerdlow himself is fully cognizant of the speculative nature of any connection between Hipparchus and the trepidation theory, for in his eighteen-page article on Hipparchus and the precession mentioned above ("Hipparchus and the Determination..."). Swerdlow's sole reference to the trepidation theory is a one-sentence footnote: "On the possible association of Hipparchus with the theory of the trepidation of the equinoxes described by Theon of Alexandria in his smaller commentary on the Handy Tables, see [Neugebauer]."[6]

We see, therefore, that Swerdlow, aware of the speculative nature of any attempt to link the trepidation theory with Hipparchus, in his own exhaustive article on Hipparchus's discovery of the precession left the theory entirely out of his discussion. Yet in his review of my book, the trepidation theory suddenly is elevated to the point of having the same status and importance as those interpretations of the precession which Ptolemy explicitly, and in detail, attributed to Hipparchus. Nowhere does Swerdlow give any arguments in support of this strange alteration in his own thinking.

In neglecting to inform his readers of the true circumstances of the trepidation theory, Swerdlow has completely obscured the relative importance of the various interpretations of the precession that he attributes to Hipparchus, misleading his readers into thinking that they are of equal value and importance. This same sort of obscuration of the facts is also evident with respect to the first of the four hypotheses that he lists in the quote above, i.e., the hypothesis in which Hipparchus suggested that it was only the zodiacal stars that were moving.

In his description of this hypothesis in the quote above, Swerdlow mentions Ptolemy's statement that this was Hipparchus's "first hypothesis." However, Swerdlow fails to give his readers an accurate understanding of the full significance of this statement of Ptolemy's. For Ptolemy's statement reveals that Hipparchus's hypothesis that only the zodiacal stars were moving was not of equal weight with his other hypotheses, but was an early or preliminary hypothesis that was later superseded by more mature conclusions. As Otto Neugebauer says,
The character of the motion of precession could not immediately become clear to Hipparchus....We know from a remark in the Almagest that at first he considered the possibility that only the longitudes of stars near the ecliptic show a slow increase with time. In other words there could have existed beside the known planets still other celestial bodies with a very slow motion in longitude. Here the invariance of the alignments of the constellations must have shown the incorrectness of this preliminary hypothesis.[emphasis mine] [7]

G.J. Toomer, author of the definitive biography of Hipparchus and of the recent definitive translation of Ptolemy's Almagest, also sees Ptolemy's phrase "first hypothesis" as indicating that this hypothesis was the earliest stage of an extended development leading toward a mature conclusion. As Toomer puts it in his biography of Hipparchus,
According to Ptolemy, the first hypothesis that [Hipparchus] suggested was that only the stars in the zodiac move. Later, in "On the Change in Position of the Solstitial and Equinoctial Points," he formulated the hypothesis that all the fixed stars move with respect to the equinoxes (or, rather, vice versa).... but he was well aware that his data were too shaky to allow any confidence in the precise amount.... Hippparchus reverted to the topic 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... [emphasis mine] [8]

The sense of development that Toomer conveys here is completely missing in Swerdlow's description of Hipparchus's different hypotheses, where the chronological dimension is so lacking that the reader is left with the misleading impression that Hipparchus held all of these hypotheses simultaneously without being able to choose between them. (Note: the second hypothesis listed by Swerdlow-- namely that all of the stars move independently of each other, and not just those in the zodiac-- is never attributed to Hipparchus by Ptolemy. Swerdlow does not say what his evidence for this is, but in a footnote in his article "Hipparchus's Determination of the Length of the Year" Swerdlow briefly speculates that Hipparchus may have thought some such thing.[9] I assume that in including this hypothesis in his list Swerdlow is relying on the same argument he makes in that footnote. In any case, since this hypothesis is no more than a logical extrapolation from the first hypothesis, if Hipparchus ever proposed it it must have been in the same early period as his first hypothesis.)

Swerdlow ends his list of Hipparchus's hypotheses by saying:
Finally, one of his suggestions was a motion of the sphere of the fixed stars through not less than one degree per century with respect to the equinoxes...

Swerdlow here gives the impression, once again, that this suggestion of Hipparchus's was simply one more among several, merely the last in a list of hypotheses understood by Hipparchus as being more or less equally valid and between which he could not choose. Swerdlow thus presents Hipparchus's hypothesis that the entire sphere of the fixed stars was in motion as if it were of no more importance in Hipparchus's mind than the other hypotheses that Swerdlow mentions in his list.

However, as we have seen, the theory of the trepidation should probably not even be in the list to begin with, since there is no proof that Hipparchus ever held this theory (indeed, as we saw, Swerdlow himself did not discuss it at all in his own article on Hipparchus's discovery of the precession ["Hipparchus's Determination of the Length of the Tropical Year and the Rate of Precession"]); and, likewise, the hypothesis that the precession was the result of the movement of individual stars was, as we have seen, an early, preliminary suggestion that Hipparchus gave up as his understanding of the precession increased.

In fact, Hipparchus's idea that the precession was caused by a previously unknown movement of the entire cosmic structure was not merely one more suggestion in a list of equally valid hypotheses. Rather, this idea was his final, mature conclusion, which he reached at the end of his investigation of the subject. It is true, as Swerdlow points out, that Ptolemy said that Hipparchus admitted that further observations would be necessary to prove this hypothesis. According to Ptolemy,
Hipparchus conceived of [the movement of the entire cosmic structure] on the basis of the phenomena available to him, but under conditions which forced him, so far as concerns the effect over a long period, to conjecture rather than to predict, since he had found very few observations of fixed stars before his own time...[10]

However, Hipparchus's caution as described here by Ptolemy is simply a manifestation of Hipparchus's scientific integrity: like any careful scientist or scholar, in his formal publications he took pains to avoid overstating the facts, and always included the necessary qualifications when presenting conclusions that were still tentative. It is no doubt for this reason that Ptolemy says that Hipparchus was "both industrious and a lover of truth."[11]

However, the fact that Hipparchus was careful in his publications to qualify his final conclusions as tentative does not change the fact that these were his final conclusions! And we know that Hipparchus's final conclusion about the precession was that it was a movement of the entire cosmic structure, for he expresses this conclusion in the very title of the first of his two works on the subject-- "On the Displacement of the Solstitial and Equinoctial Points"-- a title which can only refer to a motion of the entire cosmic structure. And, in addition, in his second work on the subject-- "On the Length of the Year"-- Hipparchus, according to Ptolemy, not only presented again the same general conclusion that he had expressed in the title and content of his earlier work, but now presented precise details about the nature of this cosmic movement. For Ptolemy tells us explicitly that in "On the Length of the Year" Hipparchus gave a precise estimate of the rate of the movement of the cosmic structure (not less than one degree per century),[12] and explained the exact orientation of this movement as being around the poles of the ecliptic.[13] Of course, Ptolemy notes, here too Hipparchus carefully qualified these details as being tentative conclusions awaiting further observations for confirmation.[14]

Indeed, Swerdlow himself admits that this was Hipparchus's final conclusion, for earlier in his review he states:
What we call the "precession of the equinoxes" (a term first used by Copernicus) was discovered by Hipparchus (2nd cent. B.C.) as a second motion of the fixed stars, in addition to the diurnal rotation. 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 durnal 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.[15]

Swerdlow here acknowledges that the final outcome of Hipparchus's work on the precession was the conclusion that it was a movement of the entire cosmic structure (either a motion of the sphere of the fixed stars or a motion of the axis of rotation of the universe-- either of these mathematically equivalent formulations represents a shift of the entire cosmic structure). It is thus very strange that later in his discussion, when he presents his list of Hipparchus's hypotheses, he does not remind the reader of what Hipparchus's final conclusion was!

Swerdlow's objection to my theory, then, is entirely unconvincing. However, one valid question does emerge out of his discussion. If Hipparchus, as Ptolemy says, saw his final conclusion as still unproven (Ptolemy says that in concluding that the precession was a movement of the entire cosmic structure Hipparchus was forced "to conjecture rather than to predict, since he had found very few observations of fixed stars before his own time..."), wouldn't the tentative nature of his conclusion have prevented anyone from taking it seriously enough to believe that it indicated something like the existence of a new god?

To this I would suggest two responses. First, the lack of proof for a claim may deter a scientist from believing the claim to be true. However, in the Mithraic mysteries we are dealing not with a scientific but with a religious phenomenon, and the stuff of religion is not the human intellect but the human imagination. Hipparchus may or may not have had definitive proof for his understanding of the nature of the precession of the equinoxes. But Swerdlow cannot deny that Hipparchus suggested in his writings the remarkable new idea that the entire cosmic structure might be moving in a previously unknown manner. Whether Hipparchus presented this as a proven fact or merely as a plausible hypothesis is of no consequence whatsoever for the religious imagination. After all, if Christians had been unwilling to act on their belief in the veracity of claims that were supported by far less evidence than Hipparchus's hypothesis, the past two thousand years would have been very different indeed!

Second, we have seen that like any good scientist, Hipparchus was careful in his published works to note when a claim of his lacked definitive proof. However, like any scholar, Hipparchus was no doubt less cautious when engaged in informal discussions with colleagues or students. We know that his final conclusion about the precession was that it was a motion of the entire cosmic structure. Regardless of the fact that he lacked absolute confirmation of this, it is hard to imagine that his colleagues and students would not have acquired a clear idea of what he thought was the most likely explanation of the precession. And here it is easy to see how Hipparchus's authority could have led to one or more of his less rigorous associates taking his conclusion as "gospel truth." Or, even if all of his associates were as careful as Hipparchus was always to keep in mind the necessary qualifications, such qualifications would no doubt often have become lost as word of Hipparchus's work spread beyond his immediate circle.

There must, therefore, have been ample opportunity for people to encounter Hipparchus's remarkable new idea not in the form of a carefully nuanced scientific exposition, but in the form of an unqualified pronouncement. Among such people, I would suggest, Hipparchus's discovery could well have catalyzed the sorts of speculations that led to the origins of the Mithraic mysteries. [16]

One last point raised by Swerdlow concerning Hipparchus's discovery of the precession deserves brief mention. Swerdlow notes that there does not survive any ancient reference to the precession from the three hundred years between Hipparchus and Ptolemy, and says,
Aside from the vagaries of the survival of writings on astronomy before Ptolemy, whose work made that of his predecessors on the whole obsolete, it is most likely that the precession was not mentioned for three hundred years because Hipparchus' description was so tentative, and so uncertain of what his observations showed, that no one paid any attention to it until Ptolemy demonstrated that it really existed. [17]

Of course, an argument from silence like this is never very strong, and arguments from silence are notoriously weak in the study of the ancient world, where what has survived is a matter of sheer chance. But in this case, as Swerdlow himself acknowledges, yet another factor is also at work. I am referring to the effect of Ptolemy himself on the preservation of earlier astronomical works. 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. [18]

And 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. [19]

In the judgement of Neugebauer and Toomer, we are dealing here not merely with "the vagaries of survival," as Swerdlow puts it: we are dealing with a complete loss, an "obliteration" of the evidence that might have informed us about the reception of Hipparchus's discovery. Under these circumstances, the fact that references to the precession made between the time of Hipparchus and the time of Ptolemy have not survived proves nothing. [20]

The truth is that the extent of interest in Hipparchus's discovery of the precession between his own time and that of Ptolemy is at present entirely unknown-- entirely, that is, unless 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.


[1] Noel Swerdlow, "On the Cosmical Mysteries of Mithras," Classical Philology 86.1 (January 1991) pp. 59-61.

[2] Noel Swerdlow, "Hipparchus's Determination of the Length of the Tropical Year and the Rate of Precession," Archive for History of Exact Sciences 21.4 (August 1980) pp. 291-305.

[3] Swerdlow, "Cosmical Mysteries," p. 59.

[4] ibid., pp. 60-61.

[5] Otto Neugebauer, A History of Ancient Mathematical Astronomy (New York, Heidelberg, Berlin: Springer-Verlag, 1975) p. 340.

[6] Swerdlow, "Hipparchus's Determination," p. 304, n. 27.

[7] Neugebauer, p. 296.

[8] G.J. Toomer, "Hipparchus," in Dictionary of Scientific Biography (New York: Charles Scribner, 1978) vol. XV, Supplement I, p. 218. Toomer's translation of the Almagest is entitled Ptolemy's Almagest (New York, Berlin, Heidelberg, Tokyo: Springer-Verlag, 1984).

[9] Swerdlow, "Hipparchus's Determination," p. 303 n. 21.

[10] Toomer, Almagest, p. 321

[11] Toomer, Almagest, p. 131.

[12] ibid., p. 328.

[13] Toomer, Almagest, 329.

[14] ibid.

[15] Swerdlow, "Cosmical," p. 54.

[16] A modern parallel to the sorts of situations I have described in the last several paragraphs can be found in the highly speculative use being made today-- both by physicists such as Fritjof Capra and Roger Penrose, and by laypeople such as "New Age" authors-- of ideas drawn from the extremely technical and not yet fully understood realm of quantum physics.

[17] ibid., p. 59.

[18] Neugebauer, p. 5.

[19] G.J. Toomer, "Astronomy," Oxford Classical Dictionary
(Oxford and New York: Oxford University Press, 1996) p. 197.

[20] I am indebted to Professor G.J. Toomer for bringing this point to my attention.

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