HIPPARCHUS'S UNDERSTANDING OF THE PRECESSION
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. 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."
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."
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.
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
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...." 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,
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] 
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] 
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.
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...
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."
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), and explained the exact orientation
of this movement as being around the poles of the ecliptic. Of course,
Ptolemy notes, here too Hipparchus carefully qualified these details as
being tentative conclusions awaiting further observations for confirmation.
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.
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
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. 
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. 
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
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.
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.
 Noel Swerdlow, "On the Cosmical Mysteries of Mithras," Classical
Philology 86.1 (January 1991) pp. 59-61.
 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.
 Swerdlow, "Cosmical Mysteries," p. 59.
 ibid., pp. 60-61.
 Otto Neugebauer, A History of Ancient Mathematical Astronomy
(New York, Heidelberg, Berlin: Springer-Verlag, 1975) p. 340.
 Swerdlow, "Hipparchus's Determination," p. 304, n. 27.
 Neugebauer, p. 296.
 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).
 Swerdlow, "Hipparchus's Determination," p. 303 n. 21.
 Toomer, Almagest, p. 321
 Toomer, Almagest, p. 131.
 ibid., p. 328.
 Toomer, Almagest, 329.
 Swerdlow, "Cosmical," p. 54.
 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.
 ibid., p. 59.
 Neugebauer, p. 5.
 G.J. Toomer, "Astronomy," Oxford Classical Dictionary
(Oxford and New York: Oxford University Press, 1996) p. 197.
 I am indebted to Professor G.J. Toomer for bringing this point to my
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