1 The Birth of Science - MSRI

82 3. Other Hellenistic Scientific Theories
elementary geometric operations, realizable with two simple instruments:
compass and protractor.
In Ptolemy’s work the number of circular motions needed to obtain
good agreement with experimental data is reduced to two — one deferent
and one epicycle — through the introduction of eccentrics (the center
of the deferent does not coincide with the earth) and equants (the circular
motion is not considered to be uniform, but to have uniform angular velocity
with respect to a point, the equant, which differs from the center of
the circle). 135 Although these modifications disrupt the symmetry of uniform
circular motion, they have the essential merit of buying flexibility
without sacrificing computational ease: the use of eccentrics and equants
amounts to a simple displacement of the point on which each of the two
fundamental instruments — compass and protractor, respectively — is to
be centered. This shows that the use of circular motions was not due, as
has often been said, to reasons of symmetry or esthetics, but to the concrete
need for an algorithm that could reduce the necessary calculations
to simple operations realizable with elementary instruments. 136
Just as we saw in Section 2.3 regarding mathematics, the connection
between theoretical scientific structures and material instruments used is
further proved by the fact that in Mesopotamia the use of clay tablets page 120
as the writing material led astronomy in a different direction from Alexandrian
astronomy. 137 Mesopotamian astronomy, in fact, did not employ
geometric constructions like Ptolemy’s epicycles, but rather the study of
numerical regularities. Although Mesopotamian astronomy is still little
known, it is clear from the cuneiform tablets deciphered during the twentieth
century 138 that, whereas paleo-Babylonian astronomy was prescientific
and qualitative, the level of the mathematical astronomy developed in
Mesopotamia during the Hellenistic period is comparable with that of the
contemporary astronomy based on geometric methods. 139 Although the
mathematical methods were distinct, it is obvious that there were cultural
135
On the actual use of eccentrics and equants one can read [Neugebauer: HAMA] or, for a briefer
treatment, any history of astronomy.
136
It seems to me that the conclusion is not warranted that Hellenistic scientists had a preference
for circles because of their “perfection”, just because this idea is present in authors of the classical
and imperial periods — the more so because imperial-age authors, who no longer mastered the
Hellenistic scientific method, often framed scientific results in conceptual schemes belonging to
prescientific natural philosophy.
137
By Alexandrian astronomy we mean, as in the case of mathematics, the homogeneous scientific
tradition developed in Hellenistic times in the Greek-speaking Mediterranean world, and having
its greatest center in Alexandria.
138
The astronomical tablets deciphered prior to 1955 have been published in [Neugebauer: ACT].
139
For a survey of what is known regarding the history of Mesopotamian astronomy in Hellenistic
times one can turn to [Neugebauer: HAMA], pp. 347–558.
Revision: 1.13 Date: 2002/10/16 19:04:00