1 The Birth of Science - MSRI

3.6 Aristarchus, Heliocentrism, and Relative Motion 75
The remark that what is seen depends only on the relative motion between
observer and observed is already in Euclid’s Optics (Proposition
51). 109
Archimedes, discussing the Aristarchan theory in the Arenarius, refrains
from objecting to it on physical grounds (though he does take issue with
the mathematical formulation; see page 78). He uses the theory only to
deduce from the absence of stellar parallax an estimate for the diameter
of the sphere of fixed stars. Thus he is interested in terrestrial motion not
in an absolute sense, but with respect to the fixed stars. Naturally, if one
believes, as Archimedes did, that there is a sphere of fixed stars, 110 the existence
of such a naturally privileged reference system decreases the importance
of relativism (and perhaps obviates the need to state it), but, as
a matter of principle, it’s one thing to refer motions to “natural” reference
bodies such as the stars, and quite a different one to consider absolute motion
(relative to the void). The essential point is that Archimedes thought
there was no way to check whether the earth moves relative to the stars
by means of earth-based experiments. 111
Ptolemy, expounding in the Almagest his own theory of the earth’s immobility,
attacks the contrary opinion, concerning in particular the daily page 112
rotation. The opinion he reports and confutes is not the assumption that
the earth rotates, but the relativistic statement made by “some people”
that the rotation can be attributed indifferently to the earth or to the heavens
— or even to both, so long as both rotations have the same axis and
their difference (the relative motion) is the one actually observed. 112 He
recognizes that this is compatible will all astronomical phenomena (that is,
with the observable motions of celestial bodies). To refute the theory and
assert the earth’s immobility, he must resort to natural philosophy arguments,
taken in large measure from Aristotle. This is not an isolated case:
imperial-age authors often frame Hellenistic scientific results by stating
first their own arguments, taken from philosophers of the classical period.
We shall see in Section 10.14 a similar situation regarding geometrical concepts.
Many Hellenistic works, or works based on Hellenistic sources, illustrate
the relativity of motion. The most famous locus is perhaps that of
109 This proposition is quoted in Section 6.3, page 6.3.
110 However, the existence of the sphere of fixed stars had already been called into question before
Archimedes, in the fourth century B.C. We will return to this point in Section 3.7.
111 Indeed Archimedes discusses the compatibility of Aristarchus’ hypotheses with the absence
of measurable parallax effects and accepts as possible the explanation based on the enormous distance
to the stars, without taking into consideration any Ptolemaic-type arguments.
112 Ptolemy, Almagest, I, vii, 24.
Revision: 1.13 Date: 2002/10/16 19:04:00