1 The Birth of Science - MSRI

246 10. Lost Science
nature is downward (toward the center of the earth); for light bodies it is
upwards; whereas heavenly bodies move according to nature in circles.
For the pebble in the sling, Plutarch’s passage might suggest that, as in
Aristotle, “according to nature” means the downward movement, due to
weight, that would occur in the absence of rotation. But the divergence
between Plutarch’s source and Aristotle is patent in the case of the moon,
which is here made to parallel that of the pebble: in Plutarch’s source,
moon and pebble had the same motion according to nature, and obviously
a uniform circular motion is not according to nature for a pebble. This a
key point, because the idea that uniform circular motion is the natural
motion of heavenly bodies is usually associated with all of Antiquity, 57
and was still shared by Galileo.
The Greek word we have translated as motion is kinesis (©). The
effect of gravity is not described as a kinesis toward the center of the earth,
but as a thrust (fora, ) toward the center. We cannot translate fora as
motion, because the motions described by Plutarch as subjected to fora
toward the center are not in general themselves directed toward the cen- page 307
ter: 58 in the case of the multi-ton boulder that, arriving at a certain speed
in the center of the earth, goes beyond it and starts to oscillate, the effect
of gravity (the “thrust toward the center”) is a decrease in speed when the
boulder is moving away from the center and an increase when it is moving
toward it; and the same can be said about the torrent of water in perpetual
back-and-forth movement. The same thrust toward the center may have
the effect of changing an object’s velocity in direction alone, leading to a
circular uniform motion, as the passage says regarding the water and the
moon. In each case the movements described as subject to fora toward the
center are those that, in modern terms, have an acceleration in that direction.
This does not mean that the scientific treatises where the theory was
presented necessarily used a mathematical concept coinciding with our
acceleration. But it does seem clear that Plutarch’s source (and also the
pseudo-Aristotelian Mechanics) regarded a motion “according to nature”
to be a uniform linear motion, so their dynamical theory was based on the
principle of inertia in some form.
57 For example, in [Koyré: EG], where the author maintains from the introduction on that the
principle of inertia was unknown in Antiquity and that circular motion starts not being regarded
as according to nature only in the modern age.
58 Nevertheless, the word is usually translated as motion in this passage — for example, by H.
Cherniss in the Loeb edition. This imprecision has led to confusion between the theory we’re discussing
(“thrust toward the center”) and the older theory of “motion toward the center” (
©), attributed to Chrysippus and it, too, reported by Plutarch (De stoicorum repugnantiis,
1054B–1055C), among others. Obviously the idea of a tendency toward a central point is as old
as the realization that the earth is round, but the theory under consideration here seems to be a
new, “dynamical” version of the old idea and is of great interest for that reason.
Revision: 1.11 Date: 2003/01/06 02:20:46