1 The Birth of Science - MSRI

11.7 Newton’s Natural Philosophy 331
the upper hand in their country) and became very popular in Renaissance
Europe. 139
Let’s turn to the question that to many may seem the only crucial one:
was the “Newtonian” law of gravitation, involving the inverse square of
the distance, known in antiquity? We don’t have Hipparchus’ work, but
we can start from what Newton himself wrote:
According to Macrobius, Pythagoras . . . applied to the heavens the
proportions found through these experiments [on the pitch of sounds
made by weighted strings], and learned from that the harmonies of
the spheres. And so, by comparing those weights with the weights
of the planets, and the intervals in sound with the intervals of the
spheres, and the lengths of string with the distances of the planets
[measured] from the center, he understood through the heavenly
harmonies that the weights of the planets toward the sun . . . are inversely
proportional to the squares of their distances. 140
It is significant that Newton thought that the inverse square law was
known to Pythagoras, even if the testimony of Macrobius does not quite page 407
justify this belief. Newton had probably read other, neo-Pythagorean, texts
on this subject.
The idea of applying the inverse square law to deduce Kepler’s laws
predates Newton. It had occurred at least to Wren and Halley, as implied
by a 1684 letter from the latter to Newton, and to Hooke, who put forth the
law in a letter to Newton of January 6, 1680. 142 In fact Hooke’s discovery of
the universal law of gravitation was one of the two main causes of New-
139 The role of such texts in the formation of modern scientific thought has probably not been
sufficiently placed in the right perspective. There have been studies of the influence of Hermetic
writings on Renaissance culture (especially after the famous [Yates] appeared) and on Copernicus,
Newton and others. But to my knowledge no one has analyzed the possible contribution of
remnants of Hellenistic science to Hermetic literature. Such an influence, if real, would help understand
why so many of the founders of modern scientific thought cultivated Hermetic knowledge.
Here we just remark that in document XVI of the Hermetic corpus — bearing the title “From Asclepius
to King Ammon” and cited, for example, by Copernicus — we read that the sun draws all
things to itself and, like a good charioteer, has bound the cosmos to itself, not letting it get away
(Corpus Hermeticum, XVI, 5 and 7). A systematic search of the Hermetic, kabbalistic, astrological
and alchemical literature that so fascinated Newton, and of which the neo-Pythagoreans were a
chief source, would likely reveal many other interesting passages.
140 “ut refert Macrobius . . . [p]roportionem vero his experimentis inventam Pythagoras applicuit
ad caelos et inde didicit harmoniam sphaerarum. Ideoque conferendo pondera illa cum ponderibus
planetarum et intervalla tonorum cum intervallis sphaerarum, atque longitudines chordarum cum
distantiis Planetarum ab orbium centro, intellexit per harmoniam caelorum quod pondera Planetarum
in Solem . . . essent reciproce ut quadrata distantiarum earum” (Classical scholia, f. 11v =
[Casini], pp. 41–42 or 32–33). The reference is to Macrobius, Commentarii in Somnium Scipionis, II, i.
142 Anyone can aspire to write interesting letters, and many succeed in doing so; but to receive
such letters all the time is a much more ambitious goal, which not many contemplate and only an
exceptional few achieve.
Revision: 1.11 Date: 2003/01/06 07:48:20