From Chapter II., Science and Religion
54. The Heavenly Bodies
The distinction between the diurnal revolution of the heavens from east to west, and the slower revolutions of the sun, moon, and planets from west to east, may also be referred to the early days of the school, and probably to Pythagoras himself.103 It obviously involves a complete break with the theory of a vortex, and suggests that the heavens are spherical. That, however, was the only way to get out of the difficulties of Anaximander's system. If it is to be taken seriously, we must suppose that the motions of the sun, moon, and planets are composite. On the one hand, they have their own revolutions with varying angular velocities from west to east, but they are also carried along by the diurnal revolution from east to west. Apparently this was expressed by saying that the motions of the planetary orbits, which are oblique to the celestial equator, are mastered (κρατεῖται) by the diurnal revolution. The Ionians, down to the Demokritos, never accepted this view. They clung to the theory of the vortex, which made it necessary to hold that all the heavenly bodies revolved in the same direction, so that those which, on the Pythagorean system, have the greatest angular velocity have the least on theirs. On the Pythagorean view, Saturn, for instance, takes about thirty years to complete its revolution; on the Ionian view it is "left behind" far less than any other planet, that is, it more nearly keeps pace with the signs of the Zodiac.104
For reasons which will appear later, we may confidently attribute to Pythagoras himself the discovery of the sphericity of the earth which the Ionians, even Anaxagoras and Demokritos, refused to accept. It is probable, however, that he still adhered to the geocentric system, and that the discovery that the earth was a planet belongs to a later generation (§150).
The account just given of the views of Pythagoras is, no doubt, conjectural and incomplete. We have simply assigned to him those portions of the Pythagorean system which appear to be the oldest, and it has not even been possible at this stage to cite fully the evidence on which our discussion is based. It will only appear in its true light when we have examined the second part of the poem of Parmenides and the system of the later Pythagoreans.105 It is clear at any rate that the great contribution of Pythagoras to science was his discovery that the concordant intervals could be expressed by simple numerical ratios. In principle, at least, that suggests an entirely new view of the relation between the traditional "opposites." If a perfect attunement (ἁρμονία) of the high and the low can be attained by observing these ratios, it is clear that other opposites may be similarly harmonised. The hot and the cold, the wet and the dry, may be united in a just blend (κρᾶσις), an idea to which our word "temperature" still bears witness.106 The medical doctrine of the "temperaments" is derived from the same source. Moreover, the famous doctrine of the Mean is only an application of the same idea to the problem of conduct.107 It is not too much to say that Greek philosophy was henceforward to be dominated by the notion of the perfectly tuned string.
102. This will be found in Chap. IV. §93.
103. I formerly doubted this on the ground that Plato appeared to represent the theory as a novelty in Laws, 822 a, but Professor Taylor has convinced me that I was wrong. What Plato is denying in that passage is this very doctrine, and the theory he is commending must be that of a simple motion in a new form. This was a discovery of Plato's old age; in the Myth of Er in the Republic and in the Timaeus we still have the Pythagorean theory of a composite motion. It is true that no writer earlier than Theon of Smyrna (p. 150, 12) expressly ascribes this theory to Pythagoras, but Aetios (ii. 16, 2) says that Alkmaion, a younger contemporary of Pythagoras, agreed with the mathematicians in holding that the planets had an opposite motion to the fixed stars. His other astronomical views were so crude (§ 96) that he can hardly have invented this.
104. See the account of the theory of Demokritos in Lucretius, v. 621 sqq., and cf. above, p. 70. The technical term is ὑπόλειψις. Strictly speaking, the Ionian view is only another way of describing the same phenomena, but it does not lend itself so easily to a consistent theory of the real planetary motions.
105. See Chap. IV. §§ 92-93, and Chap. VII. §§ 150-152.
106. It is impossible not to be struck by the resemblance between this doctrine and Dalton's theory of chemical combination. A formula like H2O is a beautiful example of a μεσότης. The diagrams of modern stereochemistry have also a curiously Pythagorean appearance. We sometimes feel tempted to say that Pythagoras had really hit upon the secret of the world when he said, "Things are numbers."
107. Aristotle derived his doctrine of the Mean from Plato's Philebus, where it is clearly expounded as a Pythagorean doctrine.
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