the heaven of the fixed stars, which revolves in twenty-four hours. Saturn, of course, comes next; for, though it has a slow motion of its own in a contrary direction, that is "mastered" (κρατεῖται) by the diurnal revolution. The other view, which gives the highest note to the Moon and the lowest to the fixed stars, is probably due to the theory which substituted an axial rotation of the earth for the diurnal revolution of the heavens.[1]
153.The likenesses of numbers. We have still to consider a view, which Aristotle sometimes attributes to the Pythagoreans, that things were "like numbers." He does not appear to regard this as inconsistent with the doctrine that things are numbers, though it is hard to see how he could reconcile the two.[2] There is no doubt, however, that Aristoxenos represented the Pythagoreans as teaching that things were like numbers,[3] and there are other traces of an attempt to make out that this was the original doctrine. A letter was produced,
- ↑ For the various systems, see Boeckh, Kleine Schriften, vol. iii. pp. 169 sqq., and Carl v. Jan, "Die Harmonie der Sphären" (Philol. 1893. pp. 13 sqq.). There is a sufficient account of them in Heath's Aristarchus, pp. 107 sqq., where the distinction between absolute and relative velocity is clearly stated, a distinction which is not appreciated in Adam's note on Rep. 617 b (vol. ii. p. 452), with the result that, while the heaven of the fixed stars is rightly regarded as the νήτη (the highest note), the Moon comes next instead of Saturn—an impossible arrangement. The later view is represented by the "bass of Heaven's deep Organ" in the "ninefold harmony" of Milton's Hymn on the Nativity (xiii.). At the beginning of the Fifth Act of the Merchant of Venice, Shakespeare makes Lorenzo expound the doctrine in a truly Pythagorean fashion. According to him, the "harmony" in the soul ought to correspond with that of the heavenly bodies ("such harmony is in immortal souls"), but the "muddy vesture of decay" prevents their complete correspondence. The Timaeus states a similar view, and in the Book of Homage to Shakespeare (pp. 58 sqq.) I have tried to show how the theories of the Timaeus may have reached Shakespeare. There is no force in Martin's observation that the sounding of all the notes of an octave at once would not produce a harmony. There is no question of harmony in the modern sense, but only of attunement (ἁρμονία) to a perfect scale.
- ↑ Cf. especially Met. A, 6. 787, b 10 (R. P. 65 d). It is not quite the same thing when he says, as in A, 5. 985 b 23 sqq. (R. P. ib.), that they perceived many likenesses in things to numbers. That refers to the numerical analogies of Justice, Opportunity, etc.
- ↑ Aristoxenos ap. Stob. i. pr. 6 (p. 20), Πυθαγόρας . . . πάντα τὰ πράγματα ἀπεικάζων τοῖς ἀριθμοῖς.
