c. The Pythagoreans further constructed the heavenly bodies of the

visible universe by means of numbers, and here we see at once the barrenness and abstraction present in the determination of numbers. Aristotle says (Met. I. 5), “Because they defined numbers to be the principles of all nature, they brought under numbers and their relationships all determinations and all sections, both of the heavens and of all nature; and where anything did not altogether conform, they sought to supply the deficiency in order to bring about a harmony. For instance, as the Ten or dekad appeared to them to be the perfect number, or that which embraces the whole essence of numbers, they said that the spheres moving in the heavens must be ten; but as only nine of these are visible, they made out a tenth, the Antichthone (_ἀντίχθονα_).” These nine are, first the milky way, or the fixed stars, and after that the seven stars which were then all held to be planets: Saturn, Jupiter, Mars, Venus, Mercury, the Sun, Moon, and in the last and ninth place, the Earth. The tenth is thus the Antichthone, and in regard to this it must remain uncertain whether the Pythagoreans considered it to be the side of the Earth which is turned away, or as quite another body.

Aristotle says, in reference to the specially physical character of these spheres (De cœlo II. 13 and 9), “Fire was by the Pythagoreans placed in the middle, but the Earth was made a star that moved around this central body in a circle.” This circle is, then, a sphere, which, as the most perfect of figures, corresponds to the dekad. We here find a certain similarity to our ideas of the solar system, but the Pythagoreans did not believe the fire to be the sun. “They thus,” says Aristotle, “rely, not on sensuous appearance, but on reasons,” just as we form conclusions in accordance with reasons as opposed to sensuous appearances; and indeed this comes to us still as the first example of things being in themselves different from what they appear. “This fire, that which is in the centre, they called Jupiter’s place of watch. Now these ten spheres make, like all that is in motion, a tone; but each makes a different one, according to the difference in its size and velocity. This is determined by means of the different distances, which bear an harmonious relationship to one another, in accordance with musical intervals; by this means an harmonious sound arises in the moving spheres”—a universal chorus.

We must acknowledge the grandeur of this idea of determining everything in the system of the heavenly spheres through number-relations which have a necessary connection amongst themselves, and have to be conceived of as thus necessarily related; it is a system of relations which must also form the basis and essence of what can be heard, or music. We have, comprehended here in thought, a system of the universe; the solar system is alone rational to us, for the other stars are devoid of interest. To say that there is music in the spheres, and that these movements are tones, may seem just as comprehensible to us as to say that the sun is still and the earth moves, although both are opposed to the dictates of sense. For, seeing that we do not see the movement, it may be that we do not hear the notes. And there is little difficulty in imagining a universal silence in these vast spheres, since we do not hear the chorus, but it is more difficult to give a reason for not hearing this music. The Pythagoreans say, according to the last quoted passage of Aristotle, that we do not hear it because we live in it, like the smith who gets accustomed to the blows of his hammer. Since it belongs to our substance and is identical with ourselves, nothing else, such as silence, by which we might know the other, comes into relationship with us, for we are conceived of as entirely within the movement. But the movement does not become a tone, in the first place, because pure space and time, the elements in movement, can only raise themselves into a proper voice, unstimulated from without, in an animate body, and movement first reaches this definite, characteristic individuality in the animal proper; and, in the next place, because the heavenly bodies are not related to one another as bodies whose sound requires for its production, contact, friction, or shock, in response to which, and as the negation of its particularity its own momentary individuality resounds in elasticity; for heavenly bodies are independent of one another, and have only a general, non-individual, free motion.

We may thus set aside sound; the music of the spheres is indeed a wonderful conception, but it is devoid of any real interest for us. If we retain the conception that motion, as measure, is a necessarily connected system of numbers, as the only rational part of the theory, we must maintain that nothing further has transpired to the present day. In a certain way, indeed, we have made an advance upon Pythagoras. We have learned from Kepler about laws, about eccentricity, and the relation of distances to the times of revolution, but no amount of mathematics has as yet been able to give us the laws of progression in the harmony through which the distances are determined. We know empirical numbers well enough, but everything has the semblance of accident and not of necessity. We are acquainted with an approximate rule of distances, and thus have correctly foretold the existence of planets where Ceres, Vesta, Pallas, &c., were afterwards discovered—that is, between Mars and Jupiter. But astronomy has not as yet found in it a consistent sequence in which there is rationality; on the other hand, it even looks with disdain on the appearance of regularity presented by this sequence, which is, however, on its own account, a most important matter, and one which should not be forgotten.