Timaeus — Plato
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Transpositio7i and transfonnation of the clcvients. 401 as Democritus (Hippolyt. Rcf. Hacr. I. 13) had said, would be, as rimaeus. he satirically observes, ' the characteristic of a very indefinite and intkoducignorant mind' (55 C, D).
'^'"'^• The twenty triangular faces of an icosahedron form the faces or sides of two regular octahedrons and of a regular pyramid (20 = 8 X 2 + 4) ; and therefore, according to Plato, a particle of v/ater when decomposed is supposed to give two particles of air and one of fire. So because an octahedron gives the sides of two pyramids (8=4 x 2), a particle of air is resolved into two particles of fire.
The transformation is effected by the superior power or number of the conquering elements. The manner of the change is (i) a separation of portions of the elements from the masses in which they arc collected ; (2) a resolution of them into their original triangles; and (3) a reunion of them in new forms. Plato himself proposes the question, Why does motion continue at all when the elements are settled in their places?
He answers that although the force of attraction is continually drawing similar elements to the same spot, still the revolution of the universe exercises a condensing power, and thrusts them again out of their natural places. Thus want of uniformity, the condition of motion, is produced (57 D if.).
In all such disturbances of matter there is an alternative for the weaker element : it may escape to its kindred, or take the form of the stronger — becoming denser, if it be denser, or rarer, if rarer. This is true of fire, air, and water, which, being composed of similar triangles, are interchangeable ; earth, however, which has triangles peculiar to itself, is capable of dissolution, but not of change (56 D ff. ).
Of the interchangeable elements, fire, the rarest, can only become a denser, and water, the densest, only a rarer: but air may become a denser or a rarer. No single particle of the elements is visible, but only the aggregates of them are seen. The subordinate species depend, not upon differences of form in the original triangles, but upon differences of size.
The obvious physical phenomena from which Plato has gathered his views of the relations of the elements seem to be the effect of fire upon air, water, and earth, and the effect of water upon earth. The particles are supposed by him to be in a perpetual process of circulation caused by inequality. This process of circulation does VOL. III. — 41 not admit of a vacuum, as he tells us in his strange account of respiration (79 B). Of the phenomena of light and heavy he speaks afterwards, when treating of sensation, but they may be more conveniently considered by us in this place.
They are not, he says, to be explained by ^ above ' and 'below,' which in the universal globe have no existence (62 D), but by the attraction of similars towards the great masses of similar substances ; fire to fire, air to air, water to water, earth to earth. Plato's doctrine of attraction implies not only (i) the attraction of similar elements to one another, but also (2) of smaller bodies to larger ones.
Had he confined himself to the latter he would have arrived, though, perhaps, without any further result or any sense of the greatness of the discovery, at the modern docljine of gravitation. He does not observe that water has an equal tendency towards both water and earth. So easily did the most obvious facts which were inconsistent with his theories escape him.
The general physical doctrines of the Timaeus may be summed up as follows: (i) Plato supposes the greater masses of the elements to have been already settled in their places at the creation : (2) they are four in number, and are formed of rectangular triangles variously combined into regular solid figures: (3) three of them, fire, air, and water, admit of transformation into one another; the fourth, earth, cannot be similarly transformed : (4) different sizes of the same triangles form the lesser species of each element: (5) there is an attraction of like to like — smaller masses of the same kind being drawn towards greater : (6) there is no void, but the particles of matter are ever pushing one another round and round {nepiuatg).
Like the atomists, Plato attributes the differences between the elements to differences in geometrical figures. But he does not explain the process by which surfaces become solids ; and he characteristically ridicules Democritus for not seeing that the worlds are finite and not infinite. § 4. The astronomy of Plato is based on the two principles of the same and the other, which God combined in the creation of the world. The soul, which is compounded of the same, the other, and the essence, is diffused from the centre to the circumference of the heavens. We speak of a soul of the universe ; but more Timaeus. truly regarded, the universe of the Timaeus is a soul, governed by mind, and holding in solution a residuum of matter or evil, which the author of the world is unable to expel, and of which Plato cannot tell us the origin.
The creation, in Plato's sense, is really the creation of order ; and the first step in giving order is the division of the heavens into an inner and outer circle of the other and the same, of the divisible and the indivisible, answering to the two spheres, of the planets and of the world beyond them, all together moving around the earth, which is their centre.
To us there is a difficulty in apprehending how that which is at rest can also be in motion, or that which is indivisible exist in space.
But the whole description is so ideal and imaginative, that we can hardly venture to attribute to many of Plato's words in the Timaeus any more meaning than to his mythical account of the heavens in the Republic and in the Phaedrus. (Cp. his denial of the ' blasphemous opinion ' that there are planets or wandering stars; all alike move in circles — Laws vii.
821, 822.) The stars are the habitations of the souls of men, from which they come and to which they return.
In attributing to the fixed stars only the most perfect motion — that which if on the same spot or circling around the same — he might perhaps have said that to ' the spectator of all time and all existence,' to borrow once more his own grand expression, or viewed, in the language of Spinoza, 'sub specie aeternitatis,' they were still at rest, but appeared to move in order to teach men the periods of time.
Although absolutely in motion, they are relatively at rest ; or we may conceive of them as resting, while the space in which they are contained, or the whole anima mujidi, revolves. The universe revolves around a centre once in twenty-four hours, but the orbits of the fixed stars take a different direction from those of the planets.
The outer and the inner sphere cross one another and meet again at a point opposite to that of their first contact ; the first moving in a circle from left to right along the side of a parallelogram which is supposed to be inscribed in it, the second also moving in a circle along the diagonal of the same parallelogram from right to left; or, in other words, the first describing the path of the equator, the second, the path of the ecliptic. The motion of the second is controlled by the first,
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