Bygone Beliefs | Page 8

discovery that there are only five such solids. These are as follows:--
The Tetrahedron, having four equilateral triangles as faces.
The Cube, having six squares as faces.
The Octahedron, having eight equilateral triangles as faces.
The Dodecahedron, having twelve regular pentagons (or five-sided figures) as faces.
The Icosahedron, having twenty equilateral triangles as faces.[1]
[1] If the reader will copy figs. 4 to 8 on cardboard or stiff paper, bend each along the dotted lines so as to form a solid, fastening together the free edges with gummed paper, he will be in possession of models of the five solids in question.
Now, the Greeks believed the world to be composed of four elements--earth, air, fire, water,--and to the Greek mind the conclusion was inevitable[2a] that the shapes of the particles of the elements were those of the regular solids. Earth-particles were cubical, the cube being the regular solid possessed of greatest stability; fire-particles were tetrahedral, the tetrahedron being the simplest and, hence, lightest solid. Water-particles were icosahedral for exactly the reverse reason, whilst air-particles, as intermediate between the two latter, were octahedral. The dodecahedron was, to these ancient mathematicians, the most mysterious of the solids: it was by far the most difficult to construct, the accurate drawing of the regular pentagon necessitating a rather elaborate application of PYTHAGORAS' great theorem.[1] Hence the conclusion, as PLATO put it, that "this [the regular dodecahedron] the Deity employed in tracing the plan of the Universe."[2b] Hence also the high esteem in which the pentagon was held by the Pythagoreans. By producing each side of this latter figure the five-pointed star (fig. 9), known as the pentagram, is obtained. This was adopted by the Pythagoreans as the badge of their Society, and for many ages was held as a symbol possessed of magic powers. The mediaeval magicians made use of it in their evocations, and as a talisman it was held in the highest esteem.
[2a] Cf. PLATO: The Timaeus, SESE xxviii--xxx.
[1] In reference to this matter FRANKLAND remarks: "In those early days the innermost secrets of nature lay in the lap of geometry, and the extraordinary inference follows that Euclid's Elements, which are devoted to the investigation of the regular solids, are therefore in reality and at bottom an attempt to `solve the universe.' Euclid, in fact, made this goal of the Pythagoreans the aim of his Elements."--Op. cit., p. 35.
[2b] Op. cit., SE xxix.
Music played an important part in the curriculum of the Pythagorean Brotherhood, and the important discovery that the relations between the notes of musical scales can be expressed by means of numbers is a Pythagorean one. It must have seemed to its discoverer--as, in a sense, it indeed is--a striking confirmation of the numerical theory of the Cosmos. The Pythagoreans held that the positions of the heavenly bodies were governed by similar numerical relations, and that in consequence their motion was productive of celestial music. This concept of "the harmony of the spheres" is among the most celebrated of the Pythagorean doctrines, and has found ready acceptance in many mystically-speculative minds. "Look how the floor of heaven," says Lorenzo in SHAKESPEARE'S The Merchant of Venice--
" . . . Look how the floor of heaven Is thick inlaid with patines of bright gold: There's not the smallest orb which thou behold's" But in his motion like an angel sings, Still quiring to the young-eyed cherubins; Such harmony is in immortal souls; But whilst this muddy vesture of decay Doth grossly close it in, we cannot hear it."[1]
[1] Act v. scene i.
Or, as KINGSLEY writes in one of his letters, "When I walk the fields I am oppressed every now and then with an innate feeling that everything I see has a meaning, if I could but understand it. And this feeling of being surrounded with truths which I cannot grasp, amounts to an indescribable awe sometimes! Everything seems to be full of God's reflex, if we could but see it. Oh! how I have prayed to have the mystery unfolded, at least hereafter. To see, if but for a moment, the whole harmony of the great system! To hear once the music which the whole universe makes as it performs His bidding!"[1] In this connection may be mentioned the very significant fact that the Pythagoreans did not consider the earth, in accordance with current opinion, to be a stationary body, but believed that it and the other planets revolved about a central point, or fire, as they called it.
[1] CHARLES KINGSLEY: His Letters and Memories of His Life, edited by his wife (1883), p. 28.
As concerns PYTHAGORAS' ethical teaching, judging from the so-called Golden Verses attributed to him, and no doubt written by one of his disciples,[2] this would appear to be in some respects similar to that of the Stoics who came later, but free from