(38) 'Now, the Greeks believed the world [material universe] to be composed of four elements--earth, air, fire, water--and to the Greek mind the conclusion was inevitable 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. Hence the conclusion, as Plato put it, that 'this (the regular dodecahedron) the Deity employed in tracing the plan of the Universe.' (H. Stanley Redgrove, in Bygone Beliefs.)

(6) We may now consider the question whether fire is the sole element existing in that celestial realm and whether there is any outgoing thence with the consequent need of renewal.

Timaeus pronounced the material frame of the All to consist primarily of earth and fire for visibility, earth for solidity- and deduced that the stars must be mainly composed of fire, but not solely since there is no doubt they are solid.

And this is probably a true account. Plato accepts it as indicated by all the appearances. And, in fact, to all our perception- as we see them and derive from them the impression of illumination- the stars appear to be mostly, if not exclusively, fire: but on reasoning into the matter we judge that since solidity cannot exist apart from earth-matter, they must contain earth as well.

But what place could there be for the other elements? It is impossible to imagine water amid so vast a conflagration; and if air were present it would be continually changing into fire.

Admitting that two self-contained entities, standing as extremes to each other need for their coherence two intermediaries; we may still question whether this holds good with regard to physical bodies. Certainly water and earth can be mixed without any such intermediate. It might seem valid to object that the intermediates are already present in the earth and the water; but a possible answer would be, "Yes, but not as agents whose meeting is necessary to the coherence of those extremes."

None the less we will take it that the coherence of extremes is produced by virtue of each possessing all the intermediates. It is still not proven that fire is necessary to the visibility of earth and earth to the solidarity of fire.

On this principle, nothing possesses an essential-nature of its very own; every several thing is a blend, and its name is merely an indication of the dominant constituent.

Thus we are told that earth cannot have concrete existence without the help of some moist element- the moisture in water being the necessary adhesive- but admitting that we so find it, there is still a contradiction in pretending that any one element has a being of its own and in the same breath denying its self-coherence, making its subsistence depend upon others, and so, in reality, reducing the specific element to nothing. How can we talk of the existence of the definite Kind, earth- earth essential- if there exists no single particle of earth which actually is earth without any need of water to secure its self-cohesion? What has such an adhesive to act upon if there is absolutely no given magnitude of real earth to which it may bind particle after particle in its business of producing the continuous mass? If there is any such given magnitude, large or small, of pure earth, then earth can exist in its own nature, independently of water: if there is no such primary particle of pure earth, then there is nothing whatever for the water to bind. As for air- air unchanged, retaining its distinctive quality- how could it conduce to the subsistence of a dense material like earth?

Similarly with fire. No doubt Timaeus speaks of it as necessary not to the existence but to the visibility of earth and the other elements; and certainly light is essential to all visibility- we cannot say that we see darkness, which implies, precisely, that nothing is seen, as silence means nothing being heard.

But all this does not assure us that the earth to be visible must contain fire: light is sufficient: snow, for example, and other extremely cold substances gleam without the presence of fire- though of course it might be said that fire was once there and communicated colour before disappearing.

As to the composition of water, we must leave it an open question whether there can be such a thing as water without a certain proportion of earth.

But how can air, the yielding element, contain earth?

Fire, again: is earth perhaps necessary there since fire is by its own nature devoid of continuity and not a thing of three dimensions?

Supposing it does not possess the solidity of the three dimensions, it has that of its thrust; now, cannot this belong to it by the mere right and fact of its being one of the corporeal entities in nature? Hardness is another matter, a property confined to earth-stuff. Remember that gold- which is water- becomes dense by the accession not of earth but of denseness or consolidation: in the same way fire, with Soul present within it, may consolidate itself upon the power of the Soul; and there are living beings of fire among the Celestials.

But, in sum, do we abandon the teaching that all the elements enter into the composition of every living thing?

For this sphere, no; but to lift clay into the heavens is against nature, contrary to the laws of her ordaining: it is difficult, too, to think of that swiftest of circuits bearing along earthly bodies in its course nor could such material conduce to the splendour and white glint of the celestial fire.

(34) In this diagram two interpenetrating pyramids are again employed, one of which represents fire and the other earth. It is demonstrated according to the law of elemental harmony that fire does not enter into the composition of earth nor earth into the composition of fire. The figures on the chart disclose the harmonic relationships existing between the four primary elements according to both Fludd and the Pythagoreans. Earth consists of four parts of its own nature; water of three parts of earth and one part of fire. The sphere of equality is a hypothetical point where there is an equilibrium of two parts of earth and two parts of fire. Air is composed of three parts of fire and one part of earth; fire, of four parts of its own nature. Thus earth and water bear to each other the ratio of 4 to 3, or the diatessaron harmony, and water and the sphere of equality the ratio of 3 to 2, or the diapente harmony. Fire and air also bear to each other the ratio of 4 to 3, or the diatessaron harmony, and air and the sphere of equality the ratio of 3 to 2, or the diapente harmony. As the sum of a diatessaron and a diapente equals a diapason, or octave, it is evident that both the sphere of fire and the sphere of earth are in diapason harmony with the sphere of equality, and also that fire and earth are in disdiapason harmony with each other.