The fourth dimension

THE FIRST CHAPTER IN THE HISTORY OF FOUR SPACE 37

either hand, towards whose existence all experience points.

In Aristotle’s definition of matter and form as the constituent’of reality, as in Plato’s mystical vision of the kingdom of ideas, the existence of the higher dimensionality is implicitly involved.

Substance according to Aristotle is relative, not absolute. In everything that is there is the matter of which it is composed, the form which it exhibits ; but these are indissolubly connected, and neither can be thought without the other.

The blocks of stone out of which a house is built are the material for the builder; but, as regards the quarrymen, they are the matter of the rocks with the form he has imposed on them. Words are the final product of the grammarian, but the mere matter of the orator or poet. The atom is, with us, that out of which chemical substances are built up, but looked at from another point of view is the result of complex processes.

Nowhere do we find finality. The matter in one sphere is the matter, plus form, of another sphere of thought. Making an obvious application to geometry, plane figures exist as the limitation of different portions of the plane by one another. In the bounding lines the separated matter of the plane shows its determination into form. And as the plane is the matter relatively to determinations in the plane, so the plane itself exists in virtue of the jetermination of space. A plane is that wherein formless space has form superimposed on it, and gives an actuality of real relations. We cannot refuse to carry this process of reasoning a step farther back, and say that space itself is that which gives form to higher space. As a line is the determination of a plane, and a plane of a solid, so solid space itself is the determination of a higher space.

As a line by itself is inconceivable without that plane