Hinton - The Fourth Dimension.pdf

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 builder; but, as regards the quarryman,
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
determination 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