Dimensional Sequences
Not only does nature everywhere geometrize, but she does so in a particular way, in which we discover dimensional sequences. Consider the transformation of solid, liquid, gas, from one to another, under the influence of heat. A solid, set in free motion, can follow only a line—as is the case of a thrown ball. A liquid has the added power of lateral extension. Its tendency, when intercepted, is to spread out in the two dimensions of a plane—as in the case of a griddle cake; while a gas expands universally in all directions, as shown by a soap-bubble. It is a reasonable inference that the fourth state of matter, the corpuscular, is affiliated to some four-dimensional manner of extension, and that there may be states beyond this, involving even higher development of space.
Next glance at the vegetable kingdom. The seed, a point, generates a line system, in stem, branches, twigs, from which depend planes in the form of leaves and flowers, and from these come fruit, solids.
“The point, the line, the surface and the sphere,
In seed, stem, leaf and fruit appear.”
A similar sequence may be noted within the body: the line-network of the nerves conveys the message of sensation from the surface of the body to some center in the solid, of the brain—and thence to the Silent Thinker, “he who is without and within,” or in terms of our hypothesis, “he who dwells in higher space.”