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."