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.”

MAN THE GEOMETER

When man essays the role of creator he cannot do otherwise than follow similar sequences:  it is easy to discern dimensional progression in the products of man’s ingenuity and skill.  Consider, for example, the evolution of a building from its inception to its completion.  It exists first of all in the mind of the architect, and there it is indubitably higher-spatial, for he can interpenetrate and examine every part, and he can consider it all at once, viewing it simultaneously from without and from within, just as one would be able to do in a space of four dimensions.  He begins to give his idea physical embodiment by making with a pencil-point, lines on a plane (a piece of paper), the third dimension being represented by means of the other two.  Next (if he is careful and wise) he makes a three-dimensional model.  From the architect’s drawings the engineer establishes his points, lays out his angles, and runs his lines upon the site itself.  The mason follows, and with his footing courses makes ponderable and permanent the lines of the engineer.  These lines become in due course walls—­vertical planes.  Floors and roofs—­horizontal planes—­follow, until some portion of three-dimensional space has been enclosed.

Substantially the same sequence holds, whatever the kind of building or the character of the construction—­whether a steel-framed skyscraper or a wooden shanty.  A line system, represented by columns and girders in the one case, and by studs and rafters in the other, becomes, by overlay or interposition, a system of planes, so assembled and correlated as to define a solid.