Of course to those whose notion of the fourth dimension is akin to that of a friend of the author who described it as “a wagon-load of bung-holes,” the idea of getting from it any practical advantage cannot seem anything but absurd.  There is something about this form of words “the fourth dimension” which seems to produce a sort of mental-phobia in certain minds, rendering them incapable of perception or reason.  Such people, because they cannot stick their cane into it contend that the fourth dimension has no mathematical or philosophical validity.  As ignorance on this subject is very general, the following essay will be devoted to a consideration of the fourth dimension and its relation to a new ornamental mode.

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II

THE FOURTH DIMENSION

The subject of the fourth dimension is not an easy one to understand.  Fortunately the artist in design does not need to penetrate far into these fascinating halls of thought in order to reap the advantage which he seeks.  Nevertheless an intention of mind upon this “fairy-tale of mathematics” cannot fail to enlarge his intellectual and spiritual horizons, and develop his imagination—­that finest instrument in all his chest of tools.

By way of introduction to the subject Prof.  James Byrnie Shaw, in an article in the Scientific Monthly, has this to say: 

Up to the period of the Reformation algebraic equations of more than the third degree were frowned upon as having no real meaning, since there is no fourth power or dimension.  But about one hundred years ago this chimera became an actual existence, and today it is furnishing a new world to physics, in which mechanics may become geometry, time be co-ordinated with space, and every geometric theorem in the world is a physical theorem in the experimental world in study in the laboratory.  Startling indeed it is to the scientist to be told that an artificial dream-world of the mathematician is more real than that he sees with his galvanometers, ultra-microscopes, and spectroscopes.  It matters little that he replies, “Your four-dimensional world is only an analytic explanation of my phenomena,” for the fact remains a fact, that in the mathematician’s four-dimensional space there is a space not derived in any sense of the term as a residue of experience, however powerful a distillation of sensations or perceptions be resorted to, for it is not contained at all in the fluid that experience furnishes.  It is a product of the creative power of the mathematical mind, and its objects are real in exactly the same way that the cube, the square, the circle, the sphere or the straight line.  We are enabled to see with the penetrating vision of the mathematical insight that no less real and no more real are these fantastic forms of the world of relativity than those supposed to be uncreatable or indestructible in the play of the forces of nature.