"Well," he resumed, after a moment's pause, "I procured the implements and the coloured blocks for practical experiment, and I followed the instructions carefully till I had arrived at a working conception of four-dimensional space.

I discovered, that is, that my ordinary three-dimensional body was but an expressiona projectionof my higher four-dimensional body!

FOUR-DIMENSIONAL VISTAS I THE QUEST OF FREEDOM

Should we observe in three-dimensional space contradictory facts our reason would be forced to reconcile these contradictions, also, and if they could be reconciled by the idea of a four-dimensional space our reason would accept this idea without cavil.

If so, such four-dimensional movement may be the proximate cause of the phenomenon of growthof those chemical changes and renewals whereby an organism is enabled to expand in three-dimensional space, just as by a three-dimensional power of movement (the act of walking) man is able to traverse his two-dimensional spacethe surface of the earth.

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.

Nature affords a sufficient number of representations of four-dimensional forms and movements to justify their consideration.

With the symmetry of solids, or symmetry with relation to an axial plane, no such simple movement as the foregoing suffices to produce or explain it, because symmetry about a plane implies four-dimensional movement.

In the mirror image of a solid we have a representation of what would result from a four-dimensional revolution, the surface of the mirror being the plane about which the movement takes place.

Thus, on the hypothesis that our space is traversing four-dimensional space, and that the forms of our space are cross-sections of four-dimensional forms, the unity and harmony of nature would be accounted for in a remarkably simple manner.

Thus, on the hypothesis that our space is traversing four-dimensional space, and that the forms of our space are cross-sections of four-dimensional forms, the unity and harmony of nature would be accounted for in a remarkably simple manner.

This reminds us of the segmentation of cell life observed under the microscope, as though a four-dimensional figure were registering its passage through our space.

THE ELECTRIC CURRENT Hinton conceived of an electric current as a four-dimensional vortex.

If Hinton's hypothesis be the true explanation, the universality of electro-magnetic action would again point to the conclusion that our three-dimensional world is superficialthe surface, that is, of a four-dimensional universe.

On the theory that the ether is an elastic solid of amazing properties, in which the light waves vibrate transversely to their direction, it assists the mind to think of the ether as four-dimensional, because then a light wave would be a superficial disturbance of the mediumsuperficial, but three-dimensional, as must needs be the case with the surface of a four-dimensional solid.

On the theory that the ether is an elastic solid of amazing properties, in which the light waves vibrate transversely to their direction, it assists the mind to think of the ether as four-dimensional, because then a light wave would be a superficial disturbance of the mediumsuperficial, but three-dimensional, as must needs be the case with the surface of a four-dimensional solid.

In the year 1877, Johann Friedrich Zöllner, professor of physics and astronomy at the University of Leipsic, undertook to prove that certain (so-called) psychic phenomena were susceptible of explanation on the hypothesis of a four-dimensional space.

Because we lack the sense of four-dimensional space, we must here have recourse to analogy, and assume three-dimensional space to be the unsensed higher region encompassing a world of two dimensions, To a hypothetical flat-man of a two-space, any portion of his plane surrounded by an unbroken line would constitute an enclosure.

All unconsciously to himself, he has called into play four-dimensional mechanics.

It is no more difficult for a four-dimensional intelligence to understand the appearance or disappearance of a body in a completely closed room, or the withdrawal of an orange from its skin, without cutting or breaking that skin, than it is for us to see the possibility of taking up a pencil point from the center of a circle and putting it down outside.

"I adopt the hypothesis that that which thinks in us has an ample experience, of which the intuitions we use in dealing with the world of real objects are a part; of which experience, the intuition of four-dimensional forms and motions is also a part.

Mr. C.W. Leadbeater in Clairvoyance specifically affirms that this higher power of sight is four-dimensional.

He concludes, "Either one of two things must be true, that four-dimensional conceptions give a wonderful power of representing the thought of the East, or that the thinkers of the East must have been looking at and regarding four-dimensional existence.

Now the flux of things corresponds to the four-dimensional aspect of the world, and with this the reason finds it impossible to deal.

From an etching by Gertrude Partington A Four-Dimensional Cover Design.