Four-Dimensional Vistas

by Claude Fayette Bragdon

Hinton conceived of an electric current as a four-dimensional vortex. He declared that on the Higher Space Hypothesis the revolution of the ether would yield the phenomenon of the electric current. The reader is referred to Hinton's book, The Fourth Dimension, for an extended development of this idea. What follows is a brief summary of his argument. First, he examines the characteristics of a vortex in a three-dimensional fluid. Then he conceives of what such a vortex would be in a four-dimensional medium of analogous properties. The whirl would be about a plane, and the contour of this plane would correspond to the ends of the axis line in the former vortex; and as before, the vortex would extend to the boundary. Every electric current forms a closed circuit: this is equivalent to the hyper-vortex having its ends in the boundary of the hyper-fluid. The vortex with a surface as its axis, therefore, affords a geometric image of a closed circuit.

Hinton supposes a conductor to be a body which has the property of serving as a terminal abutment to such a hyper-vortex as has been described. The conception that he forms of a closed current, therefore, is of a vortex sheet having its edge along the circuit of the conducting wire. The whole wire would then be like the centers on which a spindle turns in three-dimensional space, and any interruption of the continuity of the wire would produce a tension in place of a continuous revolution. The phenomena of electricity—polarity, induction, and the like—are of the nature of the stress and strain of a medium, but one possessing properties unlike those of ordinary matter. The phenomena can be explained in terms of higher space. 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 superficial—the surface, that is, of a four-dimensional universe.

THE GREATER UNIVERSE

This practically exhausts the list of accepted and accredited indications of hyper-dimensionality in our physical environment. But if the collective human consciousness is moving into the fourth dimension, such indications are bound to multiply out of all measure. It should be remembered that in Franklin's day electricity was manifest only in the friction of surfaces and in the thunderbolt. To-day all physical phenomena, in their last analysis, are considered to be electrical. The world is not different, but perception has evolved, and is evolving.

There is another field, in which some of our ablest minds are searching for evidences of the curvature of space, the field of astronomy and astro-physics. But into this the layman hesitates to enter because the experts themselves have found no common ground of understanding. The ether of space is a battlefield strewn with dead and dying hypotheses; gravitation, like multiplication, is vexation; the very nature of time, form and movement is under vivid discussion, in connection with what is known as the Theory of Relativity.

Notwithstanding these counter-currents of speculation, which should make the wise man speak smilingly of his wisdom, this summary remains incomplete without a reference to the pressure of higher space upon those adventurous minds that essay to deal with the profound problems of the greater universe, and a statement of the reasons for their feeling this pressure. These reasons are well suggested by Professor B.G. Harrison, in his Popular Astronomy. He says: "With the idea of a universe of finite dimensions there is the obvious difficulty of the beyond. The truth is that a universe of finite proportions is equally difficult to realize as one of infinite extent. Perhaps the nearest analogy to infinity that we can understand lies in our conception of a closed curve. It seems easier to imagine the endless movement of a sphere in a circular path than the case of one travelling in a straight line. Possibly this analogy may apply in some way to fourth-dimensional space, but the manner of its application is certainly not easy to understand. If we would imagine that all co-ordinates of time and space were curved, and eventually return to the same point, it might bring the ultimate comprehension one degree nearer."

A HINT FROM ASTRONOMY

The physical evidence that our space is thus curved in higher space, some have considered astronomy to furnish in what is called the "negative parallax" of certain distant stars. This cannot be passed by, though it is too deeply involved with the probable error of the observers themselves to be considered more than an interesting fact in this connection. Every one knows that the difference of angle under which an object is seen from two standpoints is called its parallax. The parallax of the stars—and the consequent knowledge of their distance—is obtained by observing them from opposite points of the earth's orbit around the sun. When a star is within measurable distance, these angles are acute, and the lines from the star to the earth at opposite sides of its orbit converge, therefore. But when these lines, as sometimes happens, appear to be divergent, the result is called a negative parallax, and is explainable by higher space relationships. Obviously, the divergence of the lines would indicate that the object lies behind the observer instead of in front of him. This anomaly can be explained by the curvature of space in the fourth dimension. If space is so curved, the path of light itself is curved also, and a man—were his vision immeasurably keen, not to say telescopic—could see the back of his own head! It is not worth while to give this question of negative parallax too much importance, by reason of the probability of error, but in this connection it should be stated that there appears to be an undue number of negative parallaxes recorded.

GRAVITATION

Gravitation remains a puzzle to science. The tendency of modern physics is to explain all material phenomena in terms of electrons and the ether, but the attempt to account for gravitation in this way is attended with difficulties. In order to cope with these, it seems necessary to assume that our universe is only a portion of a greater universe. This assumption readily lends itself to the conception of our universe as a three-dimensional meeting place of two portions of a universe of four dimensions—that is, its conception as a "higher" surface. This is a fundamental postulate of higher space speculation.