A "higher" form of space that mathematicians conceive as another direction from which a fourth line may be drawn at right angles to each of the three lines (mutually at right angles) that three-dimensional space permits to be drawn through any point in it. A highly speculative form of the theory that such a higher form of space exists has been employed in the attempt to solve certain questions concerning psychic phenomena.
For beings living on a flat surface, having no thickness, and possessing all their nerve endings on the periphery of their bodies, only two directions could exist. A circle drawn on their plane with chalk would be a closed space into which they could not penetrate except through a cut in it. Having no concept of a third dimension, they could not picture objects passing out of and into the circle if the objects did not pass through the cut.
From a third dimension, however, both the inside and out-side of the circle are visible and accessible. Similarly, for beings living in a four-dimensional world, enclosed spaces would appear open. Persons could make objects mysteriously vanish in the direction of the fourth dimension and make them reappear again in an apparent transgression of the law of impenetrability.
A similar explanation is presented for apport phenomena, the reported materialization of an object in the midst of a séance. Johann Zöllner made the first attempt at the experimental demonstration of the fourth dimension in his sittings with the medium Henry Slade. Cesare Lombroso considered it an ingenious solution to many perplexing psychic problems. W. W. Carington, in A Theory of the Mechanism of Survival (1920), hypothesizes that after physical death the individual consciousness is embodied in a vehicle made not from physical matter, but from four-dimensional matter (i.e., that which in four-dimensional space corresponds to what we call matter in three-dimensional space). The connecting link between the physical body and the four-dimensional vehicle is the etheric double.
Clairvoyants who see the front, sides, back, and every internal point of three-dimensional objects simultaneously are thus believed to employ a four-dimensional organ of sight. Traveling and medical clairvoyance are better understood by using this hypothesis.
If the four-dimensional vehicle is so pliable that it is capable of being molded by the mere power of will, apparitions will find a ready explanation, provided the percipient is receptive to supernormal impressions. Another application is the phenomenon of prevision, bound up with the riddle of time. Its adoption as a working hypothesis has also been offered as a way to bridge the gap between religious and scientific thought.
"A. Square" [E. A. Abbott]. Flatland: A Romance of Many Dimensions. 1884. 6th ed. New York: Dover Publications, 1953.
Hinton, C. H. The Fourth Dimension. London: G. Allen & Unwin, 1934.
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Rucker, Rudy von Bitter. The Fourth Dimension: Toward a Geometry of Higher Reality. Boston: Houghton-Mifflin, 1984.