[Notes on Zöllner’s “Fourth-Dimension”]

Article Selections by A. N. Aksakoff ’s “The Scientific Hypothesis Respecting Mediumistic Phenomena”| Notes by H.P.B.

[Note: Aksakoff’s article details some of the experiments performed by Zöllner, which are described in his Wissenschaftliche Abhandlungen; see Transcendental Physics.]

. . . Geometrical figures not distinguishable by our thought (similar in form, size, and the mutual relation of their parts) should not be distinguishable by our sensuous perception either; they must be brought into such relations with us as would make them identical in the effects they produce upon us. This condition is satisfied by planes (or figures of two dimensions), symmetrical figures, but it is not satisfied by equally regular solids (figures which embrace the three dimensions). Two equal triangles can always be made to perfectly fit each other by turning over one of them, i.e., through a process accomplished which involves the aid of the third dimension; but if we move these triangles in a plane only, that is to say, using but two dimensions, we would never succeed in making them fit each other, so that one of these would completely occupy the place of the other.¹

1. I think that perhaps I can make Mr. Aksakoff’s meaning a little clearer by stating the proposition in the following terms: in the case of plane figures, i.e., of two dimensions only (length and breadth) when they are of perfect equivalence we can verify that equivalence to sensuous perception by the aid of the third dimension of thickness; or otherwise expressing it, by the simple act of superposition whereby our senses verify the equivalence; but in the case of solid bodies of perfect equivalence, these possessing the third dimension already, it is obvious that there is no position of superposition which will enable our sensuous perception to verify the equivalence.

This experiment in the domain of mediumship^* has nothing substantially new in it; it belongs to a long series of phenomena which exhibit what is generally described as the passage of matter through matter.²

2. The employment of the term “dimension” to express this “passage of matter through matter,” appears to me as likely to lead to a great confusion of ideas. It would be made much more comprehensible to the general reader if Zöllner were to apply the term quality equally to length, breadth, thickness and permeability. But at best, the present discussion affords one more example of the fact I have repeatedly pointed out, that the European languages are wretchedly poor in words to express metaphysical and psychological ideas in comparison with the Oriental tongues. The property which we have here clumsily designated as a “fourth” dimension of space is known throughout the whole East by appropriate and specific terms, among not only scholars but the very “jugglers” who make boys disappear from beneath baskets. If Western scientists would familiarize themselves a little more with the Pythagorean Tetraktys, or even with the algebraical “unknown quantity” in its transcendental meaning, all difficulties in the way of accepting Zöllner’s hypothesis would disappear.