Page:Popular Science Monthly Volume 20.djvu/330

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included the development of a fourth dimension, and we know he expressed a lofty scorn for table-tippings and other things of the sort, to which the new dimension, it would seem, has thus far lent itself exclusively. Kant, it is true, admitted the possibility of other dimensions, but derived it from the impossibility of knowing what exists outside of the limits of our faculties, and consequently of legitimately affirming or denying anything about it. He suggested the possibility of other dimensions of space, and, for that matter, the possibility of no space, but not the possibility of the discovery and comprehension of either by the human mind. So far from this, he distinctly suggested the reverse, actually citing, as an example of truths "always united with the consciousness of necessity," the proposition, "Space has only three dimensions"; and, since a necessary truth is one of which the contrary is inconceivable, he could not have suggested, without self-contradiction, that space may have more than three dimensions. If other dimensions exist, they exist, according to Kant, not for man, but for other orders of beings, endowed with corresponding forms of perception—exist as parts of the original furniture of the intelligences of other spheres—hypothetical properties of hypothetical creatures in hypothetical worlds, one and all of which transcend our faculties. This, however, is by no means the theory of Professor Zöllner.

"In my first treatise, 'On Action at a Distance,'" says that distinguished physicist, "I have discussed in detail the truth, first discovered by Kant, later by Gauss and the representatives of the anti-Euclidian geometry, viz., that our present conception of space, familiar to us by habit, has been derived from experience, i. e., from empirical facts, by means of the causal principle existing a priori in our intellect. This in particular is to be said of the three dimensions of our present conception of space. If from our childhood phenomena had been of daily occurrence, requiring a space of four dimensions for an explanation which should be free from contradiction, i. e., conformable to reason, we should be able to form a conception of space of four or more dimensions. It follows that the real existence of a four-dimensional, space can only be decided by experience, i. e., by observation of facts. A great step has been made by acknowledging that the possibility of a four-dimensional development of space can be understood by our intellect, although, on account of reasons previously given, no corresponding image of it can be conceived by the mind." Probably the first thought which will occur to the intelligent reader of this passage is that Professor Zöllner mistakes Kant; and perhaps the second thought will be that the professor mistakes himself. If these impressions prove just, he may find one day that his theory of a fourth dimension has suddenly passed away more completely, if less mysteriously, than the book from the slate at Vienna, or the round-table from the sitting room at Leipsic. Let us inquire whether or not they are just.

Professor Zöllner thinks "our present conception of space" has been