94 THE FOURTH DIMENSION. 



ish years confirmed, and that in this way it has become in his mind 

 so profound a conviction that it is no longer possible for him to 

 think it away. Consonant with this argumentation, also, is Zoll- 

 ner's remark, that the same phenomenon has presented itself in 

 astronomical methods of knowledge. To explain the movements of 

 the planets, which appear to describe regular paths on the surface 

 of a celestial sphere, we were compelled in the solution of the rid- 

 dles which these motions presented, to assume in the structure of the 

 heavens a dimension of " depth," and the complicated motions in 

 the two-dimensioned firmament were converted into very simple 

 motions in three-dimensioned space. Zollner also contends that our 

 conception of the entire visible world as possessed of three dimen- 

 sions is a product of our reason, which the mind was driven to form 

 by the contradictions which would be presented to it on the assump- 

 tion of only two dimensions by the perspective distortions, coinci- 

 dences, and changes of magnitude of objects. When a child moves 

 its hand before its eyes, turns it, brings it nearer, or pushes it farther 

 away, this child successively receives the most various impressions 

 on the surface of its retina of one and the same object of whose 

 identity and constancy its feelings offer it a perfect assurance. If 

 the child regarded the changeable projection of the hand on the sur- 

 face of the retina as the real object, and not the hand which lies be- 

 yond it, the child would constantly be met with contradictions in its 

 experience, and to avoid this it makes the hypothesis that the space 

 of experience is three-dimensional. Zollner's contention is, there- 

 fore, that man originally had only a two-dimensional intuition of 

 space, but was forced by experience to represent to himself the ob- 

 jects which on the retinal surface appeared two-dimensional, as 

 three-dimensional, and thus to transform his two-dimensional space- 

 intuition into a three-dimensional one. Now, in exactly the same 

 way, according to Zollner's notion, will man, by the advancement 

 and increasing exactness of his knowledge of the phenomena of the 

 outer world, also be compelled to conceive of the material world as 

 a "shadow cast by a more real four-dimensional world," so that 

 these conceptions will be just as trivial for the people of the twen- 

 tieth century as since Copernicus's time the explanation of the mo- 



