3 2o THE POPULAR SCIENCE MONTHLY. 



to deny that he was ever a Zullnerite at all ; and, should he yield to 

 the temptation, the recording angel might fitly blot with a tear the 

 record of the lapse. At all events, Professor Zollner does not under- 

 stand Kant. 



Does he understand himself ? " If from our childhood," he says, 

 " phenomena had been of daily occurrence, requiring a space of four 

 dimensions for an explanation which should be free from contradic- 

 tions, i. e., conformable to reason, we should be able to form a con- 

 ception of space of four or more dimensions. It follows that the real 

 existence of a four-dimensional space can only be decided by experi- 

 ence, i. e., by observation of facts." Yes, it all depends on experience, 

 which, as every good Kantist will tell you, furnishes the matter of 

 our cognitions, while the mind furnishes the form, the two elements 

 uniting in the act of cognition ; insomuch that the form without the 

 matter is void, as the matter without the form is undetermined. 

 Wherefore, we can have no conception the matter of which has not 

 been furnished by experience, or, as a strict Kantist would say, by 

 sensibility. But what experience, known or conceivable, can furnish 

 the matter of the conception of a fourth dimension ? Contradictions, 

 which nothing but a fourth dimension will reconcile, answers Professor 

 Zollner such as the tying of knots in endless cords, disappearance 

 and reappearance of solid objects, passage of a shell through a table, 

 impressions cf feet on the inner sides of a closed book-slate, and other 

 " contradictions " emerging or appearing to emerge in the presence of 

 Dr. Slade. But contradictions are objects not of the sensitive faculty 

 but of the understanding, and, however amazing, do not furnish new 

 matter of conception ; they merely call for new applications or new 

 combinations of the conceptions we have. A knot tied in an endless 

 cord is, so far as presented to lis, a phenomenon within three dimen- 

 sions, and, though we may not know how the knot was tied, our igno- 

 rance of the way of tying it can give us no new matter of thought. It 

 is an appeal to our sense, not to our senses ; and the office of our sense 

 is to receive and organize the matter of thought, not give it. The 

 mind has no portal through which a fourth dimension can enter, no 

 chamber in which it may lodge. To assume that, because the contra- 

 dictions in question are irreconcilable, they ipso facto present to our 

 mind a new dimension of space, in the perception of which only they 

 become reconcilable, is to make the simple inexplicability of a prob- 

 lem not only the verification of a given solution of it, but the occa- 

 sion of a new experience in sense, and a new form in thought a 

 change, that is, in the constitution of our faculties. If a theory ex- 

 plains a phenomenon, the theory is so far confirmed ; but, if the phe- 

 nomenon is comprehensible only by a theory which is incomprehensible, 

 1 li' phenomenon itself is incomprehensible, and, a sensible person would 

 say, there is an end of it. With Professor Zollner, however, there is 

 only the beginning of it, the incomprehensibility of the phenomenon, 



