100 THE FOURTH DIMENSION. 



a number of problewhich he had here indefinitely laid aside, but 

 hoped to treat in a superior state by superior geometrical methods. 

 Leaving aside this jest, which quite naturally suggested itself, the 

 remarks of Gauss are quite correct. We possess the power to ab- 

 stract and can think, therefore, what kind of geometry a being that 

 is only acquainted with ; "0 dimensional world would have; for 

 instance, we can imagine that such a being could not conceive of 

 the possibility of making two triangles coincide which were con- 

 gruent in the sense above explained, and so on. So, also, we can 

 understand that a being who has control of four dimensions can only 

 conceive of a geometry of four-dimensional space, yet may have the 

 capacity of thinking itself into spaces of other dimensions. But it 

 does not follow from this that a four- dimensional space exists, let 

 alone that it is inhabited by reasonable beings. 



Riemann, on the other hand, speaks directly of a world of spir- 

 its. In his Neuc mathematische Principien der Naturphilosophic he 

 puts forth the hypothesis that the space of the world is filled with 

 a material that is constantly pouring into the ponderable atoms, 

 there to disappear from the phenomenal world. In every ponderable 

 atom, he says, at every moment of time, there enters and appears a 

 determinate amount of matter, proportional to the force of gravita- 

 tion. The ponderable bodies, according to this theory, are the 

 place at which the spiritual world enters and acts on the material 

 world. Riemann's world of spirits, the sole office of which is to ex- 

 plain the phenomenon of gravitation as a force governing matter, 

 is, however, essentially different from the spiritual world of Zollner, 

 the function of which is to explain supposed supersensuous phe- 

 nomena which stand in the most glaring contradiction with the es- 

 tablished known laws of the material world. 



Besides this appeal to the testimony of eminent men like Plato, 

 Kant, Gauss, and Riemann, the scientific prophet of modern spirit- 

 ualism also bases his theory on the belief, which has obtained at all 

 times and appeared in various forms among all peoples, that there 

 exist in the world forces which at times are competent to evoke 

 phenomena that ate exempt from the ordinary laws of nature. We 

 have but to think of the phenomena of table-turning which once ex- 



