60 SCIENCE ABSOLUTE OP SPACE. 



Space and Non-Euclidean Geometry (American 

 Journal of Mathematics, Vol. I, 1878, Vol. II, 

 1879) one of these, Schmitz-Dumont, as a sad 

 paradoxer, and another, J. C. Becker, both of 

 whom would ere this have shared the oblivion 

 of still more antiquated fighters against the 

 light, but that Dr. Schotten, praiseworthy for 

 the very attempt at a comparative planimetry, 

 happens to be himself a believer in the a priori 

 founding of geometry, while his American re- 

 viewer, Mr. Ziwet, was then also an anti-non- 

 Euclidean, though since converted. 



He says, ' ' we find that some of the best Ger- 

 man text books do not try at all to define what 

 is space, or what is a point, or even what is a 

 straight line." Do any German geometries de- 

 fine space? I never remember to have met one 

 that does. 



In experience, what comes first is a bounded 

 surface, with its boundaries, lines, and their 

 boundaries, points. Are the points whose 

 definitions are omitted anything different or 

 better? 



Dr. Schotten regards the two ideas "direc- 

 tion" and "distance" as intuitively given in 

 the mind and as so simple as to not require 

 definition. 



When we read of two jockeys speeding 



