86 HUMANISM v 



cerning the nature of Space, which had been consecrated 

 by the tradition of 2000 years and set forth in the 

 geometry of Euclid. The possibilities of non-Euclidean 

 spaces, which were as yet necessarily ill-defined and ill- 

 understood, promptly attracted the adherents of all views 

 for which orthodox science appeared to have no room, 

 and no notion seemed too fantastic to become credible, if 

 not intelligible, in space of four or more dimensions. 

 The mathematicians themselves, who were engaged in 

 elaborating the new conceptions, were too busy or too 

 uncertain of their ground to resist successfully this 

 inundation of extravagance, and the consequent discredit 

 into which the subject fell seems to have killed the 

 general interest in it everywhere but in France. Mean 

 while mathematicians proceeded quietly with the work of 

 analysing the new conceptions and of deducing their 

 consequences, and thereby reached a clearer consciousness 

 of their import. The result has been that saner views 

 have begun to prevail, and that the sensational features of 

 the new geometry have been mitigated or eliminated. 

 The question has become arguable without the opposing 

 champions considering each other respectively unintelli 

 gible cranks or unimaginative stick-in-the-muds. Not 

 but what the rhapsodical view still periodically finds 

 expression in print, 1 but the tendency of the interesting 

 exchange of opinions which has been going on for the 

 last few years in the French philosophical and scientific 

 journals between MM. Delbceuf, Renouvier, Poincar, 

 Calinon, Lechalas, de Broglie, etc., seems to me to be 

 decidedly in the direction of agreement based upon a 

 retreat from extreme and extravagant positions on either 

 side. In other words, the blare of trumpets which 

 announced and advertised the arrival of the new claimant 

 to scientific recognition is over, the pachydermatous ears 

 of the established conservatism have recovered from the 

 shock, and preparations are being made to assign to the 

 newcomer a definite place in the array of the sciences. 

 The time then seems to be becoming opportune for 



1 E.g. , Monist, iv. p. 483. 



