96 MATHEMATICS 



the recent history of Geometry, that the mode in 

 which the data of the senses can be idealized and 

 completed leaves a latitude in which there is a 

 considerable element of free choice left to the 

 mind. This element of free choice has been exer- 

 cised in the construction of various types of 

 Geometry, all of which are logically possible, i.e. 

 self-consistent, and several of which are equally 

 applicable for the representation of our actual 

 spatial experience. This remarkable result suggests 

 that in other sciences it is possible that the system 

 of laws forming the schematic representation of 

 the phenomena may not necessarily be unique; 

 that there may be in any given domain several, or 

 an unlimited number, of different possible schemes 

 which will all be equally valid; although, as in 

 the case of Geometry, they will not be all equally 

 simple. 



The sketch which has been given above of the 

 influence of Mathematics in other departments of 

 thought and work, has necessarily confined itself 

 in the main to a few specially striking examples. 

 Indeed it is practically certain that the number 

 and scope of the applications of Mathematical 

 methods both in the development of pure Science, 

 and in Engineering and other technical pursuits, 

 will largely increase in the not distant future. 

 As each branch of science reaches a stage of greater 

 maturity, and as each kind of technical work 

 becomes more open to scientific treatment, new 



