DEVELOPMENT OF NEW THEORY 209 



Dirac^s treatment which may have great philosophical 

 significance, independently of any question of success in 

 this particular application. The idea is that in digging 

 deeper and deeper into that which lies at the base of 

 physical phenomena we must be prepared to come to 

 entities which, like many things in our conscious experi- 

 ence, are not measurable by numbers in any way; and 

 further it suggests how exact science, that is to say the 

 science of phenomena correlated to measure-numbers, 

 can be founded on such a basis. 



One of the greatest changes in physics between the 

 nineteenth century and the present day has been the 

 change in our ideal of scientific explanation. It was the 

 boast of the Victorian physicist that he would not claim 

 to understand a thing until he could make a model of 

 it; and by a model he meant something constructed of 

 levers, geared wheels, squirts, or other appliances 

 familiar to an engineer. Nature in building the universe 

 was supposed to be dependent on just the same kind of 

 resources as any human mechanic; and when the physi- 

 cist sought an explanation of phenomena his ear was 

 straining to catch the hum of machinery. The man who 

 could make gravitation out of cog-wheels would have 

 been a hero in the Victorian age. 



Nowadays we do not encourage the engineer to build 

 the world for us out of his material, but we turn to the 

 mathematician to build it out of his material. Doubtless 

 the mathematician is a loftier being than the engineer, 

 but perhaps even he ought not to be entrusted with the 

 Creation unreservedly. We are dealing in physics with 

 a symbolic world, and we can scarcely avoid employing 

 the mathematician who is the professional wielder of 

 symbols; but he must rise to the full opportunities of the 

 responsible task entrusted to him and not indulge too 



