6o SCIENCE AND METHOD. 



know them. A few only are harmonious, and con- 

 sequently at once useful and beautiful, and they 

 will be capable of affecting the geometrician's special 

 sensibility 1 have been speaking of; which, once 

 aroused, will direct our attention upon them, and will 

 thus give them the opportunity of becoming conscious. 



This is only a hypothesis, and yet there is an 

 observation which tends to confirm it. When a 

 sudden illumination invades the mathematician's mind, 

 it most frequently happens that it does not mislead 

 him. But it also happens sometimes, as I have said, 

 that it will not stand the test of verification. Well, 

 it is to be observed almost always that this false idea, 

 if it had been correct, would have flattered our natural 

 instinct for mathematical elegance. 



Thus it is this special aesthetic sensibility that plays 

 the part of the delicate sieve of which I spoke above, 

 and this makes it sufficiently clear why the man who 

 has it not will never be a real discoverer. 



All the difficulties, however, have not disappeared. 

 The conscious ego is strictly limited, but as regards 

 the subliminal ego, we do not know its limitations, 

 and that is why we are not too loth to suppose 

 that in a brief space of time it can form more 

 different combinations than could be comprised in 

 the whole life of a conscient being. These limitations 

 do exist, however. Is it conceivable that it can form 

 all the possible combinations, whose number staggers 

 the imagination ? Nevertheless this would seem to be 

 necessary, for if it produces only a small portion of the 

 combinations, and that by chance, there will be very 

 small likelihood of the right one, the one that must be 

 selected, being found among them. 



