MATHEMATICAL DISCOVERY. 6i 



Perhaps we must look for the explanation in that 

 period of preliminary conscious work which always 

 precedes all fruitful unconscious work. If I may 

 be permitted a crude comparison, let us represent the 

 future elements of our combinations as something 

 resembling Epicurus's hooked atoms. When the mind 

 is in complete repose these atoms are immovable ; 

 they are, so to speak, attached to the wall. This com- 

 plete repose may continue indefinitely without the 

 atoms meeting, and, consequently, without the pos- 

 sibility of the formation of any combination. 



On the other hand, during a period of apparent 

 repose, but of unconscious work, some of them are 

 detached from the wall and set in motion. They 

 plough through space in all directions, like a swarm 

 of gnats, for instance, or, if we prefer a more learned 

 comparison, like the gaseous molecules in the kinetic 

 theory of gases. Their mutual collisions may then 

 produce new combinations. 



What is the part to be played by the preliminary 

 conscious work ? Clearly it is to liberate some of 

 these atoms, to detach them from the wall and set 

 them in motion. We think we have accomplished 

 nothing, when we have stirred up the elements in a 

 thousand different ways to try to arrange them, and 

 have not succeeded in finding a satisfactory arrange- 

 ment. But after this agitation imparted to them by 

 our will, they do not return to their original repose, 

 but continue to circulate freely. 



Now our will did not select them at random, but 

 in pursuit of a perfectly definite aim. Those it has 

 liberated are not, therefore, chance atoms ; they are 

 those from which we may reasonably expect the 



