CREATIVE SCIENCE 351 



tal field, which may also undergo some explicit local reworking. Par- 

 ticular features become progressively more prominent, others are 

 progressively obscured, until at last a new conceptual pattern wins 

 through to clear expression. The entire development is characterized 

 by its gradualness. At the other extreme we have the innovator who, 

 after apparently profitless preliminary study, experiences a sudden 

 flash of insight that lights up an entirely new conceptual structure. 

 Such a development— occurring most frequently, but not exclusively, 

 when the problem is a limited one— is characterized by its abruptness 

 and apparent spontaneity. 



Either of the indicated extremes may be held to represent what 

 "really" happens always. Taking the first extreme as the general case, 

 one supposes that in apparently discontinuous developments we are 

 aware only of one (or more) high point(s) in what is, however, a 

 completely gradual process. Taking the second extreme as the gen- 

 eral case, one supposes that the apparently continuous developments 

 are made up of very large numbers of essentially discontinuous small 

 spurts of insight. The evidence for choice between these and other 

 possibilities seems insufficient, and I find no pressing need to choose. 



Events falling at or near the second extreme are particularly strik- 

 ing. A classic example of such a "Eureka episode" is given by Poin- 

 care, who had for some time engaged himself in intensive studies of 

 the Fuchsian functions. 



Just at this time I left Caen, where I was then living, to go on a 

 geologic excursion under the auspices of the school of mines. The in- 

 cidents of travel made me forget my mathematical work. Having 

 reached Coutances, we entered an omnibus to go some place or other. 

 At the moment when I put my foot on the step the idea came to me, 

 without anything in my former thoughts seeming to have paved the 

 way for it, that the transformations I had used to define the Fuchs- 

 ian functions were identical with those of non-Euclidean geometry. 

 I did not verify the idea; I should not have had time, as, upon taking 

 my seat in the omnibus, I went on with a conversation already com- 

 menced, but I felt a perfect certainty. On my return to Caen, for 

 conscience' sake, I verified the result at my leisure. 



This and other such episodes seem characterized by the sudden 

 emergence of an idea, by which a problem is completely restructured, 

 from a mental state apparently free from conscious concern with the 

 problem solved. 



