SPACE AND GEOMETRY 33 



some guesses regarding those to follow. Sup- 

 pose now that the paralytic is wheeled daily 

 over the same path through a garden with vari- 

 ous beds of fragrant flowers. Might he not 

 recognize an orderly succession of odors, con- 

 stant day after day? If later he were wheeled, 

 not b}^ one path, but by many paths, through 

 the same garden, might he not acquire, perhaps 

 with great difficulty, some idea of two-dimen- 

 sional order? For example, if the whole garden 

 were surrounded by a circle of rosebushes, 

 might he not recognize that he never proceeded 

 from the unpleasant odors outside of the garden 

 to its pleasant aromas except by passing 

 through the fragrance of roses? Some entomol- 

 ogists believe that certain ants with a highly 

 developed spatial sense depend almost entirely 

 upon sensations of smell. 



Such a possibility throws doubt on Poincare's 

 dictum,^ "If there were no solid bodies in nature 



1 Poincare, Science and Hypothesis. It is a remarkable 

 evidence of the breathless speed with which we have recently 

 been scaling some of the heights of scientific understanding 

 that statements made less than a generation ago by a 

 mathematician of such extraordinary acumen as Poincare 

 should now so frequently seem untenable. He states, for 

 example, that geometrical space must be continuous and 

 must be infinite, but both of these statements have since 

 been challenged. Again he says that if through some new 

 experiment a choice were forced between holding to Euclid- 



