38 THE ANATOMY OF SCIENCE 



I must not leave my story without telling how 

 one of the canoeists was summoned before the 

 headman for beating his wife too noisily. He 

 stated in extenuation that he had sat up for 

 two hours explaining to her the principle of 

 direct paddling between Moa and Ilo, and at 

 the end she had said, "How very interesting, 

 but why is it not quicker to go straight across ?" 



I shall not dwell upon the moral of this alle- 

 gory, but I shall ask you to think of it now and 

 then, as it seems to me to contain a good deal of 

 the philosophy of science that I am attempting 

 to present to you. In particular, I have tried 

 to bring out the idea that the geometry of navi- 

 gation is a two-dimensional, non-Euclidean 

 geometry, and would very likely have been re- 

 garded as the geometry of the plane if it had 

 been familiar before the earth was known to be 

 spherical. 



The geometry of Euclid has come down to 

 us as one of the great monuments of Greek 

 thought. For over two thousand years it has 

 been employed almost without change as a text- 

 book of elementary instruction. For centuries 

 it was deemed a heresy to dispute its validity. 

 Yet during that period it has shown its vitality 

 by growth and change; otherwise it would 



