34 THE ANATOMY OF SCIENCE 



there would be no geometry." Psychologists 

 have given much attention to the development 

 of spatial ideas from our various sense impres- 

 sions, and I suppose that it will nowadays be 

 admitted that all our ideas are derived even- 

 tually from the sense impressions that we and 

 our ancestors have received. Still the process of 

 abstraction has swept us so far from the count- 

 less individual experiences which contribute to 

 our idea of space that it seems hardly more use- 

 ful to speak of visual and tactual space than it 

 would be to speak of visual and tactual number. 

 But let us hasten away from this treacherous 

 ground and introduce our discussion of geomet- 

 rical measurement by a simple allegory. 



Once upon a time the South Pacific Ocean 

 was so overcast by clouds for a number of gen- 

 erations that the islanders had only a vague 

 tradition of sun and stars. Nevertheless, their 

 civilization grew. Their cocoanut plantations 

 became so valuable that they made accurate 

 land measurements with lines of cocoanut fiber, 

 and these methods of measurement were codi- 

 fied by a great geometer, named Uli, so that 



ean geometry and to the theory that light travels in a 

 straight line, it would certainly be the latter belief that 

 would be abandoned. We shall see in the fourth chapter 

 how signally this prophecy has failed. 



