228 INTRODUCTION TO SCIENCE 



At the same time we feel bound to admit that 

 the endeavour to formulate practical lore is not 

 likely to have more than partial success, for there 

 is an unanalysable element in its higher reaches. 

 This is well known in the case of some of the ex- 

 perienced physicians of the older school whose 

 insight in diagnosis has often excited the won- 

 der and envy of their more scientific successors. 

 Perhaps there was sometimes more hard work 

 behind it than was usually supposed, but it seems 

 certain that in many fields there are men with 

 a remarkable power of intuition, born not made, 

 of whose methods even self -analysis can give no 

 account. 



There is no doubt that all the sciences not 

 excepting psychology and sociology sprang from 

 concrete experience. Mathematics is abstract 

 enough, but what does its history show? "Man 

 began arithmetic with experience of the number 

 of his fingers and toes, and geometry with expe- 

 rience of the magnitude of his hands, feet, and 

 arms. He went on to use these concrete bod- 

 ies as standards to measure other bodies. Geom- 

 etry means the measurement of lands; and the 

 most ancient Egyptian book of mathematics, the 

 papyrus of Ahmes, about 1700 B.C., measures 

 barns, pyramids, and obelisks, and treats solid 

 bodies before proceeding to abstract surfaces. 

 Mathematics, in short, began with concrete bodies, 



