14 THE ANATOMY OF SCIENCE 



terludes, amuse themselves by playing at war. 

 Armies, with their horses and elephants, are 

 brought together for the great manoeuvres, 

 which, however, prove to be costly things, so 

 that wooden replicas of men and horses and 

 elephants come to be used on a smaller ground. 

 Then the nature of the ground and the move- 

 ment of the pieces become conventionalized, and 

 convention succeeds convention until finally we 

 have that remarkably compact and perfect 

 abstraction called chess. 



Here is a concrete illustration of the ab- 

 stracting process which may serve as an intro- 

 duction to our study of the growth of scientific 

 concepts. As we now proceed to discuss these 

 concepts one by one, this examination of con- 

 crete cases will give us a better idea of the 

 power and also of the limitations of the scien- 

 tific method. We shall begin with the oldest of 

 the mathematical sciences, — arithmetic, the sci- 

 ence of numbers. 



Let me start with a simple parable. A little 

 lame boy, sitting on his doorstep, watches the 

 schoolhouse across the way, and a class of boys 

 at play and at work. He has heard them recite 

 the childish formula, "Eeny, meeny, miny, mo, 

 catch a nigger by the toe," and has adopted 



