308 DOCTRINE OF EVOLUTION 



savage, when he organized the first formed tribes, learned 

 to count the days of a journey and the numbers engaged 

 on opposite sides in battle. He employed the ^' score" 

 of his fingers and toes, and our use of this very word is a 

 survival of such a primitive method of counting. The 

 abacus of the Roman and Chinese extended the scope 

 of simple mathematical operations as it employed more 

 symbolic elements. With the development of Arabic 

 notation capable of indefinite expansion, the science 

 progressed rapidly, and in the course of long time it has 

 become the higher calculus of to-day. The conceptions 

 of geometry have likewise evolved until to-day mathe- 

 maticians speak of configurated bodies in fourth and 

 higher dimensions of space, which are beyond the powers 

 of perception, even though in a sense they exist concep- 

 tually. The behavior of geometrical examples in one 

 dimension leads to the characteristics of bodies in two 

 dimensions. Upon these facts are constructed the laws 

 of three-dimensional space which serve to carry mathe- 

 matical thought to the remoter conceptual spaces of 

 which we have spoken. It may seem that we are record- 

 ing only one phase of mental evolution, but in fact we are 

 dealing with a larger matter, namely, with the progres- 

 sive evolution of knowledge in the Kantian category of 

 number. 



Natural science began with the savage's rough classi- 

 fication of the things with which he dealt in everyday 

 life. As facts accumulated, lifeless objects were grouped 

 apart from living organisms, and in time two great divi- 

 sions of natural science took form. Physics, chemistry, 

 astronomy, geology, and the like describe the concrete 

 world of matter and energy, while the biological sciences 



