THE UTILITY OF SCIENCE 229 



such as could only be reached by means of expe- 

 rience, and only gradually receded from the con- 

 crete to the abstract, to the units of abstract 

 arithmetic, and the points of abstract geometry. 

 The Greeks achieved this analysis from concrete 

 to abstract, and thus converted mathematics from 

 analysis to synthesis, which begins with the ab- 

 stract unit as origin of number, and with the 

 abstract point as simpler than the line. But 

 the order of discovery was from the concrete and 

 analytical, although afterwards the order of de- 

 velopment was from the abstract and synthetic " 

 (Prof. T. Case, 1906, p. 6). 



It is good history that the sciences sprang out 

 of the lore of occupations, and it is also a fact of 

 no small ethical importance. " We cannot get 

 away from our ancestors. Just as a physical 

 scientist is a smith, so is the botanist a farmer 

 and shepherd, the zoologist a huntsman, the geog- 

 rapher a sailor, the historian a scald, the doctor 

 a wizard or medicine-man, and the lawyer a 

 scribe. As for the mathematician, his material 

 the oldest science of all has been drawn from 

 such a variety of occupations that, if he vividly 

 grasps the spirit of the history of his science 

 (though, unfortunately, this is rarely the case), 

 he should find himself in a very real sense the 

 heir to all the ages, and become imbued with 

 sympathy for all occupations." (Branford, 1904.) 



