xv DARWINISM APPLIED TO MAN 465 



When we turn to the more civilised races, we find the 

 use of numbers and the art of counting greatly extended. 

 Even the Tongas of the South Sea islands are said to have 

 been able to count as high as 100,000. But mere count- 

 ing does not imply either the possession or the use of any- 

 thing that can be really called the mathematical faculty, the 

 exercise of which in any broad sense has only been possible 

 since the introduction of the decimal notation. The Greeks, 

 the Romans, the Egyptians, the Jews, and the Chinese had 

 all such cumbrous systems, that anything like a science of 

 arithmetic, beyond very simple operations, was impossible ; 

 and the Roman system, by which the year 1888 would be written 

 MDCCCLXXXVIII, was that in common use in Europe down 

 to the fourteenth or fifteenth centuries, and even much later in 

 some places. Algebra, which was invented by the Hindoos, from 

 whom also came the decimal notation, was not introduced into 

 Europe till the thirteenth century, although the Greeks had some 

 acquaintance with it; and it reached Western Europe from Italy 

 only in the sixteenth century. 1 It was, no doubt, owing to the 

 absence of a sound system of numeration that the mathematical 

 talent of the Greeks was directed chiefly to geometry, in which 

 science Euclid, Archimedes, and others made such brilliant dis- 

 coveries. It is, however, during the last three centuries only that 

 the civilised world appears to have become conscious of the 

 possession of a marvellous faculty which, when supplied with 

 the necessary tools in the decimal notation, the elements of 

 algebra and geometry, and the power of rapidly communicating 

 discoveries and ideas by the art of printing, has developed to 

 an extent, the full grandeur of which can be appreciated only 

 by those who have devoted some time (even if unsuccessfully) 

 to the study. 



The facts now set forth as to the almost total absence of 

 mathematical faculty in savages and its wonderful development 

 in quite recent times, are exceedingly suggestive, and in regard 



required. But this does not alter the general fact that many low races, 

 including the Australians, have no words for high numbers and never require 

 to use them. If they are now, with a little practice, able to count much 

 higher, this indicates the possession of a faculty which could not have been 

 developed under the law of utility only, since the absence of words for such 

 high numbers shows that they were neither used nor required. 

 1 Article Arithmetic in Eng. Cyc. of Arts and Sciences. 



2 H 



