THE HINDU-ARABIC NUMERALS 60 1 



THE HIXDU-ABABIC NUMERALS* 



By EDWARD RAYMOND TURNER 



PROFESSOR OF EUROPEAN HISTORY, UNIVERSITY OF MICHIGAN 



AT present the Hindu-Arabic numerals hold nearly unlimited sway 

 in the realm of number. In China, in Japan, in southeast 

 Asia, and in parts of India, it is true, they are employed only by the 

 upper classes and by foreign traders ; but all over Europe, in Australia, 

 and in North America, they are supreme; while in South America and 

 in Africa they are used wherever civilized men make arithmetical 

 computation. 



Scarcely ever has a more wonderful device been perfected. By 

 means of these characters prodigious calculations can be made. 

 Through tables, logarithms, and counting-machines amazing swiftness 

 and accuracy are obtained. Their power and their scope seem almost 

 limitless. 



And yet there was a time when they were confined to a few districts 

 in India, and not heard of by the rest of mankind; when they were 

 cumbersome and inert and difficult to use; when they were no better 

 than number signs which had been developed elsewhere, and not nearly 

 so well known. Even when their superiority was manifest, their prog- 

 ress into other lands was uncertain, difficult, and slow. The story of 

 the development of the Hindu numerals and of their conquest of the 

 world make an interesting but oft-forgotten chapter in the history of 

 civilization. 



The idea of number originates in sense experience. The conception 

 of two and three as different from one rests fundamentally upon experi- 

 ence in dealing with one thing and with more than one thing. The ideas 

 of an object and of several objects which the mind forms through the 

 eye or through the sense of touch constitute the basis upon which all 

 knowledge of number rests. Thus gradually in infancy or during the 

 childhood of the race are obtained the conceptions of what we now call 

 in English " one," " two," and " three." 



In the lower stages of culture only dim ideas of higher number 

 exist, and the lowest, basic numbers are used in combination to express 



* In preparing this paper I have had the assistance of Dr. Louis Charles 

 Karpinski, who has put at my disposal the results of research in a field which 

 he is making peculiarly his own. By permission of Messrs. Ginn several illustra- 

 tions are reproduced from Smith and Karpinski, "The Hindu-Arabic Numerals/ ' 

 Ginn and Company, 1911, the best work upon the subject, and a work of which 

 1 have made free use. 



VOL. LXXXI. —41 



