| THE HINDU-ARABIC NUMERALS[1] |
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 progress 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 experience 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 illustrations 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 I have made free use.
