Page:Popular Science Monthly Volume 75.djvu/494

From Wikisource
Jump to navigation Jump to search
This page has been validated.
490
THE POPULAR SCIENCE MONTHLY

THE DECIMAL SYSTEM OF NUMBERS
By Dr. L. C. KARPINSKI

UNIVERSITY OF MICHIGAN

IS there a limitation placed upon our thought by the language which we use? Do the Germans take to philosophy more easily than other people because of some peculiarly philosophical bias of their language? These are speculative questions which can never be satisfactorily answered. It may, however, safely be asserted that the literature of a language is immediately dependent upon the written alphabet. It is impossible to conceive of a novel having been written in Babylonian cuneiform characters or in Egyptian hieroglyphics. Romance was the same, in its larger outlines, then as now, but writing was too serious a matter to be undertaken for such fleeting fancies. With a difficult alphabet and lack of facilities for writing, general culture was impossible. The Chinese, in modern times, furnish a striking illustration of the deadening effect of a difficult alphabet.

As literature and general culture are related to the alphabet and written language, so scientific advancement is related to the number system in use and to the system of writing numbers. A slight study of the Roman numerals gives the clue to the reason why the advancement along scientific lines lagged so far behind the general advancement achieved by the Roman peoples. The Greeks had a peculiar genius for arithmetical research,-but with them long division was a difficult operation, on account of the symbols. Only an Archimedes could overcome the clumsiness of an unscientific method, and even he could solve but comparatively simple problems.

In order to comprehend the essence of our own number system, it is necessary to distinguish between a number system and a place system. A ten system involves having symbols for 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 groups of objects, respectively, and beyond that separate symbols for the successive powers of 10—100, 1,000, 10,000, 100,000.... A five system would involve separate symbols for 1, 2, 3 and 4 groups of objects and further symbols for 5 and for the successive powers of 5—25, 125, 625, 3,125, 15,625.... A logically complete 5 system has not been developed among any people of the earth. In fact no other complete system, than a decimal system has ever been developed. Among the Mayas of Central America a 20 system was partially developed. Among the Babylonians there was in use a sixty system interwoven with a decimal system.

A decimal place system involves symbols for 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. The ideas of 10, 100, 1,000 and successive powers of ten are