49° 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 lan- 

 guage? These are speculative questions which can never be satisfac- 

 torily 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 Baby- 

 lonian cuneiform characters or in Egyptian hieroglyphics. Eomance 

 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 illustra- 

 tion 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 Eoman numerals gives the clue to the reason why the advance- 

 ment along scientific lines lagged so far behind the general advance- 

 ment achieved by the Eoman 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 ob- 

 jects 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 



