588 PRIMITIVE NUMBER SYSTEMS. 



1,000. Ill general it may be said that in the childhood of any race the 

 unniber concept is weak and the number system is correspondingly 

 limited. As civilization develops tlie number sense and the number 

 system are extended accordingly. To this law some remarkable ex- 

 ceptions have been noted, but they are exceptions and do not in the 

 least invalidate the rule. 



Respecting the bases used in the number systems of the various lan- 

 guages of the world, no full and comparative account has ever appeared 

 in Kngiish. From the earliest times in which arithmetic began to assume 

 the dignity of a science and its history to receive serious attention, it has 

 been handed down as a tradition, the truth of which was never ques- 

 tioned until recently, that all races throughout the world used in their 

 computation the decimal system. Aristotle indeed nienticnied one ob- 

 scure Thracian tribe Avhich was said to reckon with a different base, but 

 he seems to have regarded this solitary instance as the exception which 

 proved the rule, for he taught that the universality of the decimal sys- 

 tem ijroved it to have had its origin in nature. This tradition was for 

 centuries accepted as true without question, and the naturalness of the 

 decimal system was argued from the fact that the number of counters, 

 the fingers, with which nature had equipped man, was ten. IJut the 

 last three or four centuries have brought to the knowledge of civiliza- 

 tion a multitude of tribes hitherto unknown, and among them a very 

 great number have been found to use systems having some base other 

 than 10. It was also pointed out by Peacock* and others that 10 was 

 not the only natura Inumber base — that, as 5 was the number of fingers 

 on one hand, and as liO was the numbei- of fingers and toes combined, 

 either 5 or 20 constituted a base in all respects as natural as 10. Hence 

 the use by any race of either of tliese numbers for that purpose could 

 constitute no ground for surprise. Peacock indeed mentions many ex- 

 amples of Indian, negro, and Mongolian tribes, among whom such bases 

 are actually used, and his list can now be enormously increased, so great 

 has been the energy and activity displayed in anthropological research 

 during the last half century. That 10 has been, and is, the practically 

 universal base of the world's number systems is indisputably true, but 

 to this general law the list of exceptions has been found to be so great 

 that a brief consideration of the subject seems desirable. 



Of all the numbers capable of use as a system base, 12 presents the 

 greatest number of practical advantages. We have, through the 

 familiarity which custom has produced, become so accustomed to the 

 use of 10 in that capacity that the assertion just made seems unwar- 

 rantable. But a moment's reflection will show that the ten fingers of 

 the human species have entailed upon ns a number base decidedly 

 inferior to 12. In the sim})le ])usiness affairs of life we deal most 

 extensively with the three simple, familiar fractions, ^V, i, and 4, and 

 the auxiliary fractions | and ^. Such being the case it needs no argu- 



* Encifclopwdia Metropolitana, article ^'Arithmetic." 



