Taylor.] dl4: [Oct. 21, 



tutions — at least as universal as language itself. From this universality, 

 most writers have called it the "natural " system; but on examining 

 the question whether the number ten possesses any intrinsic excellence 

 or convenience to recommend it — any peculiar fitness as a ratio of geo- 

 metrical progression, we find but one answer — it has none. It differs 

 from any other number only in quantity, not in quality. So f\ir from its 

 presenting any merit or advantage over its compeers, it is almost the last 

 number which a true science of arithmetic would have selected for the 

 important function of a radix of numeration. Its universality flows sim- 

 ply from the fact that the necessities of man impelled a selection, 

 in the very earliest infancy of the race, long before the invention of 

 letters, and while yet a language was but slowly being formed ; and the 

 selection comes to us stamped with the crude impress of a most irrelevant 

 accident. Had the six-fingered giant slain by Jonathan (2 Samuel xxi, 

 20) lived early enough to be the father of the first unreasoning tribes, we 

 should have had a duodecimal arithmetic ; or if, like the fowls of the air, 

 we had usually but four toes to our extremities, we should now have 

 been able to calculate only octavally ; and in either event we should have 

 been much more skillful computers than we are at present. * 



Decimal numeration is "natural " then, only in the sense that ignorance 

 is natural. The fingers have no more real or "natural" relation to the 

 properties of number, than have any other organs or divisions of the 

 human body ; and mathematically or philosophically considered, the digit 

 is, therefore, no more a typical unit than a tooth (of which therp are 

 thirty-two), or the leg of a spider (of which there are eight), or the 

 petal of a flower (of which there may be any number). Nor have any 

 but the most ignorant races — those without a literature and an alphabet — 

 ever occasion to group and tally by their fingers. Only from unlettered 

 savages could such a scale, therefore, have deen derived. 



It has been a favorite theory with a certain class of thinkers that 

 primitive man was a highly civilized being — "a scholar and a gentle- 

 man ;" and that the decay of states, and the decline of civilizations so 

 unfortunately frequent in his history, but manifest his prevailing ten- 

 dency to degeneration. Our universal arithmetic furnishes us with one 

 of the most striking refutations of such a fancy. Wherever over the 

 broad earth, the decimal scale exists, there have we the enduring monu- 

 ment of the ancestral savage — counting by his fingers or his naked toes.f 



* " There can be no doubt that if man had been a twelve-fingered animal, we should 

 now possess a more perfect system of numeration tlian we do. Whatever he the radix 

 of the scale, it would always be a convenience to be able to subdivide it with facility, 

 without resorting to the more refined expedient of fractional language'-' {Lardner's Arith- 

 metic, chap, i, p. 21). 



t The German word for ten— se7«e;i— signifies "toes," being the plural of the word, x?ic. 

 We do not generally or readily recognize this intellectual association in our own language; 

 and yet the Saxon word— <o— a " toe," is in the plural tan. The daktal (^daKTU?.o<;^ 

 of the Greeks, and the digit (digitus) of the Romans, which signified either " finger" or 

 "toe," appear evidently affiliated to the deka (osKa^ of the one and the decern of the 



