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Updated: May 24, 2025
If we used eights or twelves instead of tens for numeration, we might of course preserve all the advantages of the Indian or Arabic numerals; in the first case, we should discard the ciphers 8 and 9, and reckon 5, 6, 7, 10; and in the second case, we should want two new ciphers for ten and eleven; and 10 would stand for twelve, and 11 for thirteen.
The difference, then, between the numerals of the Australian languages and it is undoubtedly great is no proof of any fundamental difference of structure or origin. It is just what occurs in the languages of Africa, and, in a still greater degree, in those of America. The extent to which the numeration is carried, is a matter of more importance.
In the first place, though Numeration is able to take account of organized substances, it is powerless in relation to unorganized forces, the ones being finite and the others infinite. The man who can conceive the Infinite by his intelligence cannot deal with it in its entirety; if he could, he would be God.
The number seven, therefore, must be foisted in wherever possible, and among other things, is to be made the basis of numeration, which is hereafter to be septimal instead of decimal: producing all the inconvenience of a change of system, not only without getting rid of, but greatly aggravating, the disadvantages of the existing one.
By this he told up to six; if he had any occasion to tell any farther, he began again, as we do after the number ten in our ordinary numeration; and by this method, and running them up very quick, he would count any number under thirty-six, which was six spoons of six spoons, and then, by the strength of his head, he could number as many more as he pleased, multiplying them always by sixes, but never higher.
My number being 2799, through some occult system of nautical numeration, I was detailed to the `Third, or second starboard, division of the ship's company; so I joined mess Number 38, which was on the port side on the lower deck, the first one aft of the schoolroom.
He lived in the Marais, Rue des Filles-du-Calvaire, No. 6. He owned the house. This house has since been demolished and rebuilt, and the number has probably been changed in those revolutions of numeration which the streets of Paris undergo.
After a lapse of possibly five minutes, I suddenly discovered that I could count but five holes; and while recounting to make sure, moving my eyes as slowly as possible, my numeration was cut short at four. In another moment two more had disappeared, and the remaining two immediately followed in obscurity, until no vestige of a hole of any kind was to be seen.
Possibly a numeration limited to the first three, four, or five numbers is the effect of intellectual inferiority. It is certainly a cause that continues it. As a measure of ethnological affinity it is unimportant. In America we have, within a limited range of languages, vigesimal systems like the Mexican, and systems limited to the three first units like the Caribb.
The difference between a vigesimal and decimal system arises simply from the practice of counting by the fingers and toes collectively, or the fingers alone, being prevalent; whereas the decimal system as opposed to the quinary is referrible to the numeration being extended to both hands, instead of limited to one.
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