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Updated: May 24, 2025
That progress of Science, which is to destroy Wonder, and in its stead substitute Mensuration and Numeration, finds small favor with Teufelsdrockh, much as he otherwise venerates these two latter processes.
As a basis for the notion of a whole made up of equal parts, nothing so readily suggests itself as the hand with its five, or the hands with their ten, fingers; upon this rests the decimal system. We have already observed that these elements of all numeration and measuring reach back not merely beyond the separation of the Greek and Latin stocks, but even to the most remote primeval times.
Although the meaning of the majority of these ideographs has not yet been identified, Père Scheil, who has edited the texts, has succeeded in making out the system of numeration. He has identified the signs for unity, 10, 100, and 1,000, and for certain fractions, and the signs for these figures are quite different from those employed by the Sumerians.
These "musters," it should be said, appear always to have been made with great care, and there is therefore hardly a possibility that a son, if there were one, was omitted in the numeration of the widow's family, while the name and age of the little girl, and the names and ages of the two servants, the date of their arrival in Virginia, and the name of the ship that each came in, are all carefully given.
This arises from their general method of numeration five is represented by one hand; two hands, ten; then they use the toes, and call twenty by the name of "loko," or man. They then proceed by men or scores. Thus forty-five is laboriously expressed by a word signifying two men and one hand upon it. Some of the Indian words are of great length.
Although in some there is a wide distinction, there are others in which all the Indian dialects seem to agree. In their method of numeration, especially, the first four numbers are represented by simple words. Although the Indian children learn to read and write with facility, they acquire with difficulty the simplest rudiments of arithmetic.
Just as Number the only thing in which your self-styled atheists believe organized physical creations, so arithmetic, in the employ of Number, organized the moral world. This numeration must be absolute, like all else that is true in itself; but it is purely relative, it does not exist absolutely, and no proof can be given of its reality.
But the faculty of using such means of study is not to be had for the asking; it is not to be earned by the most assiduous toil, it is not to be secured by the learning of years, it is not to be attained by the devotion of a life. No proficiency in grammar and arithmetic, no science of numeration and no scheme of prosody, will be here of the least avail.
In counting over a quantity of small articles each tenth, and afterwards each hundredth piece is put aside; which method is consonant with the progress of scientific numeration, and probably gave it origin.
Be this so or not, however, it is manifest that before the Chaldeans discovered their Saros, there must have been both a set of written symbols serving for an extensive numeration, and a familiarity with the simpler rules of arithmetic. Not only must abstract mathematics have made some progress, but concrete mathematics also.
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