be needed, that the basis of the system of counting was not determined by theoretical considerations, but by the simple elementary fact of the number of human digits being ten and not twelve.[1]
Nevertheless twelve has its turn as a favorite number; we often count by dozens, and the reason probably is that twelve admits of being quartered as well as halved, which in many cases is an advantage. Take the case of wine: a dozen bottles is a convenient quantity to take as a standard, because a customer can order half the standard number, or, if he needs a small quantity, the quarter of the same; in fact, twelve admits of being divided not only by two and four, but also by three and six, which for many purposes give it a great advantage over ten, which can be divided only by two and five, the latter division being rarely of any use. Hence the great divisibility of twelve is sufficient to mark it as a favorite number, but in the most notable instance of its use—namely, as marking the number of months in a year—we need some further explanation. The real month—that is, the number of days between two successive full moons—may be taken as measured by twenty-eight days. Thirteen times twenty-eight makes three hundred and sixty four, or as nearly as may be one year. Consequently, it would have been much more nearly true to say that thirteen months make a year than twelve. The explanation is to be found, I conceive, in the extremely awkward character of the number thirteen; it is what is called by mathematicians a prime number; that is to say, it admits of no division of any kind; had there been thirteen months in the year, the half-year and the quarter alike could not have been reckoned by months, and consequently twelve, which, as already explained, is one of the most convenient of numbers in the matter of divisibility, was encouraged and permitted to usurp the place, which, in all strictness, belonged to its next-door neighbor.
There is a somewhat parallel case with regard to the division of the circle into 360 degrees. The ancient Chinese mathematicians divided the circle into 36514 degrees, corresponding to the length of the year, or 3651⁄4 days, which number, though not exact, is very near the truth.[2] But this division of the circle is practically intolerable; it would throw mathematicians into despair; consequently the number 360, which admits of being divided by 4, by 60, by 90, and by many other numbers, ursurped the place which the Chinese righteously assigned to the awkward number which Nature suggested.
I now pass on to the consideration of the number seven. It has
- ↑ The device of place, according to which the successive figures in writing numbers represent units, tens, hundreds, thousands, etc., as we proceed from right to left, is of Indian origin. The Romans, with all their practical cleverness, did not discover this simple and ingenious device; but they equally testify to the use of ten—or rather of five and ten—as the basis of calculation by their notation of numbers I, V, X, L, C.
- ↑ Biot, "Astronomic Physique," vol.i, p.69.
