no highly civilized race has ever used an exclusively
quinary system; and all that can be said of the influence of this mode of
counting is that it gives rise to the habit of collecting objects in groups
of five, rather than of ten, when any attempt is being made to ascertain
their sum. In the case of the subsidiary base 12, for which the Teutonic
races have always shown such a fondness, the dozen and gross of commerce,
the divisions of English money, and of our common weights and measures are
probably an outgrowth of this preference; and the Babylonian base, 60, has
fastened upon the world forever a sexagesimal method of dividing time, and
of measuring the circumference of the circle.

The advanced civilization attained by the races of Mexico and Central
America render it possible to see some of the effects of vigesimal
counting, just as a single thought will show how our entire lives are
influenced by our habit of counting by tens. Among the Aztecs the universal
unit was 20. A load of cloaks, of dresses, or other articles of convenient
size, was 20. Time was divided into periods of 20 days each. The armies
were numbered by divisions of 8000;[373] and in countless other ways the
vigesimal element of numbers entered into their lives, just as the decimal
enters into ours; and it is to be supposed that they found it as useful and
as convenient for all measuring purposes as we find our own system; as the
tradesman of to-day finds the duodecimal system of commerce; or as the
Babylonians of old found that singularly curious system, the sexagesimal.
Habituation, the laws which the habits and customs of every-day life impose
upon us, are so powerful, that our instinctive readiness to make use of any
concept depends, not on the intrinsic perfection or imperfection which
pertains to it, but on the familiarity with which previous use has invested
it. Hence, while one race may use a decimal, another a quinary-vigesimal,
and another a sexagesimal scale, and while one system may actually be
inherently superior to another, no user of one method of reckoning need
ever think of any other method as possessing practical inconveniences, of
which those employing it are ever conscious. And, to cite a single instance
which illustrates the unconscious daily use of two modes of reckoning in
one scale, we have only to think of the singular vigesimal fragment which
remains to this day imbedded in the numeral scale of the French. In
counting from 7