, are as clearly
indicated as though the bargaining were being carried on in words.
The place occupied, in the intellectual development of man, by finger
counting and by the many other artificial methods of reckoning,--pebbles,
shells, knots, the abacus, etc.,--seems to be this: The abstract processes
of addition, subtraction, multiplication, division, and even counting
itself, present to the mind a certain degree of difficulty. To assist in
overcoming that difficulty, these artificial aids are called in; and, among
savages of a low degree of development, like the Australians, they make
counting possible. A little higher in the intellectual scale, among the
American Indians, for example, they are employed merely as an artificial
aid to what could be done by mental effort alone. Finally, among
semi-civilized and civilized peoples, the same processes are retained, and
form a part of the daily life of almost every person who has to do with
counting, reckoning, or keeping tally in any manner whatever. They are no
longer necessary, but they are so convenient and so useful that
civilization can never dispense with them. The use of the abacus, in the
form of the ordinary numeral frame, has increased greatly within the past
few years; and the time may come when the abacus in its proper form will
again find in civilized countries a use as common as that of five centuries
ago.
In the elaborate calculating machines of the present, such as are used by
life insurance actuaries and others having difficult computations to make,
we have the extreme of development in the direction of artificial aid to
reckoning.
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