The Number Concept | Page 7

author is familiar.
Many tribes never use the toes in counting, but signify the close of the
first 10 by clapping the hands together, by a wave of the right hand, or
by designating some object; after which the fingers are again used as
before.
One other detail in finger counting is worthy of a moment's notice. It
seems to have been the opinion of earlier investigators that in his
passage from one finger to the next, the savage would invariably bend
down, or close, the last finger used; that is, that the count began with
the fingers open and outspread. This opinion is, however, erroneous.
Several of the Indian tribes of the West[17] begin with the hand
clenched, and open the fingers one by one as they proceed. This
method is much less common than the other, but that it exists is beyond
question.
In the Muralug Island, in the western part of Torres Strait, a somewhat
remarkable method of counting formerly existed, which grew out of,
and is to be regarded as an extension of, the digital method. Beginning
with the little finger of the left hand, the natives counted up to 5 in the
usual manner, and then, instead of passing to the other hand, or
repeating the count on the same fingers, they expressed the numbers
from 6 to 10 by touching and naming successively the left wrist, left
elbow, left shoulder, left breast, and sternum. Then the numbers from
11 to 19 were indicated by the use, in inverse order, of the
corresponding portions of the right side, arm, and hand, the little finger
of the right hand signifying 19. The words used were in each case the
actual names of the parts touched; the same word, for example,
standing for 6 and 14; but they were never used in the numerical sense
unless accompanied by the proper gesture, and bear no resemblance to

the common numerals, which are but few in number. This method of
counting is rapidly dying out among the natives of the island, and is at
the present time used only by old people.[18] Variations on this most
unusual custom have been found to exist in others of the neighbouring
islands, but none were exactly similar to it. One is also reminded by it
of a custom[19] which has for centuries prevailed among bargainers in
the East, of signifying numbers by touching the joints of each other's
fingers under a cloth. Every joint has a special signification; and the
entire system is undoubtedly a development from finger counting. The
buyer or seller will by this method express 6 or 60 by stretching out the
thumb and little finger and closing the rest of the fingers. The addition
of the fourth finger to the two thus used signifies 7 or 70; and so on. "It
is said that between two brokers settling a price by thus snipping with
the fingers, cleverness in bargaining, offering a little more, hesitating,
expressing an obstinate refusal to go further, etc., 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. But instead of appearing merely as an extraneous aid
to a defective intelligence, it now presents itself as a machine so
complex that a high degree of intellectual power is required for the