The Number Concept | Page 4

Crusoe fashion; in
another, kernels or little heaps of grain; in another, knots on a string;
and so on, in diversity of method almost endless. Such are the devices
which have been, and still are, to be found in the daily habit of great
numbers of Indian, negro, Mongolian, and Malay tribes; while, to pass
at a single step to the other extremity of intellectual development, the
German student keeps his beer score by chalk marks on the table or on

the wall. But back of all these devices, and forming a common origin to
which all may be referred, is the universal finger method; the method
with which all begin, and which all find too convenient ever to
relinquish entirely, even though their civilization be of the highest type.
Any such mode of counting, whether involving the use of the fingers or
not, is to be regarded simply as an extraneous aid in the expression or
comprehension of an idea which the mind cannot grasp, or cannot
retain, without assistance. The German student scores his reckoning
with chalk marks because he might otherwise forget; while the
Andaman Islander counts on his fingers because he has no other
method of counting,--or, in other words, of grasping the idea of number.
A single illustration may be given which typifies all practical methods
of numeration. More than a century ago travellers in Madagascar
observed a curious but simple mode of ascertaining the number of
soldiers in an army.[6] Each soldier was made to go through a passage
in the presence of the principal chiefs; and as he went through, a pebble
was dropped on the ground. This continued until a heap of 10 was
obtained, when one was set aside and a new heap begun. Upon the
completion of 10 heaps, a pebble was set aside to indicate 100; and so
on until the entire army had been numbered. Another illustration, taken
from the very antipodes of Madagascar, recently found its way into
print in an incidental manner,[7] and is so good that it deserves a place
beside de Flacourt's time-honoured example. Mom Cely, a Southern
negro of unknown age, finds herself in debt to the storekeeper; and,
unwilling to believe that the amount is as great as he represents, she
proceeds to investigate the matter in her own peculiar way. She had
"kept a tally of these purchases by means of a string, in which she tied
commemorative knots." When her creditor "undertook to make the
matter clear to Cely's comprehension, he had to proceed upon a system
of her own devising. A small notch was cut in a smooth white stick for
every dime she owed, and a large notch when the dimes amounted to a
dollar; for every five dollars a string was tied in the fifth big notch,
Cely keeping tally by the knots in her bit of twine; thus, when two
strings were tied about the stick, the ten dollars were seen to be an
indisputable fact." This interesting method of computing the amount of
her debt, whether an invention of her own or a survival of the African
life of her parents, served the old negro woman's purpose perfectly; and

it illustrates, as well as a score of examples could, the methods of
numeration to which the children of barbarism resort when any number
is to be expressed which exceeds the number of counters with which
nature has provided them. The fingers are, however, often employed in
counting numbers far above the first decade. After giving the Il-Oigob
numerals up to 60, Müller adds:[8] "Above 60 all numbers, indicated
by the proper figure pantomime, are expressed by means of the word
ipi." We know, moreover, that many of the American Indian tribes
count one ten after another on their fingers; so that, whatever number
they are endeavouring to indicate, we need feel no surprise if the
savage continues to use his fingers throughout the entire extent of his
counts. In rare instances we find tribes which, like the Mairassis of the
interior of New Guinea, appear to use nothing but finger pantomime.[9]
This tribe, though by no means destitute of the number sense, is said to
have no numerals whatever, but to use the single word awari with each
show of fingers, no matter how few or how many are displayed.
In the methods of finger counting employed by savages a considerable
degree of uniformity has been observed. Not only does he use his
fingers to assist him in his tally, but he almost always begins with the
little finger of his left hand, thence proceeding towards the thumb,
which is 5. From this point onward the method varies. Sometimes the
second 5 also is told off on the left hand, the same order being observed
as in