The Number Concept | Page 3

been removed two or three
times from her, and her anxiety was excessive, as she tried to find out if
they were all present, or if any were still missing. She kept puzzling
and running her eyes over them backwards and forwards, but could not

satisfy herself. She evidently had a vague notion of counting, but the
figure was too large for her brain. Taking the two as they stood, dog
and Demara, the comparison reflected no great honour on the man....'
According to my bird-nesting recollections, which I have refreshed by
more recent experience, if a nest contains four eggs, one may safely be
taken; but if two are removed, the bird generally deserts. Here, then, it
would seem as if we had some reason for supposing that there is
sufficient intelligence to distinguish three from four. An interesting
consideration arises with reference to the number of the victims allotted
to each cell by the solitary wasps. One species of Ammophila considers
one large caterpillar of Noctua segetum enough; one species of
Eumenes supplies its young with five victims; another 10, 15, and even
up to 24. The number appears to be constant in each species. How does
the insect know when her task is fulfilled? Not by the cell being filled,
for if some be removed, she does not replace them. When she has
brought her complement she considers her task accomplished, whether
the victims are still there or not. How, then, does she know when she
has made up the number 24? Perhaps it will be said that each species
feels some mysterious and innate tendency to provide a certain number
of victims. This would, under no circumstances, be any explanation;
but it is not in accordance with the facts. In the genus Eumenes the
males are much smaller than the females.... If the egg is male, she
supplies five; if female, 10 victims. Does she count? Certainly this
seems very like a commencement of arithmetic."[4]
Many writers do not agree with the conclusions which Lubbock reaches;
maintaining that there is, in all such instances, a perception of greater
or less quantity rather than any idea of number. But a careful
consideration of the objections offered fails entirely to weaken the
argument. Example after example of a nature similar to those just
quoted might be given, indicating on the part of animals a perception of
the difference between 1 and 2, or between 2 and 3 and 4; and any
reasoning which tends to show that it is quantity rather than number
which the animal perceives, will apply with equal force to the Demara,
the Chiquito, and the Australian. Hence the actual origin of number
may safely be excluded from the limits of investigation, and, for the
present, be left in the field of pure speculation.

A most inviting field for research is, however, furnished by the
primitive methods of counting and of giving visible expression to the
idea of number. Our starting-point must, of course, be the sign
language, which always precedes intelligible speech; and which is so
convenient and so expressive a method of communication that the
human family, even in its most highly developed branches, never
wholly lays it aside. It may, indeed, be stated as a universal law, that
some practical method of numeration has, in the childhood of every
nation or tribe, preceded the formation of numeral words.
Practical methods of numeration are many in number and diverse in
kind. But the one primitive method of counting which seems to have
been almost universal throughout all time is the finger method. It is a
matter of common experience and observation that every child, when
he begins to count, turns instinctively to his fingers; and, with these
convenient aids as counters, tallies off the little number he has in mind.
This method is at once so natural and obvious that there can be no
doubt that it has always been employed by savage tribes, since the first
appearance of the human race in remote antiquity. All research among
uncivilized peoples has tended to confirm this view, were confirmation
needed of anything so patent. Occasionally some exception to this rule
is found; or some variation, such as is presented by the forest tribes of
Brazil, who, instead of counting on the fingers themselves, count on the
joints of their fingers.[5] As the entire number system of these tribes
appears to be limited to three, this variation is no cause for surprise.
The variety in practical methods of numeration observed among savage
races, and among civilized peoples as well, is so great that any detailed
account of them would be almost impossible. In one region we find
sticks or splints used; in another, pebbles or shells; in another, simple
scratches, or notches cut in a stick, Robinson