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