of the greatest interest to find that other numbers have, in exceptional
cases, been used for this purpose. Two centuries ago the distinguished
philosopher and mathematician, Leibnitz, proposed a binary system of
numeration. The only symbols needed in such a system would be 0 and 1. The
number which is now symbolized by the figure 2 would be represented by 10;
while 3, 4, 5, 6, 7, 8, etc., would appear in the binary notation as 11,
100, 101, 110, 111, 1000, etc. The difficulty with such a system is that it
rapidly grows cumbersome, requiring the use of so many figures for
indicating any number. But Leibnitz found in the representation of all
numbers by means of the two digits 0 and 1 a fitting symbolization of the
creation out of chaos, or nothing, of the entire universe by the power of
the Deity. In commemoration of this invention a medal was struck bearing on
the obverse the words

Numero Deus impari gaudet,

and on the reverse,

Omnibus ex nihilo ducendis sufficit Unum.[166]

This curious system seems to have been regarded with the greatest affection
by its inventor, who used every endeavour in his power to bring it to the
notice of scholars and to urge its claims. But it appears to have been
received with entire indifference, and to have been regarded merely as a
mathematical curiosity.

Unknown to Leibnitz, however, a binary method of counting actually existed
during that age; and it is only at the present time that it is becoming
extinct. In Australia, the continent that is unique in its flora, its
fauna, and its general topography, we find also this anomaly among methods