of counting. The natives, who are to be classed among the lowest and the
least intelligent of the aboriginal races of the world, have number systems
of the most rudimentary nature, and evince a decided tendency to count by
twos. This peculiarity, which was to some extent shared by the Tasmanians,
the island tribes of the Torres Straits, and other aboriginal races of that
region, has by some writers been regarded as peculiar to their part of the
world; as though a binary number system were not to be found elsewhere.
This attempt to make out of the rude and unusual method of counting which
obtained among the Australians a racial characteristic is hardly justified
by fuller investigation. Binary number systems, which are given in full on
another page, are found in South America. Some of the Dravidian scales are
binary;[167] and the marked preference, not infrequently observed among
savage races, for counting by pairs, is in itself a sufficient refutation
of this theory. Still it is an unquestionable fact that this binary
tendency is more pronounced among the Australians than among any other
extensive number of kindred races. They seldom count in words above 4, and
almost never as high as 7. One of the most careful observers among them
expresses his doubt as to a native's ability to discover the loss of two
pins, if he were first shown seven pins in a row, and then two were removed
without his knowledge.[168] But he believes that if a single pin were
removed from the seven, the Blackfellow would become conscious of its loss.
This is due to his habit of counting by pairs, which enables him to
discover whether any number within reasonable limit is odd or even. Some of
the negro tribes of Africa, and of the Indian tribes of America, have the
same habit. Progression by pairs may seem to some tribes as natural as
progression by single units. It certainly is not at all rare; and in
Australia its influence on spoken number systems is most apparent.

Any number system which passes the limit 10 is reasonably sure to have
either a quinary, a decimal, or a vigesimal structure. A binary scale