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 could, as it is developed in primitive languages, hardly extend to 20, or even to 10, without becoming exceedingly cumbersome.  A binary scale inevitably suggests a wretchedly low degree of mental development, which stands in the way of the formation of any number scale worthy to be dignified by the name of system.  Take, for example, one of the dialects found among the western tribes of the Torres Straits, where, in general, but two numerals are found to exist.  In this dialect the method of counting is:[169]

1. urapun. 2. okosa. 3. okosa urapun = 2-1. 4. okosa okosa = 2-2. 5. okosa okosa urapun = 2-2-1. 6. okosa okosa okosa = 2-2-2.

Anything above 6 they call ras, a lot.

For the sake of uniformity we may speak of this as a “system.”  But in so doing, we give to the legitimate meaning of the word a severe strain.  The customs and modes of life of these people are not such as to require the use of any save the scanty list of numbers given above; and their mental poverty prompts them to call 3, the first number above a single pair, 2-1.  In the same way, 4 and 6 are respectively 2 pairs and 3 pairs, while 5 is 1 more than 2 pairs.  Five objects, however, they sometimes denote by urapuni-getal, 1 hand.  A precisely similar condition is found to prevail respecting the arithmetic of all the Australian tribes.  In some cases only two numerals are found, and in others three.  But in a very great number of the native languages of that continent the count proceeds by pairs, if indeed it proceeds at all.  Hence we at once reject the theory that Australian arithmetic, or Australian counting, is essentially peculiar.  It is simply a legitimate result, such as might be looked for in any part of the world, of the barbarism in which the races of that quarter of the world were sunk, and in which they were content to live.

The following examples of Australian and Tasmanian number systems show how scanty was the numerical ability possessed by these tribes, and illustrate fully their tendency to count by twos or pairs.