The Number Concept | Page 8

mere grasp of its construction and method of working.
CHAPTER II.
NUMBER SYSTEM LIMITS.
With respect to the limits to which the number systems of the various
uncivilized races of the earth extend, recent anthropological research
has developed many interesting facts. In the case of the Chiquitos and a
few other native races of Bolivia we found no distinct number sense at
all, as far as could be judged from the absence, in their language, of
numerals in the proper sense of the word. How they indicated any
number greater than one is a point still requiring investigation. In all
other known instances we find actual number systems, or what may for
the sake of uniformity be dignified by that name. In many cases,
however, the numerals existing are so few, and the ability to count is so
limited, that the term number system is really an entire misnomer.
Among the rudest tribes, those whose mode of living approaches most
nearly to utter savagery, we find a certain uniformity of method. The
entire number system may consist of but two words, one and _many_;
or of three words, one, two, many. Or, the count may proceed to 3, 4, 5,
10, 20, or 100; passing always, or almost always, from the distinct
numeral limit to the indefinite many or several, which serves for the
expression of any number not readily grasped by the mind. As a matter
of fact, most races count as high as 10; but to this statement the
exceptions are so numerous that they deserve examination in some
detail. In certain parts of the world, notably among the native races of
South America, Australia, and many of the islands of Polynesia and
Melanesia, a surprising paucity of numeral words has been observed.
The Encabellada of the Rio Napo have but two distinct numerals; tey, 1,

and cayapa, 2.[20] The Chaco languages[21] of the Guaycuru stock are
also notably poor in this respect. In the Mbocobi dialect of this
language the only native numerals are _yña tvak_, 1, and yfioaca, 2.
The Puris[22] count omi, 1, curiri, 2, prica, many; and the
Botocudos[23] mokenam, 1, uruhu, many. The Fuegans,[24] supposed
to have been able at one time to count to 10, have but three
numerals,--kaoueli, 1, compaipi, 2, maten, 3. The Campas of Peru[25]
possess only three separate words for the expression of number,--patrio,
1, pitteni, 2, mahuani, 3. Above 3 they proceed by combinations, as 1
and 3 for 4, 1 and 1 and 3 for 5. Counting above 10 is, however,
entirely inconceivable to them, and any number beyond that limit they
indicate by tohaine, many. The Conibos,[26] of the same region, had,
before their contact with the Spanish, only atchoupre, 1, and rrabui, 2;
though they made some slight progress above 2 by means of
reduplication. The Orejones, one of the low, degraded tribes of the
Upper Amazon,[27] have no names for number except nayhay, 1,
nenacome, 2, feninichacome, 3, ononoeomere, 4. In the extensive
vocabularies given by Von Martins,[28] many similar examples are
found. For the Bororos he gives only couai, 1, maeouai, 2, ouai, 3. The
last word, with the proper finger pantomime, serves also for any higher
number which falls within the grasp of their comprehension. The
Guachi manage to reach 5, but their numeration is of the rudest kind, as
the following scale shows: tamak, 1, _eu-echo,_ 2, _eu-echo-kailau,_ 3,
_eu-echo-way,_ 4, localau, 5. The Carajas counted by a scale equally
rude, and their conception of number seemed equally vague, until
contact with the neighbouring tribes furnished them with the means of
going beyond their original limit. Their scale shows clearly the
uncertain, feeble number sense which is so marked in the interior of
South America. It contains wadewo, 1, wadebothoa, 2, wadeboaheodo,
3, wadebojeodo, 4, wadewajouclay, 5, wadewasori, 6, or many.
Turning to the languages of the extinct, or fast vanishing, tribes of
Australia, we find a still more noteworthy absence of numeral
expressions. In the Gudang dialect[29] but two numerals are
found--pirman, 1, and ilabiu, 2; in the Weedookarry, ekkamurda, 1, and
kootera, 2; and in the Queanbeyan, midjemban
, 1, and bollan, 2. In a
score or more of instances the numerals stop at 3. The natives of

Keppel Bay count webben, 1, booli, 2, koorel, 3; of the Boyne River,
karroon, 1, boodla, 2, numma, 3; of the Flinders River, kooroin, 1,
kurto, 2, kurto kooroin, 3; at the mouth of the Norman River, lum, 1,
buggar, 2, orinch, 3; the Eaw tribe, koothea, 1, woother, 2, marronoo,
3; the Moree, mal, 1, boolar, 2, kooliba, 3; the Port Essington,[30] erad,
1, nargarick, 2, nargarickelerad, 3; the Darnly Islanders,[31] netat, 1,
naes, 2, naesa netat, 3; and so on through a long list of tribes whose
numeral scales are equally