hing above this they speak of in an uncertain way, as _mano mano_ or
_tini tini_, which may, perhaps, be paralleled by our English phrases
"myriads upon myriads," and "millions of millions."[205] It is most
remarkable that the same quarter of the globe should present us with the
stunted number sense of the Australians, and, side by side with it, so
extended and intelligent an appreciation of numerical values as that
possessed by many of the lesser tribes of Polynesia.

The Luli of Paraguay[206] show a decided preference for the base 4. This
preference gives way only when they reach the number 10, which is an
ordinary digit numeral. All numbers above that point belong rather to
decimal than to quaternary numeration. Their numerals are:

1. alapea.
2. tamop.
3. tamlip.
4. lokep.
5. lokep moile alapea = 4 with 1,
or is-alapea = hand 1.
6. lokep moile tamop = 4 with 2.
7. lokep moile tamlip = 4 with 3.
8. lokep moile lokep = 4 with 4.
9. lokep moile lokep alapea = 4 with 4-1.
10. is yaoum = all the fingers of hand.
11. is yaoum moile alapea = all the fingers of hand with 1.
20. is elu yaoum = all the fingers of hand and foot.
30. is elu yaoum moile is-yaoum = all the fingers of hand and foot with
all the fingers of hand.

Still another instance of quaternary counting, this time carrying with it a
suggestion of binary influence, is furnished by the Mocobi[207] of the
Parana region. Their scale is exceedingly rude, and they use the fingers
and toes almost exclusively in counting; only using their spoken numerals
when, for any reason, they wish to dispense with the aid of their hands and
feet. Their first eight numerals are:

1. iniateda.
2. inabaca.
3. inabacao caini = 2 above.
4. inabacao cainiba = 2 above 2;
or natolatata.
5. inibacao cainiba iniateda = 2 above 2-1;
or natolatata iniateda = 4-1.
6. natolatatata inibaca = 4-2.
7. natolata inibacao-caini = 4-2 above.
8. natolata-natolata = 4-4.

There is probably no recorded instance of a number system formed on 6, 7,
8, or 9 as a base. No natural reason exists for the choice of any of these
numbers for such a purpose; and it is hardly conceivable that any race
should proceed beyond the unintelligent binary or quaternary stage, and
then begin the formation of a scale for counting with any other bas