Lakota Concept of Zero

[Koontz John E]

On Tue, 17 Jan 2006, Rory M Larson wrote:
> Even regular counting terms probably haven't been around too long.  The
> fact that just about everybody seems to use a base-10 counting system shows
> that it started out by matching fingers to quantity.  Finger names are
> pretty volatile, and in a lot of obviously related languages the higher
> counting terms don't agree.  I think across Siouan, the numbers 2, 3, 4,
> and possibly 1, are cognate.  Within MVS, I believe 5, 6, and 10 are added.
> 7, 8, and 9 were apparently not standard counting numbers until perhaps a
> few centuries ago, maybe about the time of proto-Dakotan.  Even Osage and
> OP seem to differ on 8 and 9.

And 12, I think.

> It looks like counting terms and mathematics have been developing in crude
> parallel all over the world in the last ten thousand years or so along with
> the shift to settled dwelling, agriculture, private property, trade, and
> administration.  Our foraging ancestors, however, apparently did not need
> arithmetic.  Native North Americans were foragers much more recently than
> Europeans were, and the mathematical component of their languages will
> likely reflect this.

I agree.  I think there are several books on early Mesopotamian
mathematics and accounting.  I think the accounting aspects are missing
for the state-organized parts of the Americas, perhaps due to choice of
medium, but the astronomical aspects are available.  Agriculture and
astronomical observations and more integrated states seem to lead pretty
immediately to mathematics everywhere.

However, where we have information or reconstructions it looks it doesn't
take much for numbering up into the hundred and thousands to break out.

My suspicion is that Siouan counting isn't reconstructable above five
(except for ten) because numerals are much more variable over time than
Indo-Europeanists have traditionally believed.  Siouan and its neighbors
reflect a certain amount of borrowing of numerals, and also of descriptive
terms alternating with more opaque terms.  I suspect Proto-Siouan speakers
could count as well as historical Siouan speakers, but time has been
harder on the evidence for "higher numerals."  I think the higher numerals
are just more likely to change.

However, I agree that numeration systems show certain natural states and
that simpler states were common until recently.  I suspect that numeral
systems were fairly sophisticated in Eastern North America with the
beginning of widespread trading networks and horticulture.

I noticed recently a remark in Dorsey's paper on dwellings, tools, etc.,
that the Omaha dealt with arrows in standardized sets - there is even a
word for such a set - and not as individual artifacts.  Since sets were
usually of ten arrows each, it seems on that basis that the urge to count
by tens may go back at least as far as the introduction of the bow.  On
the other hand, perhaps throwing spears were also handled in sets, though
maybe smaller ones. Another instance of systematized counting might be the
use of bundles of sticks to represent honors.  Men are reported to have
recounted their honors by working through their sets of sticks.  The
handgame also involves a system of formal counters, though the modern form
is fairly recent and I don't know if the counters are earlier.

Rory - what do you think about the use of kku'ge 'box' for 'thousand'?
Does this imply that 1000 is a new concept, or is it a new word for an old
concept?  How widespread is 'box' in this sense?  I just noticed in the
texts that kku'ge often appears glossed 'box' when a numerical
interpretation is clearly meant.