Re: [HM] First kind of writing

Milo Gardner (milo.gardner@24stex.com)
Sat, 21 Nov 98 15:07:52 -0800

Origins of writing, seen from world-wide points of view may be
important subjects to discuss on this history of mathematics
list-server. Three aspects of such a discussion will be outlined
in the hope that a prior basis of abstract arithmetic and/or
political will be implied as interesting side-lights, if not
primary considerations for writings' birth.

First, Denise S-B's well known views do include the use of
Piaget's 'finger and toes' arithmetic as an aspect of Sumer's
development of writing. However, is there one (1) other culture
that independently developed writing that also employed 'fingers
and toes' type of thinking? The remainder of this post will focus
on finding a second culture, to tend to confirm or tend to refute
Denise S-B's central thesis.

Second, for several reasons, that will be briefly touched upon,
several professional linguists (if not a majority) have strongly
disagreed with Denise S-B's views in important respects. I recall
seeing a SCIENCE NEWS article published around 1990 that suggested
(among other points):

1. Elam also developed writing about the time that Sumer writing
emerged. However, to date scholars have not attempted to equally
document Elamite writing, even though there are significant
artifacts available to commence such a study. When is this study
going to be commenced and completed?

2. Outside of Sumer and Elam, writing was 'invented' several times.
China and Mesoamerica are two examples that also can be studied
for 'Piaget' and other related arithmetic or political actions
that birthed complete writing systems.

That is, Sumer's proposed use of 'fingers and toes' thinking should
be open for confirmation. If the method worked once, why would it not
work a second or a third time?

Third, there are well documented cultures nearby to Mesoamerica that
did not develop writing. I am keenly aware of California cultures
that were very active culturally before the time that the Spanish
arrived.

Kroeber writing in HANDBOOK OF THE INDIANS OF CALIFORNIA documented
several number bases (4, 8, 10, 12, 16, 20 and combinations thereof)
and well developed systems of astronomy showing that many of Denise
S-B's pre-writing Piaget foundations existed. However not one of 45
separate 'tribes' that Kroebe documented in the 1920's as pre-
Columbian developed writing. Could it be that since there was no
unifying political force in California, as noted by the continuous
use multiple number bases, that formal writing systems could not
emerge?

Please also contrast Mesoamerica and California, regions of
comparable size. The first did not develop writing, and the second
region was politically unified, as the unified number base 20 system
implies, and did develop writing. Could it be that before writing
emerged in the New World, in any independent way, that previous
political and mathematical unifications were required?

Just a few thoughts.

Milo Gardner
Sacramento, Calif.