Subject: Re: [HM] comments
From: Milo Gardner (milo.gardner@24stex.com)
Date: Wed Jan 05 2000 - 05:58:01 EST
Dear HM List members:
I wish to thank Beatrice for her most interesting quipu related post.
The Aymara use of a 'cubit' in the form of 28 fingers expressed as
seven four finger palms reminds me of the Egyptian practice of writing
2/7 = 1/4 + 1/28.
Could Marcia Ascher, or another scholar that has access to the growing
number of quipu's, look up the Inca method(s) of writing fractions?
Could have vulgar or unit fractions been used at one time in a mixed or
separate form? What is the common view for Incan fractions?
From the Egyptian side of a possible South American diffusion subject,
cocaine has been found in at least one Egyptian mummy. I'll have to ask
around to find the date(s) that cocaine has been connected to Egypt
begin a search for a hint on the form of unit fractions that MAY exist
in one of 200 + quipu's that Marcia graciously discussed here not long
ago.
One day a majority of the existant quipu's may be read on the web, or
by telneting to a U. of Michigan computer. Is such a project being
considered? A clear citation of the contents of quipus, as read from
different points of view seems important to 'declare to public'. In this
manner all hints of academia's long practice of holding back texts, as
the Dead Sea Scrolls, as one of the worst examples, can begin to erase
this 'holding back' from the history of mathematics and science communities.
Concerning Bea's mentioning of racist's practices, and motivations for
under reporting native texts, I prefer George C. Joseph's term of
Eurocentric, as used in Crest of the Peacock. I understand the term to
mean pro-Greek (pro-Hellene). In this light I sadly recall Otto Neugebauer
admitting in The Journal for the History of Astronomy in 1989, related to
his 17 year debate with David Pingree, that one of his motivations for not
accepting Pingree's 1972 statement was only based on Greek 'feelings' (or
words to that effect).
Specifically mentioning South America, and modern cultural reasons why the
early 1925 discussion of quipu's was conducted on a low level, and has
slowly improved since, a look into a range of Latin cultural practices
yields damning evidence. In Latin American there is a 500 year practice
of Ladinoziation, known in many forms. Ladinoization is the negative side
of the censure and political control of native peoples, as easily seen in
Chiapas, Mexico and all of Latin America Clearly stated, a native American
living in Latin American in the year 2000 can not gain simple modern
political rights without first ACCEPTING the dominant Latin culture (and
virtually ignoring his/her native culture, as the 1600 Jesuit attempt to
be more sensitive has been discussed here on HM). Ladinoization is racists,
as Bea suggests, however, a precise term exists in this cultural context,
and therefore I recommend the use of Ladinoization.
Returning to Bea's discussion of Egyptian fractions, I thank her for
mentioning a brief summary of my views. One day a broader debate may be
conducted on HM, considering the small set of unit fraction documents that
exist (recalling David Fowler's reason for the attraction for amateurs)
beyond the RMP and its 2/nth table. Considering, for example, the EMLR and
its small set of 1/p and 1/pq methods that vividly wrote unit fraction
series, duplation is not found in all of the 26 EMLR series
(1/8 = 1/25 1/15 1/75 1/200, being one). That is, the context of my Occam's
razor, as Bea cited, should consider a wider range of unit fraction
documents (to all those that are available, at some point).
Finally, let me close mentioning Bea's stressing that differences between
Babylonian and Egyptian arithmetic (number theory) (and algebra, geometry
and so forth) are not important to discuss. Concerning only Babylonian number
theory, their inverse tables were ALWAYS written in terms of infinite series,
consistent with their base 60 numeration system. Egyptians, very early (to
accept Bea's time period term) wrote between finite and infinite series,
almost as needed by the scribe.
Charles Shute, writing in The Rhind Mathematical Papyrus (co-authored by his
Egyptologist wife), stressed the finite and infinite series point, while
only considering the duplation aspects of the finite series. Why did not
Babylonians pick up the finite series technique? One easily seen reason is
found in our modern base 10 decimal point of view, one that is only infinite
in scope, one often ignoring important finite arithmetic points.
Regards,
Milo Gardner
This archive was generated by hypermail 2b28 : Wed Jan 05 2000 - 11:04:16 EST