Subject: [HM] comments
From: Beatrice Lumpkin (Bealumpkin@aol.com)
Date: Tue Jan 04 2000 - 19:41:01 EST
Dear friends,
As you know, a number of conferences are taking place in India on the
occasion of the 1500th anniversary of Aryabhata. I hope to attend the
conference meeting January 12-16, but before I leave I wanted to share two
items with HM forum participants. The first is a suggestion for David E.
Zitarelli's student; second, a comment on one of Milo Gardner's messages.
Zitarelli wrote:
The student is from Argentina and some American basketball fans might
know of his exploits at Temple University. Anyway, he is a history major
so his knowledge of mathematics ends with calculus. Can anyone on this
list suggest a book in Spanish that is along the lines of Struik's
Concise History? Moreover, can anyone suggest any additional reading on
the history of mathematics in South America?
David E. Zitarelli
A small research project may interest Zitarelli's student. It occurred to
me on a recent visit to a museum in La Paz, Bolivia where I bought "Ciencia
Astronomica y Sociologia Incaica" by Dick E. I. Grasso, editorial Los Amigos
del Libro, La Paz, 1982. On page 15, a list of Inca measures gives for the
outer length of the forearm (I assume from elbow to middle finger tip) the
equivalent of 28 fingers or seven 4-finger palms. I was struck by the
similarity with ancient Egyptian measure of the royal-cubit equivalent to 28
fingers or seven 4-finger palms. I had checked this ratio with a number of my
classes and only the relatively long-limbed, slim people matched this ratio.
The rest of us averaged 6 or fewer palms, which I guessed was true of the
indigenous people I saw in and around La Paz. Was there contact between the
ancient Egyptian and the contemporary Aymara civilizations? Not necessarily,
but I would not dismiss it out of hand.
Now it is true that Grasso believes that the inside length, rather than outer
length of the forearm was used by the Inca although both are attested to
among the Aymara. It is also true that my Castellano or Espanol is far below
professional proficiency and I may have slipped in my translation. Still a
study of body ratios inferred by Inca and Aymara measures and a comparison
with proportions of people today could be a fascinating project.
ON ANCIENT EGYPTIAN FRACTIONS
Our friend Milo Gardner has sent us a number of messages with interesting
suggestions on the number theory developed in ancient Egypt for expansion of
fractions as a sum of unit fractions. As Gardner writes (and I agree) this
early beginning of number theory has been under-reported. On under-evaluation
of the level of ancient Egyptian mathematics, see the discussion by Katz and
Lumpkin in HPM Newsletter no 35 July 1995, also Richard J. Gillings, 1972,
Mathematics in the Time of the Pharaohs, pp 240-41. In my opinion,
under-evaluation results in part from the institutionalized racism that
affects the United States and other countries. I also believe, on the
positive side, that many historians are now working to give proper
recognition to those whose contributions had been left out--people of color
and women.
For these reasons, I think a word of caution could be helpful here. Gardner
suggests "the use of Occam's Razor such that the easiest method is reported
as the historical one." We may BELIEVE that the simplest method was used but
we cannot report that it was indeed used unless we have evidence to that
effect. Similarly, I have learned to try to use terms such as "very early" or
"one of the earliest" rather than "earliest." Mesopotamian mathematicians
were also developing number theory c 1850, the date of the papyrus copied by
Ahmose in the RMP. I believe that battles over priority of these two early
civilizations are pointless and inconclusive. Their early achievements speak
for themselves.
Beatrice Lumpkin
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