[APH]
> I seem to recall that Julio mentioned once a cooperation of Claude
> Levi-Strauss and A. Weil, but I don't remember if they coauthored
> something.
Good memory, Antreas! Here goes a few tidbits:
Date: Tue, 2 Dec 1997 02:22:07 -0200
From: Julio Gonzalez Cabillon <jgc@adinet.com.uy>
Subject: Weil and Levi-Strauss
[...]
Ravindra remarked:
| I heard that Andre Weil wrote an appendix to a book of Claude
| Levi-Strauss. Is this correct?
Positive.
All this issue began in the late forties when, at Levi-Strauss's request,
Andre Weil wrote an appendix (pp 278-285) to Claude's famous book "Les
structures elementaires de la parente" [Paris: Presses universitaires de
France, xiv, 639 pages, 1949].
[See also pp 221-227 of C. Levi-Strauss's "The Elementary Structures of
Kinship", rev. edition. Translated from the French by James Harle Bell,
John Richard von Sturmer, and Rodney Needham, Boston: Beacon Press, xlii,
541 pages, 1969]
In the addendum, the great Weil describes the algebraic study of certain
types of marriage laws, known as the Murngin system.
WEIL, LEVI-STRAUSS, DREYFUS (SA~O PAULO ...)
"...
In New York, I had met the sociologist Levi-Strauss,
and we had hit it off quite well. I had solved for him
a problem of combinatorics concerning marriage rules
in a tribe of Australian aborigines. He had taught
for several years at the humanities section of the
University of Sao Paulo in Brazil. In 1944, he
introduced me to the geneticist Dreyfus, the dean of
that institution, who was then on a research trip to
the United States. The University of Sao Paulo, only
recently founded, had at first chosen French scholars
to teach disciplines in the humanities and Italians
for the sciences. Because war had been declared between
and Brazil and Italy, the Italian professors had been
obliged to repatriate; there was thus a chair in
mathematics that needed to be filled. To my great good
fortune, Levi-Strauss and Dreyfus thought of me for the
position. My official appointment to it followed shortly.
"But it was not enough to be selected on the Brazilian
end. Because of the state of war, no foreigner was
allowed to leave the United States without an exit visa
issued by the Immigration Service. I therefore applied
for a visa for myself and my family, including my parents,
who did not want to be left behind in New York. To my
great surprise, my request was denied.
..."
I invite you to keep on reading the passage [cf page 185 of Andre Weil's
"The Apprenticeship of a Mathematician", Basel-Boston-Berlin: Birkhaeuser
Verlag, 1992]
Now, variations of the same algebraic model have been discussed in many
publications.
Labib Haddad and Yves Sureau [Universite de Clermont-Ferrand II (Blaise
Pascal)] decided to merge math and ethnomath in "Les groupes, les hyper-
groupes et l'enigme des Murngin -- the Murngin case" [Journal of Pure
and Applied Algebra, vol 87, no 3, pp 221-235, 1993], which Sandra Lach
Arlinghaus has reviewed it for MR as follows:
"It is always nice to visit with old friends; Haddad and
Sureau revisit the classical Murngin kinship structures
of mathematical anthropology, first written about in 1949
by Claude Levi-Strauss and Andre Weil. In the spirit of
Weil's algebraic characterization of these structures using
group theory, Haddad and Sureau align concepts from hyper-
groups and semi-direct products of groups with ethnological
structures. The partition of Murngin marriages into two
types (regular and alternate) suggests this sort of formal
algebraic approach. The authors hope not only to offer a
different analysis of the particular systems presented, but
also to contribute to the broader abstract issues involved
in making this algebraic-ethnographic alignment. This work
seems to flow naturally from some of the more abstract work
by Sureau on hypergroups.
"There are no formal theorems; that is a step that no doubt
will follow the initial meshing of concepts. The presentation,
in French with an English abstract, is clear, interesting
to social scientific readers, and easy to follow. There are
ample, well-drafted figures and tables that also ease readers
who need it through some of the more difficult portions of
the text. The document is divided into sections using anthro-
pological concepts (such as matrilineal or patrilineal cycles)
which are analyzed internally using the algebraic structures
and linked by descriptive commentary. The interweaving of
mathematical and social scientific material is well done and
mirrors current trends in this sort of application (others
include, for example. P. Hage and F. Harary [Exchange in
Oceania: a graph theoretic analysis, Clarendon Press, Oxford,
1991]. Readers who appreciate this sort of art, and understand
not only its difficulty but also its interdisciplinary
importance, will want to be sure to read this article!"
Hans Lausch has also shed light on the subject in his "Uncontroversial
Murngin" (pp 189-196) [in "Contributions to General Algebra 6. Dedicated
to the Memory of Wilfried Noebauer", edited by D. Dorninger et al, Wien:
Hoelder-Pichler-Tempsky (HPT); Stuttgart: B. G. Teubner, 1988. ISBN:
3-209-00782-9 (HPT) / ISBN: 3-519-02765-8 (Teubner)].
The following summary reveals the threefold purpose of the article:
1. to 'vindicate' Andre Weil by using the original method of
his seminal paper on Murngin kinship in order to 'compute'
a kinship system which does not occur explicitly in Weil's
paper, but was described by other authors;
2. to show that Weil's method is by far the easiest of all
the methods offered so far to describe the Murngin;
3. to demonstrate that mathematical machinery is not required
to produce a complete solution to the Murngin problem, just
mathematical reasoning which could also be called common
sense.
Last but not least a most interesting article, "The Problem with Algebraic
Models of Marriage Structure", was addressed by James M. Cargal [Troy
State University Montgomery] at the Joint Mathematics Meetings, [January
10-13, 1996, Orlando, Florida]. Fortunately, is it online at:
http://forum.swarthmore.edu/orlando/cargal.orlando.html
Cheers! JGC
PS: Oh, there is much more on the variations of the same algebraic model.
I almost forget to quote "Marcia Ascher's classic, "Ethnomathematics:
A Multicultural View of Mathematical Ideas" [California: Brooks-Cole,
1991], and even the delightful review of it by Judith V. Grabiner in the
_Monthly_ [vol 100, no 3, pp 304-308, March 1993]. Oh well, it is 2:20 am
here in Montevideo, and my eyes can hardly see what I'm typing. So, chau!
_____________________________________________
"_Ethnomathematics_ is fascinating reading
for anyone who views mathematical thought
as a supreme expression of the human spirit"
[Judith V. Grabiner]
_____________________________________________
* * * * * * * * * * * *
'Adding more ice(cream) to the cake', let me air the following anecdote
that fellow listmember James Landau told me some months ago:
"When I was an undergraduate, a friend who was a biology student told me
the following story about the Hardy-Weinberg Law: one of Hardy and Weinberg
(my student friend did not remember which) was talking to a biologist about
the then-recent findings in genetics, and told the biologist that it was
"obvious" that heredity was governed by the mathematical rule in the H-W
Law. "Well, it's not obvious to a biologist", said the biologist, "so why
don't you publish it?" So mathematician published it, and it was forever
after known by the combination of his name and that of the other, independent
discoverer. Which is ironic, since he never otherwise established a name
for himself as a mathematician.
When I heard this story, I assumed that the "unknown" mathematician was
Weinberg, since Hardy was well known to anyone who had ever looked into
Newman's four-volume _The World of Mathematics_. I have recently discovered
that Weinberg was a physician,and therefore the "unknown" mathematician had
to be Hardy. It seems that to biologists, Hardy was a nonentity who never
accomplished anything other than the Hardy-Weinberg Law."