The Double Twist: From Ethnography to Morphodynamics

Joan Lovisek, Ph.D., is a consulting anthropologist and ethnohistorian
in British Columbia.

In 1955, French anthropologist Claude Lévi-Strauss introduced a
mathematical formula that attempted to represent his understanding that
every myth was an aggregate of all its variants. (The formula is
expressed as the canonical formula: fx(a):fy(b)::fx(b):fa-1(y), where :
means “transforms itself into” and :: “is a resemblance between
two transformations.”) Despite its long existence, few working
anthropologists use it.

The Double Twist presents an excellent collection of 10 papers by
international scholars from a variety of disciplines who explain the
formula, test its applicability, and illuminate its value as both
metaphor and mathematical formulation. The collection is introduced by
Lévi-Strauss, who extends his formula to cross-cultural religious
architecture, focusing on the hourglass forms of Fijian temples. Luc
Racine demonstrates how the formula cannot be reduced or understood as a
simple analogy. Erich Schwimmer considers the ability of structuralism
to cope with history by testing the formula on cultural data from Papua
New Guinea. Pierre Maranda explores gender relations in Melanesia
following the advent of Christianity and uses the formula to map this
transformation. Lucien Scubla provides a detailed historical review of
the canonical formula and applies it to Hesiodic myth. Sбndor Darбnyi
uses data from Asia Minor to demonstrate the correspondence between the
geometric and spatial interpretation involved in the formula.
Christopher Gregory compares two kinds of binary logic (Boolean and
Ramistic) by analyzing an Indian myth, and concludes that the formula
based in binary logic is actually Ramistic. The volume concludes with
technical mathematical papers by Alain Cфté, Andrew Quinn, and Jean
Petitot.

These authors confirm that the canonical formula is an intelligent
means of grasping mythical transformation and cognitive structures.
Structuralism is based on a concept of universal truth, which is
contrary to postmodernist thought: that may partly explain why the
formula has been widely ignored. The difficulty in understanding the
formula is probably another reason. Although this collection adds to
that understanding, it is most suitable for advanced students of
anthropology and semiotics.