# The Double Twist: From Ethnography to Morphodynamics

Edited by PIERRE MARANDA
https://www.jstor.org/stable/10.3138/9781442681125

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1. Front Matter
(pp. i-iv)
(pp. v-vi)
3. Contributors
(pp. vii-viii)
4. Acknowledgments
(pp. ix-2)
5. Introduction
(pp. 3-12)
Pierre Maranda

In 1955, Claude Lévi-Strauss proposed a mathematical-looking ʹCanonical Formulaʹ (hereafter CF) for the structural analysis of myth (Lévi-Strauss 1955: chap. 11). It purported to investigate the dynamics of a basic semiotic structure: what we would now call the ʹgenerative engineʹ of myth. This book focuses on, and offers tests and developments of, Lévi-Straussʹs pioneering endeavour. While some scholars consider the CF ʹa meaningless abracadabra,ʹ others have acclaimed it ʹan intelligent formulaʹ (see the first sections of chapters 5 and 10 for sources). For the mathematician and semiotician Solomon Marcus (1997), ʹLévi-Straussʹ explicit mathematics is poor, but the mathematical potential of...

6. ### Part One: Ethnography and the Canonical Formula

• 1 Hourglass Configurations
(pp. 15-32)
Claude Lévi-Strauss

It was in 1977, in Japan, facing the Ise Shrine, that the reflections I am sharing here took shape in a somewhat disorderly fashion. I was struck, as would be most people, by the roof frames, of which the principal rafters cross in an X and jut out past the ridge (see figure 1). The Izumo Shrines, also of archaic style, have a similar appearance, but due to crossbeams which are not part of the structure but are affixed to the roof as a decoration.

This is reminiscent, of course, of islands in the South Seas where the roofs of...

• 2 Analogy and the Canonical Formula of Mythic Transformations
(pp. 33-55)
Luc Racine

Can the canonical formula of mythic transformations be reduced to an analogy of the type ʹa is to b as c is to dʹ? This is the central question to be addressed in the present paper. The discussion is based on the two cases of the application of this formula in which Claude Lévi-Strauss manifestly attempted to be as clear and pedagogical as possible in this regard. Thus, it will be possible to determine whether analogy and mirror symmetry, itself a substructure of the former, are related to and premised by the formula. There is no question here of reducing...

• 3 Is the Canonic Formula Useful in Cultural Description?
(pp. 56-96)
Eric Schwimmer

Claude Lévi-Strauss enunciated the canonic formula in 1955. He did not refer to it frequently in his publications for many years, but towards the end of his career he found several occasions to say that it was fundamental to his scheme of structural analysis of myth and, hence, to structural anthropology. The paradox is that although his scheme for structural anthropology has been immensely influential, hardly any working anthropologists knew what to do with his canonic formula. Recent studies by several specialists, especially Marcus, have cleared up most of the obscurities that made application of the formula virtually impossible. This...

• 4 Mapping Cultural Transformation through the Canonical Formula: The Pagan versus Christian Ontological Status of Women among the Lau People of Malaita, Solomon Islands
(pp. 97-120)
Pierre Maranda

This paper consists, first, of a concise ethnographic description of basic aspects of the traditional life in the Lau Lagoon, Malaita, Solomon Islands. Next, it takes up the ʹontologicalʹ transformation of Lau society through the advent of Christianity. Finally, it applies Claude Lévi-Straussʹs Canonical Formula to summarize the dynamics of a deep cultural change. Thus, the paper begins with a brief monographic presentation of the Lau people, focusing on their traditional life, on their linguistic and mythic expresssions of gender, and on womanhood as the architectural principle of their traditional ontology. Section 2 bears on the subversion of womanhood by...

7. ### Part Two: Analyses, Tests, and Contextualizations of the Canonical Formula

• 5 Hesiod, the Three Functions, and the Canonical Formula of Myth
(pp. 123-155)
Lucien Scubla

Instead of considering the variants of a myth as lacunary or distorted versions of a single prototypic tale to be reconstructed by theorists, Claude Lévi-Strauss proposed defining a myth as the collection of all the possible variants or ʹtransformationsʹ of a tale, the mythical characteristics or connotations of which would merely result from its belonging to such a ʹgroup of transformations.ʹ He further suggested that any myth, thus defined, could be represented in logico-mathematical terms by a universal formula – the ʹcanonical formulaʹ of myth – which would read as follows:${{\text{f}}_{\text{x}}}\text{(a) : }{{\text{f}}_{\text{y}}}\text{(b) : : }{{\text{f}}_{\text{x}}}\text{(b) : }{{\text{f}}_{{{\text{a}}^{\text{-1}}}}}\text{(y)}\text{.}$

Since 1955, the Lévi-Straussian definition of myth as...

• 6 Classical Myths and Transformation: Computer Observation of the Lévi-Strauss Formula at Work
(pp. 156-176)
Sándor Darányi

My study of the texts related to Attis goes back to a short treatise about this Phrygian deity from Asia Minor whose cult was imported to Greece and Rome (Trencsényi-Waldapfel 1981). In an earlier article, I suggested that these myths are but one subset of otherwise typical stories about flower heroes such as Hyakinthos, Narkissos, Kyparissos, or Adonis, who characteristically are wounded and turned into plants at the storyʹs climax. Following this repetitive action, I also offered a Proppian segmentation of the respective myth variants (Darányi 1986). My aim with this study is to suggest the applicability of multivariate classification...

• 7 Ramistic Commonplaces, Lévi-Straussian Mythlogic, and Binary Logic
(pp. 177-196)
Christopher A. Gregory

In this article I want to consider a suggestion first put forward by some linguists¹ that Claude Lévi-Straussʹs thought can be seen as a partial rehabilitation of the Ramist tradition of thought that flourished in the sixteenth and early seventeenth century.² This tradition covered grammar, rhetoric, and logic, but I restrict myself to the latter here. The Ramist logical tradition, which has its origins in AristotleʹsTopics, was superseded by the rise of the what is now called ʹformalʹ or ʹmathematicalʹ logic. The work of Descartes and Leibniz in the seventeenth century was the beginning of the end of Ramist...

8. ### Part Three: The Logico-Mathematical Status of the Canonical Formula

• 8 The Set of Canonical Transformations Implied in the Canonical Formula for the Analysis of Myth
(pp. 199-221)
Alain Côté

Claude Lévi-Straussʹs canonical formula (CF) for the analysis of myth has been the object of several scholarly papers (see Scubla 1998), but it still remains a mystery of sorts. Controversy persists on its interpretation. Should it be discarded as nonsense, as some would have it? Or is it still to be better understood? Actually, as one may learn from the history of mathematics, it remains imperative to be cautious when dealing with that kind of issue.

Remember the controversies about irrational numbers. Pascal and Barrow saw them merely as symbols – as some do with Lévi-Straussʹs canonical formula. By contrast,...

• 9 On Some Philosophical Dynamic and Connectionist Implications of the Canonical Formula of Myth Seen as Space Categorization
(pp. 222-266)
Andrew William Quinn

This chapter stems from a question formulated by Pierre Ouellet in his presentation of an issue of the periodicalRS/SI, entitled ʹSymbolic Representation and Spatial Organizationʹ (1992), and proposes a series of reflections on Lévi-Straussʹs renownedcanonical formula of mythinvolving certain cognitivist themes. The question was as follows: ʹHow does the topological or morphological structure of space give rise to different symbolic representations of a perceptual, conceptual or more broadly socio-cultural nature?ʹ (Ouellet 1992: 186).

We shall address the question on a background of Kantian philosophy by first presenting the Connectionist (hereafter CN) Paradigm and its commitments along with...

• 10 A Morphodynamical Schematization of the Canonical Formula for Myths
(pp. 267-312)
Jean Petitot

This new reflection on the canonical formula for myths (CF) proposed in 1955 by Claude Lévi-Strauss provides me with the opportunity to clarify the morphodynamical model I proposed in 1988 in the journalLʹHomme(H1).¹ During the exciting seminar organized by Professor Solomon Marcus at the Collège de France in Paris in the fall of 1993, I clarified some of its epistemological difficulties. This work was published inLʹHommein 1995 (H2).² I will attempt here to explain in further detail the so-called double cusp model presented inH1. My basis will be the pioneering work of Pierre Maranda³ and...

9. Conclusion
(pp. 313-316)
Pierre Maranda

This conclusion draws from comments made on the manuscript by Claude Lévi-Strauss, Lucien Scubla, Solomon Marcus, and Sándor Darányi. Lévi-Straussʹs remarks bear on types and ranges of application of his CF and also on its capacity to deal with diachrony (le temps du récit / le temps historique). On convergent lines, Scubla offers a threefold and technical classification of static versus dynamic interpretations of the CF. Finally, Marcusʹs and Darányiʹs points explore – the first, briefly, the second, somewhat more at length – the epistemological status of the formula. Actually, Darányi happens to develop an aspect of Marcusʹs statement about...

10. Back Matter
(pp. 317-318)