nLab canonical formula of myth

La première expression de la réalité serait de dire que la langue (c’est à dire le sujet parlant) n’aperçoit ni l’idée a, ni la forme A, mais seulement le rapport $\frac{a}{A}$; cette expression serait encore tout à fait grossière. Il n’aperçoit pas vraiment que le rapport entre les deux rapports $\frac{a}{AHZ}$ et $\frac{abc}{A}$, ou $\frac{b}{ARS}$ et $\frac{blr}{B}$, etc. C’est là ce que nous appelons le QUATERNION FINAL. de Saussure (2002, p.39)

Idea

The canonical formula of mythical transformation is an expression proposed in 1955 by the anthropologist Lévi-Strauss in order to account for the abstract relations occuring between characters and their attributes in a myth understood as the collection of its variants. The vagueness of the initial proposal has been lifted by several mathematical interpretations in the aftermath.

The original formulation

In Lévi-Strauss (1955, p.442) the canonical formula is introduced as the “algebraic” expression:

$f_x(a): f_y(b)\cong f_x(b):f_{a^{-1}}(y)$ .

An example

The quaternionic interpretation

Jack Morava (2003, 2004) proposed to interpret the canonical formula as the existence of an anti-isomorphism of the quaternion group.

Some history

Related entries

• Claude Lévi-Strauss

• kinship

• structuralism

• quaternion group

• quaternionic set

• code loop

Related pages

• French wikipedia entry: (link)

References

• Numéro spécial La formule canonique des mythes, L’Homme 35 no.135 (1995). (link)

• Mauro William Barbosa de Almeida, A fórmula canônicado mito, ms. University of São Paulo 2009. (Available online)

• S. Darányi, P. Wittek, K. Kitto, The Sphinx’s New Riddle: How to Relate the Canonical Formula of Myth to Quantum Interaction, pp.47-58 in LNCS 8369 (2014).

• Maurice Godelier, Lévi-Strauss, Seuil Paris 2013.

• Lucien d’Huy, Cosmogonies - La Préhistoire des mythes, La Découverte Paris 2020. (pp.247-252)

• Jacques Lacan, Le mythe individuel du névrosé, Seuil Paris 2007.

• H. G. Landau, On dominance relations and the structure of animal societies: Effect of inherent characteristics, Bull. Math, Biophysics 13 (1951) pp.1-19,245-62.

• Claude Lévi-Strauss, The Structural Study of Myth, J. American Folklore 78 no. 278 (1955) pp.428-444.

• Claude Lévi-Strauss, Anthropologie Structurale, Plon Paris 1958.

• Claude Lévi-Strauss, D’un oiseau à l’autre, L’Homme 25 no.93 (1985) pp.5-12. (link)

• Claude Lévi-Strauss, La Potière Jalouse, Plon Paris 1985.

• Juan Pablo Lucchelli, Le mythe individuel revisité, L’information psychatrique 82 no.2 (2006) pp.155-158. (link)

• Juan Pablo Lucchelli, Lacan et la formule canonique des mythes, Les Temps Modernes no.660 (2010) pp.116-131.

• Pierre Maranda (ed.), The Double Twist, University of Toronto Press 2001.

• Jack Morava, On the Canonical Formula of C. Lévi-Strauss, arXiv:2003.0306174v2 (2003). (abstract)

• Jack Morava, Une interprétation mathématique de la formule canonique de Claude Lévi-Strauss, Cahiers de L’Herne 88 (2004) pp.216-218.

• Jack Morava, From Lévi-Strauss to Chaos and Complexity, in Mosko, Damon (eds.), On the Order of Chaos, Berghahn Oxford 2005.

• Jack Morava, On the Canonical Formula of C. Lévi-Strauss II, arXiv:2002.12813 (2020). (abstract)

• Michael Oppitz, Notwendige Beziehungen - Abriß der strukturalen Anthropologie, Suhrkamp Frankfurt am Main 1992. (pp.245ff)

• Jean Petitot?, Approche morphodynamique à la formule cannonique des mythes, L’Homme 28 no.106-107 (1988) pp.24-50. (link)

• A. Rapoport, Outline of a Probabilistic Approach to Animal Sociology, Bull. Math. Biophys. 11 (1949) pp.183-196, pp.273-281.

• Elisabeth Roudinesco, Jacques Lacan, Fayard Paris 1993.

• Ferdinand de Saussure, Écrits de linguistique générale, Gallimard Paris 2002.

• Lucien Scubla, Lire Lévi-Strauss, Odile Jacob Paris 1998.

• M. Thuillard, J.-L. Le Quellec, A phylogenetic interpretation of the canonical formula of myths by Lévi-Strauss, Cultural Anthropology and Ethnosemiotics 3 no.2 (2017) pp.1-12.