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\begin{document}

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\section*{canonical formula of myth}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{philosophy}{}\paragraph*{{Philosophy}}\label{philosophy}

[[!include philosophy - contents]]

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{the_original_formulation}{The original formulation}\dotfill \pageref*{the_original_formulation} \linebreak
\noindent\hyperlink{an_example}{An example}\dotfill \pageref*{an_example} \linebreak
\noindent\hyperlink{the_quaternionic_interpretation}{The quaternionic interpretation}\dotfill \pageref*{the_quaternionic_interpretation} \linebreak
\noindent\hyperlink{some_history}{Some history}\dotfill \pageref*{some_history} \linebreak
\noindent\hyperlink{related_entries}{Related entries}\dotfill \pageref*{related_entries} \linebreak
\noindent\hyperlink{related_pages}{Related pages}\dotfill \pageref*{related_pages} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak


\begin{quote}%
\emph{La premi\`e{}re expression de la r\'e{}alit\'e{} serait de dire que la langue (c'est \`a{} dire le sujet parlant) n'aper\c{c}oit ni l'id\'e{}e a, ni la forme A, mais seulement le rapport $\frac{a}{A}$; cette expression serait encore tout \`a{} fait grossi\`e{}re. Il n'aper\c{c}oit 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 l\`a{} ce que nous appelons le QUATERNION FINAL. de Saussure (\hyperlink{Saussure02}{2002}, p.39)}


\end{quote}
\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

The \textbf{canonical formula of mythical transformation} is an expression proposed in 1955 by the anthropologist [[Claude Lévi-Strauss|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.

\hypertarget{the_original_formulation}{}\subsection*{{The original formulation}}\label{the_original_formulation}

In L\'e{}vi-Strauss (\hyperlink{LS55}{1955}, p.442) the canonical formula is introduced as the ``algebraic'' expression:

$^f x(a)\quad : \quad^f y(b)\qquad\cong\qquad ^f x(b)\quad :\quad^f a-1(y)$ .

\hypertarget{an_example}{}\subsection*{{An example}}\label{an_example}

\hypertarget{the_quaternionic_interpretation}{}\subsection*{{The quaternionic interpretation}}\label{the_quaternionic_interpretation}

[[Jack Morava]] (\hyperlink{Morava03}{2003}, \hyperlink{Morava04}{2004}) proposed to interpret the canonical formula as the existence of an anti-isomorphism of the [[quaternion group]].

\hypertarget{some_history}{}\subsection*{{Some history}}\label{some_history}

\hypertarget{related_entries}{}\subsection*{{Related entries}}\label{related_entries}

\begin{itemize}%
\item [[Claude Lévi-Strauss]]


\item [[kinship]]


\item [[structuralism]]


\item [[quaternion group]]


\item [[code loop]]



\end{itemize}
\hypertarget{related_pages}{}\subsection*{{Related pages}}\label{related_pages}

\begin{itemize}%
\item French wikipedia entry: (\href{https://fr.wikipedia.org/wiki/Formule_canonique_du_mythe}{link})

\end{itemize}
\hypertarget{references}{}\subsection*{{References}}\label{references}

\begin{itemize}%
\item Num\'e{}ro sp\'e{}cial \emph{La formule canonique des mythes} , L'Homme \textbf{35} no.135 (1995). (\href{http://www.persee.fr/issue/hom_0439-4216_1995_num_35_135}{link})


\item Maurice Godelier, \emph{L\'e{}vi-Strauss} , Seuil Paris 2013.


\item Jacques Lacan, \emph{Le mythe individuel du n\'e{}vros\'e{}} , Seuil Paris 2007.


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


\item [[Claude Lévi-Strauss]], \emph{The Structural Study of Myth} , J. American Folklore \textbf{78} no. 278 (1955) pp.428-444.


\item [[Claude Lévi-Strauss]], \emph{Antropologie Structurale} , Plon Paris 1958.


\item [[Claude Lévi-Strauss]], \emph{D'un oiseau \`a{} l'autre} , L'Homme \textbf{25} no.93 (1985) pp.5-12. (\href{http://www.persee.fr/doc/hom_0439-4216_1985_num_25_93_368539}{link})


\item [[Claude Lévi-Strauss]], \emph{La Poti\`e{}re Jalouse} , Plon Paris 1985.


\item Juan Pablo Lucchelli, \emph{Le mythe individuel revisit\'e{}} , L'information psychatrique \textbf{82} no.2 (2006) pp.155-158. (\href{http://www.cairn.info/revue-l-information-psychiatrique-2006-2-page-155.htm}{link})


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


\item Pierre Maranda (ed.), \emph{The Double Twist} , University of Toronto Press 2001.


\item [[Jack Morava]], \emph{On the Canonical Formula of C. L\'e{}vi-Strauss} , arXiv.0306174v2 (2003). (\href{http://arxiv.org/abs/math/0306174}{abstract})


\item [[Jack Morava]], \emph{Une interpr\'e{}tation math\'e{}matique de la formule canonique de Claude L\'e{}vi-Strauss} , Cahiers de L'Herne \textbf{88} (2004) pp.216-218.


\item [[Jack Morava]], \emph{From L\'e{}vi-Strauss to Chaos and Complexity} , in Mosko, Damon (eds.), \emph{On the Order of Chaos} , Berghahn Oxford 2005.


\item [[Jean Petitot]], \emph{Approche morphodynamique \`a{} la formule cannonique des mythes} , L'Homme \textbf{28} no.106-107 (1988) pp.24-50. (\href{http://www.persee.fr/doc/hom_0439-4216_1988_num_28_106_368968}{link})


\item A. Rapoport, \emph{Outline of a Probabilistic Approach to Animal Sociology} , Bull. Math. Biophys. \textbf{11} (1949) pp.183-196, pp.273-281.


\item Elisabeth Roudinesco, \emph{Jacques Lacan} , Fayard Paris 1993.


\item Ferdinand de Saussure, \emph{\'E{}crits de linguistique g\'e{}n\'e{}rale} , Gallimard Paris 2002.


\item Lucien Scubla, \emph{Lire L\'e{}vi-Strauss} , Odile Jacob Paris 1998.



\end{itemize}
[[!redirects canonical formula]] [[!redirects Canonical formula]] [[!redirects canonical formula of mythical transformation]] [[!redirects canonical formula for myth]]



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