Beyond formalism: Group theory in the symmetries of culture

This paper addresses group‐theoretic isomorphisms which have been exploited in theories of prescriptive kinship, classifications in cosmology, and repeating patterns in visual design. Some of the isomorphisms extend to more than one type of institution and include common devices of reduction to homomorphic images.

Substantive explanations have emphasised either the mind and cognition or social practices.

The theory proposed here requires generative processes in both cognition and institutionalisation. Cognitive capacity, defined as formal operational thought, is only a necessary background condition, and the theory depends on abstract conceptual properties of diverse practices. Competence can be specified at this abstract level in terms of the limited possibilities for combining different types of transitions.

Notes

I thank Emily Lyle for her enthusiasms in these matters, for inviting me to the “Three Axes and Eight Sections” Symposium, and for comments on an early draft of this paper. I thank Patrick Doreian and three referees for advice and constructive comment. My thanks are due also to T. Marshall for preparation of the manuscript. Parts of the arguments have been taken from Lucich (1987), (1989a) and (1989b) which provide analyses and evidence in greater elaboration.