Kinship networks and discrete structure theory: Applications and implications

Abstract

Confusions between substantive and relational concepts of kinship as a social network have led to a number of problems that are clarified by a temporally ordered relational theory of network structure. The ordered-network approach gives rise to a novel means of graphing the social field of kinship relations, while allowing kinship to be locally defined in culturally relative terms. Its utility is exemplified in applications to kinships among US Presidents, Old Testament Canaanites, and native Australians of Groote Eylandt. The formal concepts treated in the mapping of kinship networks are: kinship axioms, parental graph structure, core, circuits of consanguineally and affinally linked kin, sides and divides, homeomorphic mappings, homomorphisms as potentially simplifying mappings of kinship, elementary structure, and order-structure. Representational theorems are proven about homeomorphisms, cores and circuits, and the ambiguity of elementary structures. The last set of theorems leads to clarifying and redefining some of the basic concepts of elementary, semi-complex and complex structures of kinship in terms of properties of generationally ordered networks. The conclusions of the formal argument are 'post-structural' in the narrow sense of demonstrating the need for specifying contingent historical processes in the structural analysis of kinship as a social field. The open-ended approach to change, one that is implied by the study of ordered structures that unfold in a temporal succession, connects to issues of population variability, selection, and evolutionary processes. The kinship structures that are mapped in this approach are not intended as any sort of complete representations of kinship 'systems', but merely as scaffoldings that help to bring into view kinship as a social field, providing a baseline for other mappings (which may be superimposed) of social processes such as communicative fields, exchange processes, transmission of learned behaviors, social rights and inheritance, political and religious succession, and the like.

The grounding of computational psychoanalysis: A comparative history of culture overview of Matte Blanco bilogic

“…Indeed, the elusive-allusive-illusive modality, the incrustations of rhetorical figures, the kaleidoscopic erudition, the intentional ambiguity, the grandiose expression, the perverse echoes of past authors, the oblique irony, the disdain of logical sequence, the humour and sarcasm, are all forms of an affected and precious modality with which Lacan wanted to deliberately show, with his celebrated verbal eloquence, what perverse manners are used by the unconscious to manifest itself. 21 In this regard, see also what is said in section 5. of the preface, by…”

“…double bind, and all that Following [21], it was André Weil and Robert R. Bush to give, starting from Murngin system, a first attempt to formalize kinship by means of permutation group structures, exposed in a very interesting appendix to chapter XIV of the celebrated Claude Lévi-Stauss 1949 work Les Structures Élémentaires de la Parenté; see also [22]. While the empirical cultural content remains to be filled in, the problem of formal representation of kinship is concerned with the relations or orderings between culturally given unions such as reproductive or other types of matings, not the cultural characteristics of the unions themselves.…”

“…On the other hand, the Matte Blanco epistemological program consists just in searching to explain unconscious phenomenology by means of rational thought. Therefore, in this only apparently contradictory sense, the Lauro-Grotto formal view must be understood, based on ultrametric spaces 21 . In any case, this last 18 Like in apprehension.…”

The Anthropology of Family Business: An Imagined Ideal

“…(Stewart & Miner, 2011). What is the relationship between kinship and other relations, such as economic, religious or political (White & Jorion, 1996)? These questions have long been debated.…”

Les anneaux matrimoniaux : une approche formelle

“…A pgraph (cf. [White;Jorion 1992Jorion , 1996White 1997;Brudner, White 1997;White, Schweizer 1998;Harary, White 2001] is a multigraph with two arc classes which can be derived from a canonical k-graph by defining a p-node for each couple of edge-adjacent k-nodes as well as for each k-edge-isolate, and by defining an arc between two p-nodes whenever there is at least one arc between the corresponding k-nodes, where two p-arcs are of the same class if the corresponding k-nodes point to nodes of the same Linknodes _(G a ) = 2(n -n*) -n + c = n -2n* + c and _(S) = _(G a ) + n* -c, so that the cyclomatic number of a regular k-graph is independent of the number of edges. Removal of all edges of a matrimonial ring thus necessarily decomposes it into a number of trees which, since there are no more partner nodes, are all ancestral trees.…”