Structure and Dynamics

Introduction to the Special Issue on "Formalization as a tool for empirical research: what it buys us and what it doesn't.”

In this article, I present an analysis of the results of a memory task (free listing) about social relationships administered to Tongans of Polynesia. Contrary to claims by Weller and Romney (1988) and Ross (2004), the free listing activity did not yield the expected results, i.e., salient social individuals occupying positions at the top of the list. The strategy used to report the village population was prominently spatial. Besides, the analysis of accurate geographical renditions of the memory lists (memory routes), revealed spatial strategies in line with the preferences already documented about spatial relationships (Bennardo, 2000a, 2002b). A discussion of the implications of such findings for an hypothesized Tongan foundational cultural model closes the article.

Experimental economics and bounded rationality are very different from one another, but both claim to offer a more general and more empirical type of economic theory. Experimental economists, in addition, claim that their game-theoretic analyses provide rigorous, calculable, inferences from individual decisions to society as a whole. They claim to be describing the basis of social stability, although the argument depends on a unitary conception of “society” that ethnologists have now largely rejected. Both groups view rationality as inherently or originally individualistic and “utility maximizing” rather than inherently or originally social—albeit for entirely different reasons. Neither recognizes rationality as inherently bound up with organizations. These views have no basis in ethnography and are sharply in conflict with the stress on local knowledge in the most successful contemporary development policies. A crucial empirical issue is the nature and power of indigenous decision algorithms. The economists treat them as non-existent, insignificant, or erroneous. I show that they are organizationally situated and part of the organizational process, genuinely optimizing, and the basis of cultural ecological adaptation. Moreover, it is this external adaptation, not an internal game-like system of self-perpetuating rules, that is the ultimate basis of social stability, as well as dynamism.

Two kinds of formal models need to be distinguished: data models derived from patterned observations and theory models derived from theories about processes that produce the patterned observations. These correspond to the difference between the phenomenal domain of observations and the ideational domain of theories. Explanation can be characterized by isomorphism between data models and theory models. The physical, biological and cultural domains differ by what constitute the relevant structuring processes for each of these domains. The cultural domain associated with human societies is far more complex than the other two because the domain of observation must include cultural idea systems. One of the primary roles of formal models for cultural idea systems is to determine the necessary consequences (through mathematical reasoning) of processes hypothesized to provide their internal coherency.

I am concerned with the distinction between data processing, modeling and actual theory formation, with the generating of empirically interpretable additional theorems, and in particular how formalization, far from abstracting away from data, makes one look at levels of detail one never before even noticed.

I shall begin by examining a conjecture (due to my pupil Zhang Wenyi) about the formalism for distinguishing crowds and ‘groups’ from corporations/corporateness: the former are what I may call event-theoretical topologies (neighborhoods) event theory having to do with temporal-aspectual-modal categories, on which I have written elsewhere. In turn, this has everything to do with the whole controversial question of fuzziness, which I shall go into here. I shall argue that so-called fuzzy sets are topologies, particularly having to do with the saliency of the ‘extent’ of a field, such that, as Zadeh, the originator of Fuzzy Set theory, himself long since pointed out, fuzziness is essentially a matter of Decision Theory rather than a theory defining a species of conceptual categories as such. This, in turn, leads me into a brief consideration of set topology, namely the distinction between open and closed sets and so on with regard in particular to events. This is all about inclusion, exclusion and well-boundedness.

The foregoing will take me into a consideration of a certain problem in kinship-group theory, namely, whether one can properly talk of cognatic (‘non-unilineal’) ‘descent groups’. The solution, again, depends upon reconsideration of the role of ‘choice’ (decision-theoretically understood) in the theory of kin-groupings and thus the matter of defining ‘modes of lineation’ in the space of genealogical reckoning, and thus in turn the whole theory of ‘descent’ itself. Here my foil is the work of Fortes, of course.

Finally, I want to adduce a specific example of the way a formal theory of the map from Primary Genealogical Space (PGS) to a particular system of kin-categorization (and terminology) has led directly to a theorem that clarifies a hitherto controversial idea, namely Fortes’s notion of ‘complimentary filiation’ in the context of his argument against ‘alliance theory’ in the sense of Leach. It turns out that this matter is resolved by a theorem of the formal account of an asymmetric-alliance terminology.

Formalization is typically associated by both supporters and detractors of formal methods with an emphasis on form over content or meaning. However well founded, this association fails to capture why we employ (or not) formal descriptions of what we are describing.

One problem arises when we try to directly link human thought to human behavior (or vice versa); assuming the process of going from one to the other is complex and idiosyncratic, but direct. In this paper I examine an approach to developing a formal system that helps us represent the relationship between ideational and behavioral aspects of socio-cultural phenomena in a manner that is consistent with, and helps address the connections between, symbolic and materialist approaches.

People embedded in cultural processes demonstrate remarkable powers of creation, transformation, stability and regulation. Culture gives agents the power to hyper-adapt: not only can they achieve local minima and maxima, they modify or create the conditions for new adaptations. Culture transcends material and behavioral contexts. Cultural solutions are instantiated in material and behavioral terms, but are based in large part on ‘invented’ symbolic constructions of the interaction space and its elements. We will present an example of how a symbolic system 'drives' the material organization of human groups, explore how symbolic systems act over material domains as a general case, and examine some of the implications of this for multi-agent modelling as a theory-building process.

From Darwin’s time in biology and even before Darwin in linguistics, the tree diagram has been the primary formal depiction of descent. The underlying logic of the dendrogram depends on a branching process: units fission, then diversify through time. This model of differentiation is generally correct for the evolution of species, languages, and genes. However, at the level of human populations, subject to the ramifying effects of gene flow and natural selection, a better model is a reticulating network. This paper will critically examine genetic dendrograms based on “classical” loci as well as mitochondrial DNA in the context of the history of Malaysian Orang Asli populations.

Models of theoretically generated relations among analytic entities have formal properties which enable them to accurately represent some desired relationships, but not necessarily all imaginable relationships. One important part of the modeling task is matching the properties of the model type with the relevant formal properties that one ascribes to the relationships being modeled. Some kinds of mismatches render the model type inappropriate for the given use while others may make it inadequate.

As an example: Tree models can represent “descent” relations among languages. They presume languages have single parents but possibly multiple children—entailing a distinction between elements present through descent and elements “borrowed” or otherwise created. Their interpretation typically includes assuming a smooth temporal transition from minimal dialect differences to separate languages. Two other change processes, interpretable within a family tree but not modeled by it, are: 1) the creation of pidgins and 2) the hiving off of a cross-section of a language community to form a new, contrasting language community. By contrast, a multiple parents claim would be incompatible with the tree model.

Galton’s Problem is one of identifying functional relationships in a set of observations where the observations may be related through borrowing or descent. The problem has long been recognized in the fields of anthropology and cross-cultural research, but has been neglected in economics, even in cases where it is likely to be most acute, such as in regression models where each observation is a nation. The appropriate treatment for Galton’s Problem was developed in the 1980s by Malcolm M. Dow, Douglas R. White, and Michael L. Burton. Their solution is to estimate spatial models, where weight matrices for physical distance control for relationships of borrowing, and weight matrices for linguistic similarity control for relationships of descent. This paper documents a method for estimating a weight matrix based on language phylogenetic relationships. The method is applied to the 186 cultures of the Standard Cross-Cultural Sample, and applied to a set of 216 nations. The resulting weight matrices are made available for any researchers wishing to control for Galton’s Problem.