ARTICLES: Studying Cognition in Flux: A Historical Treatment of Fu in the Shifting Structure of Oksapmin Mathematics

This article extends a framework for the study of culture–cognition relations to problems of historical research and diachronic analysis. As an illustrative case, we focus on mathematics in Oksapmin com-munities located in a remote highland area in central New Guinea. The Oksapmin, like their neighbor-ing Mountain-Ok groups to the West, traditionally use a 27-body-part counting system for number, and there is no evidence that Oksapmin used arithmetic in prehistory. We present a coordinated analysis of shifts in functions of a word form based on field studies completed in 1978, 1980, and 2001. These shifts are related to changing collective practices of economic exchange in which arithmetical activi-ties are increasingly important. The word form fu has changed from its use as an intensive quantifier that means “a complete group of plenty ” to one that means double a numerical value. We show how the analytic framework affords a multilevel inquiry into genetic processes of change in the Oksapmin case and argue that the approach is useful for understanding the interplay between cultural and developmen-tal processes in cognition more generally. PROLOGUE In June 2001, four of us left Berkeley for two Oksapmin valleys located in the highlands of central