Mathematical Modeling in the Social and Life Sciences

CHAPTER 12

Two Models of Cultural Stability

Anthropology needs mathematics, not because mathematics is glamorous these days, but because mathematics can help anthropologists . . . solve the kinds of problems anthropologists want to solve.

—Paul Kay

I. Introduction

Communities of people cannot long survive unless the basic needs of the inhabitants are met. In a rudimentary “society” each individual might take care only of his own requirements. He would find food, gather and prepare it, build his own shelter, and provide his own entertainment, medical care, and transportation. In most societies, however, people are dependent on one another for various goods and services. There is a division of labor among the residents. One person or group of persons specializes in constructing houses while another harvests the crops. Certain members debate and modify the laws, while others ensure that violators are apprehended and punished.

Furthermore, the obligations and the privileges of a single member of the society are different at different stages of the person's life. The social and economic contributions to the community of a 7-year-old, for example, vary from that of a 47-year-old. These in turn are not the same as those of a person of age 77.

Other factors besides age are often important in determining what is expected of an individual or what she is allowed to do. The person's gender, race, sexual orientation, religion, and perhaps even height and weight can control what occupations ...