Single-Variable Theories: Examples

Fri, 21 Apr 1995 11:26:17 CST

B. D. Hume calls for examples of explanations of one variable in terms
of one other one. (At least, I hope this is an acceptable gloss, since
the concept of causality is such a morass.) I am happy to oblige. The
period of a simple pendulum is explained by the length of the pendulum.
Specifically, the period is proportional to the square root of the
length; when length is measured in meters, period in seconds, theconsta
not of proportionality is two.Therefore we explain the fact that a given
pendulum has a period of six seconds by reference to the law; the
stipulation that our pendulum is a simple one; and that its length is
nine meters (2 X sq. rt. of 9 equals 2 x 3 = 6). This law, devised by
Galileo, later was itself explained by subsumption under laws devised
by Newton. In anthropology, a good example is Robert Carneiro's
explanation of political evolution in terms of a single variable:
warfare over scarce agricultural land. Actually, though it is a "good"
example, it lacks rigor--a problem I have worked on a lot. A very nice
single-variable theory can be formulated, in which the number of people
per society is theorized to increase with the square of population
density; warfare is merely the main mechanism by which density produces
political integration. My littlebook presenting this in detail is just
out; I would gladly send ordering information to anyone who craves
theoretical rigor and can stomach elementary algebra! --Bob Graber