Intercity Telephone and Airline Traffic Related to Distance and the "Propensity to Interact

Abstract

The relationship between spatial distance and the frequency of interactions (such as telephone calls, visits, or mail) has been the subject of several investigations in recent years. Best known are the studies by George Zipf (13, 14) John Stewart (9, 10), and Stuart Dodd (4, 5). Related to the same problem are various articles on migration and the many papers on residential propinquity as a factor in mate selection (3). Furthermore, traffic engineers have made similar studies which are usually not so well known among sociologists, and which often suggest the same formulas independently.2 These investigations evoked so much interest probably because they led to generalizations which seemed clearly defined, verifiable, and applicable to a great variety of phenomena-conditions not easily met in social science. The pioneers in this area, therefore, were tempted to build universal theories on their rather limited statistical evidence. Zipf, for example, concluded-on the basis of an imperfect statistical analysisthat there was a linear relationship between the frequency of interactions and distance. Then he proceeded to demonstrate theoretically why this relation had to be linear. However, upon closer scrutiny, neither his analysis nor other studies on this topic prove the existence of a linear relationship.' As will be shown below, our evidence suggests rather a nonlinear function. Actually, the rectification of the distance function may not be of great