This article demonstrates how innovations are diffused via “face-to-face” social networks.  Its primary method is a probabilistic Monte Carlo algorithm to simulate, and approximate, an observed pattern of innovation adoption.  In this case, Hagerstrand studies two farm subsidy programs in Sweden and traces the pattern of their adoption over space and time.

As a side note, Hagerstrand’s body of work after this paper deal with both the temporal aspects of analysis and an attempt to discern social pattern by examining the activities of a group of individuals rather than an aggregation of the group’s social patterns.  (“What about People in Regional Science?” 1970). Both themes are present in “A Monte Carlo Approach to Diffusion”.

Considering the 1965 publication, and its quantitative nature, a few research themes emerge.  First, the paper is published in The European Journal of Sociology, not Geography.  This would suggest that established Geographers had not fully entered into the mindset that Geography could be used to analyze a variety of subject matter in the social sciences.  Beyond a generalized entry into the social sciences, Hagerstrand aligns himself with that contemporary embrace of quantitative methods and scientific rigor in Geography during the late 1950’s and early 1960’s.  Additionally, he follows the trend of time for social scientists to borrow concepts found in the canon of chemistry and physics.  His nod to chemistry is quite overt by using “diffusion” in his title.  His discussion of physics is more subtle.  For example, in describing the frequency of telephone calls with respect to distance he states on page 371 that “… the relative frequency of calls decreases on average very nearly with the square of the distance.”   This is the distance decay parameter found in the definition of Newton’s formulation of gravity.

The access of computational methods in the 1960s, coupled with a need for scientific rigor and quantification positions Hagerstrand as an early leader in the foundations of Geographic Information Sciences.  The particular innovation was a Monte Carlo methodology, developed in the body of statistics literature, to study of geographic patterns with social implications.  His reliance on probabilistic methods and the use the use of computation methods to analyze geographic distributions reverberates to this day.  For example, in the 1990s, Monte Carlo methodologies were used to stabilize outcomes found in aggregations the Modifiable Areal Unit Problem.

Hagerstrand faced many problems while testing the results of his models.  The computational requirements to develop simulations that are more advanced were not available at the time.  Additionally, he notes at the time of publication, no one had carried out a simulation allowing for direct comparison of an observed pattern.  He describes this problem in both simulations.  In his first test, even with his assumptions of a uniform population distribution, no barriers to communication, and single adopter in the first generation, a pattern emerges that is visually similar to that of the observed pattern.  However, the results are too generalized for direct comparison.  He says the same thing about the second simulation, which did factor the uneven population distribution, barriers to communication and the observed three adopters of the bovine tuberculosis subsidy into the simulation.

Hagerstrand believes the spatial data required for this analysis is the location of the adopters and the universe of eligible adopters.  In addition, a gridded framework of areal units is required so that both the observed and simulated data can be, in modern terminology, georeferenced.  Additionally, probabilities based on observed population and barriers to communication are necessary in approximating the empirical pattern.  The location of telephone calls and their receivers and a “to-from” matrix of intra-region migratory patterns, are necessary data for understanding the social network of “face-to-face” communication of innovations.

In this paper, two distinct pieces emerge that reinforce each other.  The first is the analysis of a social hypothesis that the “diffusion of techniques and ideas (…occur…) through the network of social contacts.”  The second is a well-developed methodology for analyzing the hypothesis.  The discipline of Geography had not seen this methodology and this paper helped solidify the use in of computational techniques in general and Monte Carlo techniques in particular.

Outline below the fold

» Read more: Review: A Monte Carlo Approach to Diffusion – Torsten Hagerstrand