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

Introduction

• “The nebula-like cluster is a common trait in the spatial picture of man’s attributes.”
• No simple explanation…
• One process is important:  diffusion of techniques and ideas through the network of social contacts

The Neighborhood Effect
Diffusion – movement of innovation over space and time
Author sought to analyze spatial aspects of diffusion of innovations.  Ideal case:

• first introduction of innovation
• individual adopters and non-adopters can be discerned

Example innovation:  Two different farm techniques followed over 5 years

• Subsidy for improvd pasture-land on small farms (to encourage farmers to not use forests for grazing).
  • Of all eligible farms, First two years, 3 adopters…  7 more adopters in year 3… 9 in year 4… 5 in year 5
• Systematic control of bovine tuberculosis
  • All farms eligible
  • Spatial order, over time

Reactions of farmers for both innovations

• Adopters in more isolated areas step-by-step northward as time progresses

Literature has shown:

• “Nearness” plays a role – this pattern of a cluster of adopters, subsequent adopters are located closest to the original clusters from the next set (3rd year) of adopters
• patterns detectable at all scales (a hierarchy of scales)

The Network of Social Communication
Author will attempts to demonstrate this pattern of innovation adoption with theoretical experiments

• “… evident that nobody can adopt an innovation without first having gained knowledge of its existence”
• “adoption not immediate”
• Why aren’t the subsequent adopters hearing about the subsidy from the government (or mass media) rather than their neighbors?  The original adopters are able to show the subsequent adopters that the program works.  To address this issue, the author assumes one means of communicating innovation.
• Scalar effects
  • Three groups operating at local, regional and international scales
  • some operate locally, some operate locally and regionally, some operate at all 3 scales
  • “Those belonging to the wider range and having links in common with the lower ones form the channels through which information disseminates between levels

Telephone Traffic

• Telephone traffic as a proxy for face-to-face communication
• Longer distance phone calls can be inferred to have originated for “supplies” from central places
• Shorter distance phone calls are social/fraternal contacts
• Phone calls decrease with distance… the relative frequency of calls decrease very nearly with the square of the distance (Distance Decay function/Gravity models)

• Gravity models and trip distribution theory  (M Schneider – Papers in Regional Science, 1959)

Local Migration
Assumption: constant rates of local migration (Marriage, labor exchange, farm sales) and within existing framework of social connections

The Diffusion Model I
Monte Carlo:  A computational method where an existing pattern is approximated and a series of of sample sets are randomly and iteratively generated to simulate that pattern.  A model is then generated that uses each iteration of samples to comparing an empirical pattern to the simulated sets.

Revolution:  Adoption of physics model, Quantitative Revolution, access to computational methods, use of algorthmic methods to model an empirical pattern, foundation of GIScience, discerning social patterns through individualized activities rather from an aggregate point of view

Input Data I
Local Migration

Direct comparison with empirical pattern in generalities only as simulation is idealized, but provides us with a way to study to variations of outcomes on an isotropic surface.
Suggestion to model on a plane that has some irregularities:  unevenly distributed population and barriers to communication

Input Data II

• Telephone samples
• Sample grid framework expanded so that “bouncing” of adoption could be modeled
• Each cell assigned a probablity so that cells with many inhabitants have a greater likelihood of being adopted and into account for barriers to communication
• Adopters near barriers were less influential as they have fewer contacts
• Instead of one adopter from first simulation, 22 potential adopters were chosen and approximated the empirical pattern of eligible farms

Comparisons Between Simulation and Empirical Data

• Raw numbers not useful, so isolines are based on percentage of adopters (even though base is raw population base is small)
• In Figure 7 (graphs), we see that percentages of adopters to potential adopters shows a negative relationship.  as the percentage of potential adopters increases, the percentage of adopters decrease.

Conclusion:  The simulation approximates the empirical observations

Questions that you should be ready to answer after reading Torsten Hagerstrand’s “Monte Carlo Approach to Diffusion”.

• If you were asked to write one sentence describing the subject matter of this paper, what would you write?
• In which of the major research traditions in geography would you place this paper?
• Does this paper differ in important ways from most other papers in this research tradition published around this time?
• Could this article have been written in 1955 rather than in 1965?
• What geospatial data, abstractly defined, does Hagerstrand say is essential for a researcher to have to conduct research in the area he describes?
• Does Hagerstrand have anything to say about predicting future spatial distributions?
• What are the different roles that empirical evidence plays in this paper?
• What are the issues Hagerstrand faced in testing the results of his model?
• What other disciplinary sources can you recognize as contributing significant ideas to this paper—other than geography?
• Are there other questions you think are important in evaluating this paper?