The Validity and Usefulness of Laws in GIS and Geography

This article first briefly described GIS, gave us an account of general laws in GIS and geography, compared and contrasted GIS and geography, then discussed:
1) The validity of Tobler’s First Law
2) Its role in GIS and geography 
3) The possibility of additional laws 
4) The possibility of extending Tobler’s First Law outside GIS and geography

When GIS is considered a location science and not a tool used in the development of technologies, disagreement about what makes a principle of GIS a law becomes relevant.  Some say that a law must be without any counterexamples, and expectations for laws vary across the sciences.  For example, in the social sciences it’s largely impossible to create a purely deterministic law that a human can never violate.  This is why history is unpredictable in certain ways, as are market forces.  In these circumstances, principles are used as norms against which reality is compared in order to simplify our thinking about systems that might be otherwise incomprehensible.  The author tells us that “GIS focuses on how the world looks, and not how it works” – this is a simplification for the purposes of initiating GIS newcomers, as any application of GIS will be integrating GIS into a model of how the world works. 

Tobler’s First Law: closer things are more related.

This law can be read as form (related = similar) or process (related = mechanistic); this article focused on form.  The author asks us to imagine a world in which this law is not true – one version of this is that all spaces would contain other spaces – and takes this to be evidence that TFL is obvious and common sense. 

Tobler's First Law underlies many aspects of GIS design:

1) The characterization of complex geographic landscapes using a high degree of generalization, such as large polygons representing large homogeneous regions

2) The representation of surfaces using isolines

3) The reliability of spatial interpolation, resampling, contour mapping, and all other procedures involving inferring complete surfaces from a set of finite distribute measurements

4) Why it’s possible to rely on GIS data bases to provide accurate estimates of relative location or relative elevation 

d    5) All important GIS data models

These are a few of the other possible laws the author discusses:

1) The principle of spatial heterogeneity

a. geographic variables exhibit uncontrolled variance - one can find any extreme condition if one searches far enough or waits long enough
b. the result of spatial analysis will change if the study area is moved

3     2) Uncertainty principle  

a.     the geographic world is infinitely complex and any representation must contain elements of uncertainty

One may extend Tobler’s First Law by asking whether it’s applicable to other spaces such as the number pi, the spaces being created by the internet, or the “small-world” spaces of social (rather than spatial) interaction.

Goodchild, Michael F.  (2004).  The Validity and Usefulness of Laws in Geographic Information Science and Geography.  Annals of the Association of American Geographers,  94(2), 300-303.