A theory of heterogeneity?

Are Scale, Perspective, and Heterogeneity Unifying Ecology Science?

Last week during a roundtable the visiting scholar challenged us, as scientists in the geospatial realm, to think about the theory underlying our studies. They specifically mentioned further development of a “theory of heterogeneity.” I think that heterogeneity/homogeneity (dis/similarity) is a concept that transcends disciplines of science. The terms are two sides of the same coin, or maybe the same side of a one-sided coin – it depends on which one you want to measure.

Whether you subscribe to a reductionist or holistic approach to science you probably spend time splitting or grouping observations to understand the level of heterogeneity. Perhaps it seems obvious, but the degree of heterogeneity you detect in the system you are measuring is going to depend on the *perspective* of the measurement. The ultimate end of a reductionist approach seems to be finding the most homogeneous state (what then?), while a holistic approach would seemingly account for all the heterogeneity in the system simultaneously (even possible?). The debate about either a reductionist or holistic approach being the best way to understand a system seems nonsensical to me – you require both to find solutions and probably are using methods related to each approach simultaneously. So, maybe at best you can be a holistic reductionist (or whatever the vice-versa of that would be)?

I think that experience and training in geography and ecology can illuminate how perspective and heterogeneity are related, and how that relationship influences my understanding of the world. This is at least partly because I have spent time and received training on “thinking spatially.” For example, Tobler’s Law, the first (and only) “law” of geography, states:

“Everything is related to everything else, but near things are more related than distant things.” – Waldo Tobler

This leads me to expect that the amount of heterogeneity I am measuring will increase with the size of the area measured. On the face this seems correct, but I think it requires another piece, which is that this only holds true if the grain size of the measurement remains the same as the extent is expanded. Through physics I think this can be related to time, though it might be an inverse relationship where as the length of time over which the observations are made grows the more homogeneous the system becomes. This would be due to entropy and the 2nd Law of Thermodynamics(?).

I am no expert in theoretical physics and Tobler was an economist studying the growth and development of cities, but maybe there is something useful in trying to describe a general theory of heterogeneity. It may be a matter of perspective.

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