Tobler's first law of geography

The First Law of Geography, according to Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things."^[1] This first law is the foundation of the fundamental concepts of spatial dependence and spatial autocorrelation and is utilized specifically for the inverse distance weighting method for spatial interpolation and to support the regionalized variable theory for kriging.^[2]

Tobler first presented his seminal idea during a meeting of the International Geographical Union's Commission on Qualitative Methods held in 1969 and later published by him in 1970. Though simple in its presentation, this idea is profound. Without it, "the full range of conditions anywhere on the Earth's surface could in principle be found packed within any small area. There would be no regions of approximately homogeneous conditions to be described by giving attributes to area objects. Topographic surfaces would vary chaotically, with slopes that were everywhere infinite, and the contours of such surfaces would be infinitely dense and contorted. Spatial analysis, and indeed life itself, would be impossible."^[3]

Less well known is his second law, which complements the first: "The phenomenon external to an area of interest affects what goes on inside".^[4]

Foundation and background

The theory is based upon the concept of the friction of distance "where distance itself hinders interaction between places. The farther two places are apart, the greater the hindrance",^[5] or cost. For example, one is less likely to travel across town to purchase a sandwich than walk to the corner store for the same sandwich. In this example hindrance, or cost, can readily be counted in time and transportation costs which are added to the price of the purchase and thus result in high levels of friction. The friction of distance and the increase in cost combine causing the distance decay effect.

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