others face when devolving political power is determining the critical limit
between successfully decentralizing authority, or undermining the geographic
integrity of the state.
Distance Decay
Distance decay is a concept linking geography and the occurrence or frequency of
a pattern of activity. Some literature uses the term “distance lapse rate” to identify
this connection. The underlying principle is that any phenomenon or influence
diminishes in intensity as the distance from the point of origin increases. This is
due to the effect offriction of distance. The concept is enshrined in the geogra-
pher Waldo Tobler’s famous dictum that all things are related, but those that are
nearest to one another are more related than those located at a greater distance.
Distance decay is an important precept of spatial analysis, especially forspatial
interaction modelsand notions ofcultural diffusion. Distance decay is inherent
in various applications of gravity models in economic and urban geography and
underlies some of the fundamental theoretical models in these subfields of geogra-
phy, including Christaller’sCentral Place Theoryand theVon Thunen modelof
agricultural development. Gravity model theorists, for example, suggest in their
simpler propositions that a precise mathematical relationship exists between the
strength of a spatially expressed phenomenon and the distance over which it is dis-
tributed, in a formula closely akin to Isaac Newton’s equation defining gravita-
tional force. Whereas Newton proposed that the force of gravity is directly
proportional to the mass of the objects in question and a mathematical constant, di-
vided by the square of the distance between them, geographers using gravity
theory in their work attempt to construct a similar model analyzing labor or trade
flows, transportation, shifts in population, diffusion of languages, religions, tech-
nologies, etc. Just as Newton’s theorem postulates that the force of gravity
between two objects declines with distance, so too do gravity models in geogra-
phy, based on the concept of distance decay. A simple example would be a model
that attempts to gauge the influence of German as a first language used in business
transactions. Such a model would likely show a high degree of use in Germany
(center of gravity), with moderate use in surrounding countries in Europe (weak-
ening gravity with distance from the center), and little use in North America or
Africa (decay of gravitational influence with distance). More sophisticated
approaches attempt to integrate a geometric component into the model, because
in real world applications the rate of decay with distance is dependent to some
Distance Decay 103