Demographic Gravitation
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Demographic gravitation is a concept of "social physics", introduced by
Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...
astrophysicist John Quincy Stewart in 1947.Stewart, John Q., "Demographic Gravitation: Evidence and Applications," ''Sociometry'', Vol. 11, No. 1/2. (February–May 1948), pp. 31–58. It is an attempt to use equations and notions of
classical physics Classical physics refers to physics theories that are non-quantum or both non-quantum and non-relativistic, depending on the context. In historical discussions, ''classical physics'' refers to pre-1900 physics, while '' modern physics'' refers to ...
, such as
gravity In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...
, to seek simplified insights and even laws of
demographic Demography () is the statistics, statistical study of human populations: their size, composition (e.g., ethnic group, age), and how they change through the interplay of fertility (births), mortality (deaths), and migration. Demographic analy ...
behaviour for large numbers of human beings. A basic conception within it is that large numbers of people, in a city for example, actually behave as an attractive force for other people to migrate there. It has been related to W. J. Reilly's law of retail gravitation, George Kingsley Zipf's Demographic Energy, and to the theory of trip distribution through gravity models. Writing in the journal ''
Sociometry Sociometry is a quantitative method for measuring Social relation, social relationships. It was developed by psychotherapy, psychotherapist Jacob L. Moreno and Helen Hall Jennings in their studies of the relationship between social structures an ...
'', Stewart set out an "agenda for social physics." Comparing the
microscopic The microscopic scale () is the scale of objects and events smaller than those that can easily be seen by the naked eye, requiring a lens or microscope to see them clearly. In physics, the microscopic scale is sometimes regarded as the scale betwe ...
versus
macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenome ...
viewpoints in the methodology of formulating
physical laws Scientific laws or laws of science are statements, based on reproducibility, repeated experiments or observations, that describe or prediction, predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, a ...
, he made an analogy with the
social sciences Social science (often rendered in the plural as the social sciences) is one of the branches of science, devoted to the study of society, societies and the Social relation, relationships among members within those societies. The term was former ...
:
Fortunately for physics, the macroscopic approach was the commonsense one, and the early investigators Boyle, Charles, Gay-Lussac were able to establish the laws of gases. The situation with respect to "social physics" is reversed... If Robert Boyle had taken the attitude of many social scientists, he would not have been willing to measure the pressure and volume of a sample of air until an encyclopedic history of its molecules had been compiled. Boyle did not even know that air contained argon and helium but he found a very important law.
Stewart proceeded to apply Newtonian formulae of gravitation to that of "the average interrelations of people" on a wide geographic scale, elucidating such notions as "the demographic force of attraction," demographic energy, force, potential and gradient.


Key equations

The following are some of the key equations (with plain English paraphrases) from his article in
sociometry Sociometry is a quantitative method for measuring Social relation, social relationships. It was developed by psychotherapy, psychotherapist Jacob L. Moreno and Helen Hall Jennings in their studies of the relationship between social structures an ...
: : F = \frac (''Demographic force = (population 1 multiplied by population 2) divided by (distance squared)'') : E = \frac (''Demographic energy = (population 1, multiplied by population 2) divided by distance; this is also Zipf's determinant'') : PN_1 = \frac (''Demographic potential of population at point 1 = population at point 2, divided by distance'') : P = \frac (''Demographic potential in general = population divided by distance, in persons per mile'') : \text = \frac (''Demographic gradient = persons per (i.e. divided by) square mile'') The potential of population at any point is equivalent to the measure of proximity of people at that point (this also has relevance to
Georgist Georgism, in modern times also called Geoism, and known historically as the single tax movement, is an economic ideology holding that people should own the value that they produce themselves, while the economic rent derived from land—includ ...
economic rent In economics, economic rent is any payment to the owner of a factor of production in excess of the costs needed to bring that factor into production. In classical economics, economic rent is any payment made (including imputed value) or bene ...
theory Economic rent#Land rent). For comparison, Reilly's retail gravity equilibrium (or Balance/Break Point) is paraphrased as: : \frac = \frac (''Population 1 divided by (distance to balance, squared) = Population 2 / (distance to balance, squared)'') Recently, a stochastic version has been proposedRybski, Ros, Kropp "Distance-weighted city growth", Physical Review E, Vol 87 (2013), p. 042114, doi:10.1103/PhysRevE.87.042114 according to which the probability p_j of a site j to become urban is given by : p_j=C\frac where w_k=1 for urban sites and w_k=0 otherwise, d_ is the distance between sites j and k, and C controls the overall growth-rate. The parameter \gamma determines the degree of compactness.


See also

* Reilly's law of retail gravitation *
Trip distribution Trip distribution (or destination choice or zonal interchange analysis) is the second component (after trip generation, but before mode choice and route assignment) in the traditional four-step transportation forecasting model. This step matche ...
: gravity model * George Kingsley Zipf's demographic energy *
Central place theory Central place theory is an urban geographical theory that seeks to explain the number, size and range of market services in a commercial system or human settlements in a residential system.Goodall, B. (1987) The Penguin Dictionary of Human G ...
*
Johann Heinrich von Thünen Johann Heinrich von Thünen (24 June 1783 – 22 September 1850), sometimes spelled Thuenen, was a prominent nineteenth-century economist and a native of Mecklenburg-Strelitz, now in northern Germany. Even though he never held a professorial p ...
's spatial economics * Walther Christaller's
central place theory Central place theory is an urban geographical theory that seeks to explain the number, size and range of market services in a commercial system or human settlements in a residential system.Goodall, B. (1987) The Penguin Dictionary of Human G ...
*
Alfred Weber Carl David Alfred Weber (; 30 July 1868 – 2 May 1958) was a German economist, geographer, sociologist, philosopher, and theoretician of culture whose work was influential in the development of modern economic geography. His other work ...
's least cost location theory. *
Economic rent In economics, economic rent is any payment to the owner of a factor of production in excess of the costs needed to bring that factor into production. In classical economics, economic rent is any payment made (including imputed value) or bene ...
: Land rent. * John Quincy Stewart, 1947. Empirical Mathematical Rules Concerning the Distribution and Equilibrium of Population, Geographical Review, Vol 37, 461–486. * John Quincy Stewart, 1950. Potential of Population and its Relationship to Marketing. In: Theory in Marketing, R. Cox and W. Alderson (Eds) ( Richard D. Irwin, Inc., Homewood, Illinois). * Zipf, G. K., 1946. The P1 P2/D Hypothesis: On the Intercity Movement of Persons. American Sociological Review, vol. 11, Oct * Zipf, G. K., 1949. Human Behaviour and the Principle of Least Effort. Massachusetts


References

{{DEFAULTSORT:Demographic Gravitation Demography