Demographic Gravitation
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Demographic gravitation is a concept of "social physics", introduced by
Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...
astrophysicist
John Quincy Stewart John Quincy Stewart (September 10, 1894 – March 19, 1972) was an American astrophysicist. He obtained his Ph.D. in physics from Princeton University in 1919. He taught astrophysics at Princeton from 1921 until he retired in 1963. Stewar ...
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 is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major paradigm shift, then the ...
, such as
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
, to seek simplified insights and even laws of
demographic Demography () is the statistical study of populations, especially human beings. Demographic analysis examines and measures the dimensions and dynamics of populations; it can cover whole societies or groups defined by criteria such as ed ...
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 relationships. It was developed by psychotherapist Jacob L. Moreno and Helen Hall Jennings in their studies of the relationship between social structures and psychological well-being, and u ...
'', 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 be ...
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 phenomena a ...
viewpoints in the methodology of formulating
physical laws Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) ...
, he made an analogy with the
social sciences Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of so ...
:
Fortunately for physics, the macroscopic approach was the commonsense one, and the early investigators Boyle, Charles,
Gay-Lussac Joseph Louis Gay-Lussac (, , ; 6 December 1778 – 9 May 1850) was a French chemist and physicist. He is known mostly for his discovery that water is made of two parts hydrogen and one part oxygen (with Alexander von Humboldt), for two laws ...
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 relationships. It was developed by psychotherapist Jacob L. Moreno and Helen Hall Jennings in their studies of the relationship between social structures and psychological well-being, and u ...
: : 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
economic rent In economics, economic rent is any payment (in the context of a market transaction) to the owner of a factor of production in excess of the cost needed to bring that factor into production. In classical economics, economic rent is any payment m ...
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
/ref> 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 matches ...
: 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 Geo ...
*
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.He "ranks alongside Marx as the greatest Ge ...
'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 Geo ...
*
Alfred Weber Alfred Weber (; 30 July 1868 – 2 May 1958) was a German economist, geographer, sociologist and theoretician of culture whose work was influential in the development of modern economic geography. Life Alfred Weber, younger brother of the ...
's least cost location theory. *
Economic rent In economics, economic rent is any payment (in the context of a market transaction) to the owner of a factor of production in excess of the cost needed to bring that factor into production. In classical economics, economic rent is any payment m ...
: Land rent. *
John Quincy Stewart John Quincy Stewart (September 10, 1894 – March 19, 1972) was an American astrophysicist. He obtained his Ph.D. in physics from Princeton University in 1919. He taught astrophysics at Princeton from 1921 until he retired in 1963. Stewar ...
, 1947. Empirical Mathematical Rules Concerning the Distribution and Equilibrium of Population, Geographical Review, Vol 37, 461–486. *
John Quincy Stewart John Quincy Stewart (September 10, 1894 – March 19, 1972) was an American astrophysicist. He obtained his Ph.D. in physics from Princeton University in 1919. He taught astrophysics at Princeton from 1921 until he retired in 1963. Stewar ...
, 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