The Dictionary of Human Geography

activating the disjunctures and displace-
ments between different voices and voca-
bularies, and so ensuring that theoretical
work is ‘relentlessly transformative’ and
elaborates ‘lines of escape’.
(2) There has been a parallel debate about
the capacity of any single theoretical sys-
tem to account for the world (cf.essen-
tialism; foundationalism). Many,
perhaps most, human geographers seem
to accept: (a) that no single theoretical
system can possibly ask all the interesting
questions or provide all the satisfying
answers; and (b) that most scholars ne-
cessarily work in the spaces between over-
lapping, often contending theoretical
systems, which redoubles the importance
of theoretical critique to clarify disson-
ances, reveal erasures and evaluate con-
sequences (Gregory, 1994, pp. 100–6).
But these nostrums have neither soothed
geographers’ anxieties nor dispelled their
ambitions. Much of the controversy at-
tached to Harvey’s historico-geographical
materialism, for example, centres on his
attempt to develop a totalizing critique
through what his critics see as the annex-
ation, incorporation and marginalization
of other politico-intellectual traditions
(Castree and Gregory, 2006). And while
few geographers have pursued the
Ariadne’s thread linking Humboldt’s
grand eighteenth-century vision of the
Cosmos to Chorley and Haggett’s
twentieth-century vision of a unified
field theory for Geography, there has
been considerable interest in theoretical
systems that trouble the divide between
the human sciences and the natural sci-
ences: for example,chaos theoryand
complexity theory. If Manson and
Sullivan (2006, p. 678) are right to de-
scribe complexity as ‘the grand theory to
end all grand theories’, perhaps Grand
Theory always rings twice.dg

Suggested reading
Curry (2006).

graph theory A branch of mathematics that
studies topological phenomena that can be
represented bynetworkdiagrams comprising
nodes and the links between them: the classic
pioneering work was that of Leonhard Euler
(1707–83) on the Ko ̈nigsberg bridge problem
(see http://www.contracosta.cc.ca.us/math/
konig.htm).topologyrefers to spatial connec-
tions and relationships that are unchanged

after distortion: for example, Canada has a

border with the USA regardless of which

datum andmap projectionsystem is used to

map the Earth. Graph theory was first deployed

by geographers in the study of a range of net-

work types – such as river systems and road

networks (Haggett and Chorley, 1969) – but

is widely deployed through the social sciences

to study the structure and functioning of a

range of social networks and how information

flows through them (a field known as socio-

metrics). (See alsooptimization.) rj

Suggested reading

Biggs, Lloyd and Wilson (1986).

gravity model A mathematical and statis-

ticalmodel used to represent many types

ofspatial interaction and flow patterns

inhuman geographyandregional science

(such asmigrationand commodity flows),

and subsequently extended for use as a plan-

ning tool. The original formulation, as devised

by members of thesocial physicsschool, was

based on an analogy with Newton’s equation

of gravitational force:

Gij¼gMiMj=dij^2 :

This can be interpreted as follows: the gravita-

tional force (Gjj) between two masses (Miand

Mj) is proportional to a gravitational constant

(g) and to the product of their masses (MiMj)

and inversely proportional to the square of the

distance between them (dij^2 ). The analogy for

migration was therefore given as

Fij¼gPiPj=dij^2 ,

where the migrant flow (F) fromitojwas

modelled as being proportional to the product

of their populations and inversely proportional

to the distance between them. In such an ap-

plication, the constantgwas empirically deter-

mined from the data set by simple arithmetic

methods. At a later stage the model was fitted

byregressionmethods in logarithmic form,

and bothgand the exponent for distance were

empirically determined by calibration. This

basic form of the model is unconstrained,

and empirical studies demonstrated that the

model fitted much better if origin and destin-

ation constraints (e.g. the total numbers of

people starting or ending in each region)

were incorporated. This was most effectively

developed by Alan Wilson in hisentropy-

maximizingformulation of the model, based

on an analogy with statistical physics rather

Gregory / The Dictionary of Human Geography 9781405132879_4_G Final Proof page 316 2.4.2009 6:30pm

GRAPH THEORY