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From this we may see that, between timetand
timetþ1, 80 per cent of the population in A
remain there, 15 per cent move to B and 5 per
cent to C, and similarly for movements from
regions B and C in rows 2 and 3. By repeated
operation of the matrix, the population pattern
redistributes to a stable pattern independent of
the initial pattern (assuming no births, deaths
or movements in or out of the total system).
This Markov model has been used to study
population migration, epidemicprocesses,
the growth and movement of firms, and trends
in regional economic convergence and diver-
gence, and is a component of more sophisti-
cated demographic modelling. lwhSuggested readings
Collins, Drewett and Ferguson (1974); Rees and
Wilson (1977).Marxism The body of ideas and practices
developed by Karl Marx (1818–83) and
greatly elaborated since his death by his fol-
lowers. His voluminous writings fall into sev-
eral broad categories. First, there are those
writings that develop a broad theory of history
(historical materialism) as a succession of
modes of production, in which changes in
economic andclassstructures play a central
dynamic role. Second, there are writings (such
as the three volumes ofCapital) that develop
a more detailedpolitical economyofcapit-
alism as a mode of production, using the
labour theory of valueto explore its under-
lying contradictions and tendencies tocrisis.
Third, there are various, more sketchy,
writings on dialectical philosophy and method
(see dialectics). Fourth, there are a wide
range of analyses of contemporary events,
often designed to illustrate broader theories
(such as The eighteenth brumaire of Louis
Napoleon), polemical addresses and a mass of
journalistic writings for various newpapers.
Marx did not present a single, codified ver-
sion of his ideas, which in any case changed
over the course of his lifetime. Some later
Marxists, such as Louis Althusser (see Althus-
ser and Balibar, 1970), have even claimed to
detect a major ‘epistemological break’ in his
work between the earlier more philosophical
and ‘humanist’ texts, strongly influenced by
Hegel, and the later, more ‘scientific’, analyses
of political economy. Gouldner (1980) also
sees a distinction between a younger and
older Marx, but more in terms of a tension
between a voluntaristic ‘Critical Marxism’
and a more deterministic ‘Scientific Marxism’.
Even those (the majority of commentators)who prefer to stress the underlying continu-
ities in his work differ in the emphases they
place on different themes and texts. As a result
of such multiple possible readings, Marxism
has become more a family of theories with
many strands than a single codified frame-
work. This is part of its attraction and contrib-
utes to its continuing vitality.
Histories of Marxism usually identify several
phases of development and divergence (McLel-
lan, 1979). The first codified version of ‘ortho-
dox Marxism’ was developed after Marx’s death
by Engels, Kautsky, Bernstein and Plekhanov,
who published systematic expositions of histor-
ical and dialectical materialism, the nature of
capitalism and the theory of revolution. Lenin
subsequently adapted Plekhanov’s orthodox
‘stages’ view of history to justify revolution in a
backward capitalist state such as Russia. How-
ever,withthedegenerationofthe revolution and
the onset of Stalinism, ‘Marxism–Leninism’
rapidly hardened into the official ideology of
the centralized Soviet state.
TheWestern Marxismof Lukacs, Korsch,
Gramsci and the Frankfurt School (Horkhei-
mer and Adorno) was developed partly as a
reaction against this dogmatism, shifting the
emphasis away from political economy more
towards neglected aspects ofculture,ideol-
ogyandart. A return to Hegel and his influ-
ence on Marx provided an underlying
philosophical thread to this work (see also
critical theory).
The post-Second World War period has
been marked by increasing internal diversity
within the Marxist tradition, as Marxists have
responded to, and interacted with, other
developments inphilosophyandsocial the-
ory. Jean-Paul Sartre tried to blend a reinter-
pretation of Marxism with the philosophy of
existentialism. Althusser developed a re-
reading of Marxism – indebted, in part, to
structuralism – that attempted to save
Marxism from what he regarded as the twin
deviations of historicismandeconomism.
Althusserian Marxism presented a science of
social systems, with a relative autonomy of
levels ‘structured in dominance’ and an econ-
omy only ‘determinant-in-the-last-instance’.
Althusser’s structuralism provoked strong
reactions, leading to a proliferation of new
currentsoverrecentdecades. Harvey (1999
[1982]) has preferred to go back to Marx’s
own writings, demonstrating the continuing
potential of an essentially ‘orthodox’ version
of Marxism. The architects of analytical
marxism, such as Cohen, Roemer and
Elster (Mayer, 1994), have sought to buildGregory / The Dictionary of Human Geography 9781405132879_4_M Final Proof page 444 1.4.2009 3:19pmMARXISM