ancient cities

different path from central place theory. Many
authors noticed the strong differentiation in the
sizes of cities belonging to any system of cities
(usually today from 10 3 inhabitants to 10 6 for
medium-sized countries, up to 10 7 in the most
populated countries). Friedrich Auerbach, in 1913,
first suggested a model of the regular shape of hierarchies
in urban systems, which was formalized by
George Kingsley Zipf in 1941 under the expression
“rank size-rule”: The number of cities above a
given size (equivalent to the rank) is an inverse
geometric progression of this size. Zipf explained
this statistical regularity as an equilibrium generated
by counteracting forces of concentration (for
the efficiency of markets) and dispersion (of natural
resources). The first formalization of a growth
process generating the hierarchy of city sizes (as a
lognormal distribution) was proposed by the
French statistician Robert Gibrat in 1931. He
demonstrated that this distribution is produced by
increases in population that are, on every short
time interval, proportional to the initial size of cities,
with stochastic fluctuations. Tests of growth
processes in urban systems have shown that
Gibrat’s model holds in a first approximation only
and that systematic correlations of growth rates
with city sizes and temporal autocorrelation of
growth rates have to be explained by modeling the
interactions between cities.
Functional Diversity, Specialization,
and Economic Cycles
Urban growth rates are linked with innovation
cycles involving a changing relationship with city
size: At the beginning of a cycle, larger cities tend
to grow faster, growth rates equalize, and then
small towns tend to grow faster. This process was
described by Torsten Hägerstrand as the hierarchical
diffusion of innovations. The consequence of
the early adoption of innovation by large cities is
that they draw greater benefit from the innovation
(the initial advantage), and this is translated into
growth rates slightly above the average of towns
and cities overall. Contemporary studies of
“metropolization” rediscovered a process that has
long constituted the dynamics of systems of cities at
a time when the globalization trends and the general
conversion to the “information society” are
creating new cycles of innovation. This hierarchical
Urban System
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selection is reinforced by the tendency of smaller
towns to have growth rates below the mean, either
because they adopt innovation when the associated
benefits are becoming smaller or because they are
never reached by innovation. The latter is especially
the case when rapid transportation modes or
infrastructures are considered. The historical trend
toward greater speed of communications, known
as space–time convergence, has certainly contributed
to reinforcing the inequalities in city size,
while on a lower scale it has widened the perimeter
of urban areas.
Besides the effects of hierarchical selection,
there is a second type of asymmetry that is created
in urban systems by the innovation process.
Sometimes, the resources for exploitation of an
innovation are not available in every location. The
result is urban specialization because the related
economic activities can develop in only a few
urban sites. Usually, the development of a new
urban specialization produces exceptionally high
growth rates as the booming cities attract migrants
as well as profit-oriented investments. This was the
case when certain mineral resources became
exploitable, such as coal mines in the British
Midlands or Belgian Wallonia, gold in California,
or diamonds at Kimberley in South Africa. But
several location factors that explain the emergence
and success of many towns and cities are also geographical
“accidents” of another kind—for example,
those influencing the layout of long-distance
trade routes, such as wide valleys or topographic
corridors, estuaries and bays for maritime routes,
major crossroads, or contact points between different
regions. Among the more recently exploited
spatially concentrated resources are mountain
slopes for skiing or coastlines for tourism. Places
where public funds have been injected to create a
local concentration of skill and knowledge can
also be considered as nodes of possible concentration
of investment and urban specialization, for
instance, the large universities that have generated
“technopoles.”
Thus innovation is an essential driving force in
urban dynamics. Knowledge and information,
reflexivity, and the ability to learn and invent provide
the impetus for urban development. The crucial
role that cities have played in generating
innovations—intellectual and material, cultural
and political, institutional and organizational—is