Travel Reference
In-Depth Information
of the value of quantitative analysis of networks as well as other mobilities; as Hall (2005a:
96) argued, 'it is important in developing a new social physics of mobility that we do not
ignore the old one'; if the physics analogue 'is to be maintained we can argue that macro-level
quantitative accounts of patterns of human mobility can be regarded as classical Newtonian
physics while micro level accounts of individual human behaviour can be likened to quantum
physics. The task in physics, as it is in examining human mobility, is to unify these under-
standings into a comprehensible whole'.
Within the spatial analysis literature there is often a sentiment that much of the criticism
of quantitative geography came from individuals who had little or no understanding of
mathematical methodologies (Robinson, 1998; Fotheringham
et al.
, 2000). Given such a
perspective, it is therefore valuable to review different approaches to spatial analysis and
interaction while noting their continued relevance to contemporary tourism geography.
Spatial interaction
The various stages of the evolution of spatial theory put forward by Fotheringham
et al.
(2000) provide a useful outline of the way in which traditions of spatial analysis in tourism
geography have developed.
Spatial interaction as social physics
In this approach the movement of people between locations was regarded as analogous to the
physical model of gravitational attraction between celestial bodies (Ravenstein, 1885).
Although this version of the model was 'theoretically empty' (Fotheringham
et al.
, 2000), it
has long been noted that the model produces reasonably accurate estimates of spatial fl ows in
what was termed 'social physics' (Zipf, 1949; Stewart and Warntz, 1958). One of the simplest
and most common ways of describing the curves that relate fl ows and distance is with the
Pareto function of the form:
F
=
aD
−b
(1)
where
F
= the fl ow,
D
= the distance and
a
and
b
are constants. Low
b
values indicate a curve
with a gentle slope with fl ows extending over a wide area. High
b
values indicate a curve
with a steep slope with fl ows confi ned to a limited area (Haggett, 1975). Behind the Pareto
form of the distance decay function is the gravitational concept, which suggests that spatial
interaction falls off inversely with the square of the distance
F = aD
−2
(2)
which can be rewritten as
F = a
.
1
(3)
D
2
This inverse square relationship is analogous to that used by physicists in estimating gravita-
tional attraction. The inverse 'distance effect' is capable of a series of mathematical transfor-
mations which have usually been addressed as logarithmic functions (Taylor, 1971). However,
constants tend to be different in different regions and in expressing different sets of spatial
