Rui
When you use the term topological - is there a non-metric implication? This
gives cause for concern as it is fundamental in analytic topology that a
metric space is a topological space.
The concept of a topologica network can have a non-metric implication in the
"Russian Doll" sense but equally it can have metric interpretation.
It is clear to me that there is an opportunity for someone who has a grasp
of mathematical topology to look closely at the SS philosophy and to produce
a set of clear and unambiguous definitions. Perhaps the basis of a good
honours project or a masters project.
Dr HA Donegan
Reader (Mathematics Division)
School of Computing and Mathematics
University of Ulster
Jordanstown
BT37 0QB
Tel: 028 90 366589 or 90 366841
----- Original Message -----
From: "Rui Carvalho" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Monday, June 26, 2006 11:55 AM
Subject: SS Networks are topological, not spatial
space syntax, as a field, relies on spatial elements: axial lines, convex
spaces or isovists. But SS networks are topological, as the edges (i.e.
relations between these elements (axial lines, isovists or convex spaces))
have, so far, been purely topological.
There is a very long tradition in geography to work with spatial networks.
These are networks where the edges are spatial (see e.g. ‘Network Analysis
in Geography’ by Haggett and Chorley, 1969) and network edges are weighted
by Euclidean distance between the nodes.
Most of Ratti's critique to SS could be rephrased as a statement that SS
is non spatial, as the edges do not take in consideration euclidean
distance.
Hillier and Penn reply in the ‘Rejoinder to Ratti’ p 505:
“As soon as topological measures of an axial map are weighted by, say,
length of segment, the integration pattern resulting from configurational
analysis will always focus on the geometric centre of the system (because
that is in general metrically closer to all other parts of the system),
and decrease smoothly from centre to edge. This has two effects. First, it
means that a short backstreet close to a main centre of the system will
appear configurationally more `integrated' than a major line remote from
the geometric centre. Second, it will make the model so sensitive to the
choice of boundary that it will be this that defines where the centre of
integration is.”
In other words: SS stops working once we shift from topological to spatial
networks, which is why SS networks were never spatial.
The question then remains: why are those at the helm filling every
possible web page with "spatial analysis" and "spatial networks"?
Perhaps it's time for more than rhetoric games...
BR,
Rui
_____________________________
Rui Carvalho
http://www.casa.ucl.ac.uk/people/Rui.htm
Senior Research Fellow
Centre for Advanced Spatial Analysis
1-19 Torrington Place
University College London
Gower Street
London WC1E 6BT
United Kingdom
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