Wrong again Rui - 

> 
> Take home messages:
> i) What Hillier and Penn wrote in the reply to Ratti is basically a dead
> end for this field: SS doesn't work when the edges are weighted with
> distance, so SS networks will be topological at a time when everybody else
> is working with spatial (weighted) networks;
> 
> ii) Hillier and colleagues are claiming on Wikipedia that "A particularly
> advanced form of spatial network derives from the theory of space syntax".
> This is incorrect. In fact, SS networks are a limited and primitive form
> of spatial networks. Further, see i) above.
>

As you correctly point out weighted networks were around before space syntax
analysis. In fact these were the orthodoxy, and in a way they still are for
large sections of the wider 'networks' community (as Kuhn said, old
paradigms fight hard). 

Space syntax took a new approach. Instead of representing street segments as
weighted edges and so ending up with road intersections as nodes in the
graph, it chose to represent the 'architectural elements' of space (rooms,
convex spaces, longest lines) as nodes. This might seem like a simple
reversal, however it does two things:
-  First it internalises into the 'representation' stage of the process
specific aspects of the geometry of architectural space. In the case of the
axial map continuity down the street alignment translates into
representation as a single node, whilst change of direction translates into
a link. As Carlo Ratti demonstrates in his paper this representation is
sensitive to the local metric and geometric properties of built form, you
change the metrics slightly by moving the corner of a building block
relative to others and a single line may break into two. This representation
stage is almost completely elided in the previous paradigm (can anyone point
me to a 'rigorous definition' of the road centre line and the disposition of
nodes and segments in the networks they give rise to?); 
-  Second, it allows for different aspects of the local geometry and
sociology of space to be represented separately, analysed and compared in
terms of the same graph metrics. This approach turned out to have
considerable explanatory power. For example axial, convex and room function
representations of house plans when compared to one another shed light on
the relationship between domestic space configuration and culture. Take a
look at Julienne Hanson's book on this.

Space syntax, by the way, is not averse to using weighted graphs. We use
them a lot and they are part of our standard repertoire. Take a look at
Hillier & Iida's 2005 paper in which the same segment graph representation
is used, but weighted in three different ways. First, by giving a 0 weight
to continuation and a 1 weight to any change of direction (approximating the
'topological' axial graph), second by weighting according to metric distance
from segment to segment, and third by weighting for angular deviation from
segment to segment. It turns out that weightings 1 and 3 (topological and
angular) correlate much better with observed pedestrian and vehicular flows
than weighting 2 (metric) which is only poorly correlated. What might be
inferred from this finding? Well perhaps it is that so far as urban systems
are something that people move around, topological and angular deviations
account better for the (cognitive) cost function than metric distance. Of
course this is something that cognitive scientists have been aware of for a
long time, and should come as no surprise to people working in this field.

It is not then that SS is somehow defined by the use or non-use of weighted
networks. It is that we develop and use methodology to investigate and test
hypotheses. It is a hypothesis to be tested that metric distance is a key
component in defining people's movement patterns. The hypothesis (so far)
has been found wanting. Other hypotheses account better for the observed
data. 

This is perhaps where the early history of 'metric weighted networks' and
space syntax really are at variance. It is worth reading the introduction to
Mike Batty's 'Urban Modelling' for a very clear distinction between the aims
of 'modelling the world' and the aims of 'understanding the world'. Space
syntax is about the latter and so continually develops and adapts methods to
test hypotheses. Much of the 'spatial networks' community comes out of the
former tradition driven by a need to intervene in the world (to build road
networks for example) at a time when there was actually a lack of
explanatory theory about urban systems - modelling was what needed to be
done, and it worked well for the purpose (and continues to do so).

Space syntax by the way is not alone in working the way it does. Take a look
at physicists such as Sneppen et al and Hu et al who have both independently
come up with network representations very similar to the axial graph. This
is not a problem, it is just the way that science works. 

Time to stop sniping perhaps and get on with research?

Alan Penn

> As for your PhD, well... I would start worrying if I were you...

Rui, remember I have read your PhD :-0  Lucas, want to borrow a copy ?  :-)