It seems to me that space syntax has to throw off its structuralist
pretentions before it can really be taken seriously.  This doesn't just
go for space syntax, but also geographers using GIS.  Both are eminently
structuralist tools, and both have to be careful to understand their
limitations.

For example, look at these two sentences from Alan:

> These theories are testable - falsifiable in Popper's terms - and
> are at the centre research debate.

> I content myself in the belief that space syntax papers are a model
> of clarity compared to anything written by Lacan or Derrida or any
> of their followers.

(Surely *anything* is a model of clarity compared to Derrida?! :-)

Usually at this stage I say "everyone knows Popper was wrong", at which
point somebody pipes up to say that it does seem to make sense.  Exactly
the trap, and incidentally why Derrida is unreadable.  So, to
arbitrarily repeat Kuhn: no theory is testable because the grounds on
which you test it are rooted within the paradigm of the theory.  It's
actually much, much deeper than that: Godel's theorem threw theorems out
of the window.  Grasping this is essential, because it seems much of
post-structuralism is really just a reactionary response to the sudden
realisation that we can't prove (or say) anything.

Anyway, I digress.  These statements demonstrate that syntax is still a
structuralist enterprise.  Even though the text of Alan's message does
imply that there is no 'one' axial map it is surrounded by assertions of
the opposite:

> The reduction to fewest line maps by computer has been
> demonstrated

> Some aspects of these - specifically those about how space can
> be constructed are mathematical and certain

> complete and mathematical protocols for constructing spatial
> representations and for measuring their properties

> The same goes for using space, it is 'lawful', and we use that
> lawfullness

With the exception of the last statement, no, no and thrice no.  Even
with the last statement: yes if we are structuralist, but we *cannot be*
structuralist, we know too much.  Is using space lawful?  Okay, let me
concede one point: I believe we should be entering a phase of
"re-structuralism", i.e., a non-naive structuralism which understands
the implications of post-structuralism.  Yes, I believe that there are
probably "laws" governing how a space is used --- as Alan says, we are
currently working on agent based models to investigate further.

So, what does this have to do with what an axial line is?  Well, the
point is, pragmatism and empiricism (those of you who know me will also
know I'm a keen adherent to van Fraassen).  An axial line does not need
a mathematical definition.

Firstly note: 1. drawing them inherently involves many decisions about
what is and is not important to the social usage of a space (as Alan
rightly says, 2m walls and so on). 2. it's mathematically impossible to
generate a (single) fewest line axial map for an arbitrary map. (VGA
does solve the second problem).

Now, does this matter?  The answer is actually "no".  Precisely because
it is impossible to create a consistent formalism *in any scientific
enterprise*.  I suspect the trouble to Tom Dine's friends is that with
most science they cannot see this impossibility because it is hidden
from them in men in white coats who call themselves "experts" and hence
they must be above suspicion.  But they can see the impossibility with
syntax because (a) it so obviously involves a human step (b) it's done
by architects not scientists or engineers.

To Tom: ask your friends to consider a CFD (Computational Fluid
Dynamics) analysis of a building.  Start with the small problems: CFD
involves breaking a space into aggregation units to make it computable.
So how do you decide how to break the space up into blocks?  Then move
onto the large ones: in built environments CFD is used to model airflows
(Yes, I know) Is air a fluid? (No) so can you apply C *fluid* D to air?
(Usually I find: don't know).  The answer is: yes you can apply CFD to
airflows in buildings, *so long as you know the limitations of the
technique*.  If you want a direct comparison with "what is an axial
line", call the aggregation cube by some technical sounding name, and
then get them to define one.

So what is an axial line?  I would suggest as difficult to define as any
term you try to define... (I took an MSc in artificial intelligence, now
what's that?!)

Best wishes,

Alasdair