Dear Tony
Apology for the misleading sentence.
When I was alluding to topology as weak coding of geometrical form - I was not referring to the mathematical formalisation literally or analogically - indeed, as you reminded everybody, it is formalised and rigorously so - usually mathematic is. Even fuzzy set theory is so, or modal logic too, despite that they may not sound like it when taking their name too literally. This is probably the analogical-imagery impulse that you are referring to. Similarly, I was not meant to limit topology extent to whatever.
Thank you to correct it, if this was the perception. What I was referring to, was that within the design "closure" process - in architectural design or urban design - topology gives you much less definition than say geometry - strategical more than tactical - less definition in the sense of defining precisely what the exact geometry is going to be - in other words, topology as informal coding, anexact, in relationship to the closure in term of form geometry definition is what I was referring to. The foreground of this conversation is design, design process and the use of Space Syntax in relationship to it.
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Alain Chiaradia
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-----Original Message-----
From: Tony Donegan [mailto:[log in to unmask]]
Sent: 26 July 2004 14:16
To:
Subject: Configurational Analysis
I am intrigued by the current debate on the philosophical niceties of SS.
Perhaps the SS community should agree to do what mathematicians have been
doing for centuries - accept the fact that certain entities can not be
defined. For example it is well known that the following entities of
mathematics defy definition - "a point", "a set", "an angle"
I am intrigued by the current debate on the philosophical niceties of SS.
Perhaps the SS community should agree to do what mathematicians have been
doing for centuries and that is to agree that certain concept defy
definition. It is well known that the foundations of mathematics teaches us
to be prepared to become acquainted with new ideas by degrees, rather than
starting with a watertight definition, which can be assimilated at once.
Examples of concepts, which defy definition, include:
'a point'
'an angle'
'a set'.
For an interesting analogy (which the SS reader will have to make) with the
development of SS see the easily readable text "The foundations of
mathematics" by Ian Stewart and David Tall.
Perhaps I should remark on the following recent statement that appeared in
the debate, namely:
"Topology is a sort of informal coding of geometrical form - a rather weak
one, a very limited coding that is still very efficient in its economy even
for a designer."
Statements like this are really misleading. Topology (there are many
branches) is far from being informal, it is a very precise axiomatic subject
studied by mathematicians and is an active research area, which if studied
formally by those interested in the architecture of space, might well
provide some of the answers being sought. The concepts go far beyond the
network analogy, which unfortunately for many, is the perceived extent of
topology. May I suggest that an appreciation of the formality of the Klein
bottle (after Felix Klein 1849-1925) is an excellent starting point for
researchers of space utility.
I have enjoyed the debate.
Dr HA Donegan
Reader
School of Computing and Mathematics
University of Ulster
Jordanstown
BT37 0QB
Tel: 028 90 366589
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