Dear All,
Alan is quite right to nit pick with me, as in an effort to avoid too
much philosophy I made a few sweeping statements. So, some
clarification:
"Theorem threw theorems" is a facetious alliteration, and Alan makes the
valid point that this is not a genuine result of Goedel's theorem.
"Theorem" is one of the few actual words found in mathematics papers to
this day (the others notably being "Proof", "Lemma" and "Axiom"). The
distinction between these words is quite technical, but one should at
least be aware of the house of cards mathematics is built on.
Hofstadter's book, "Godel, Escher, Bach" eloquently describes the
impossibiliy of complete axiomatic descriptions of such basics as
geometry.
Now, although I wanted to point this out, I did not intend to say that
"all science is therefore bunkum". I was trying to point out instead
that if you tried for a complete description of *exactly* what an axial
line is, you would find yourself in the realm of impossibility. Perhaps
the greatest example of such a flawed exercise was Russel and
Whitehead's monumental Principia Mathematica (again, don't get me wrong,
a lot of our knowledge of the principles of mathematics is still
contained in these volumes).
The trouble I was getting at is that I believe, perhaps in order to
justify the methodology to a sceptical scientific community, some
proponents of space syntax try to be too precise about exactly what an
axial line is. Now, yet again, don't get me wrong, Goedel-type dilemmas
are not usually encountered, and a definition can be very precise before
finding its flaws. What I was trying to say, though, is that there is
no need to write three volumes of Principia Mathematica in order to try
to describe something that, when you come down to it, is impossible to
say.
When I hear criticisms of Syntax (and believe me, I frequently do), the
argument is often a lack of reproducibility, so this is obviously a
problem that needs to be dealt with. What I am saying is that proper
defence is *not* to invoke mathematical certainty. One real reason is
that, in the case of axial lines, there are simple obvious cases that
can have no single axial map. Now, I do not believe that this is a
problem with the methodology, there is nothing wrong with there being
more than one solution, or indeed, calling several different solutions
all "good" axial maps. The problem is deciding what is a "bad" axial
map. As Alan writes:
(A) > but it essential to note that results are reproducible,
(B) > and when people draw axial maps badly we find that their
> explanatory power is reduced
So what are our criteria for "bad" axial maps? Instead of a priori
mathematical arguments, I would instead suggest an a posteriori approach
(note, I'm cutting into the original thread of my re-structuralist
argument). Perhaps it would be a good idea to write a program that
analyses different axial maps to find common threads with "good" and
"bad" maps (perhaps someone already has!). This would give us a
theoretical basis not on exactly how to draw an axial maps, but on what
should be avoided and what should not --- i.e., a scientific basis for
the received wisdom which is taught on the AAS course at UCL.
There is a final unrelated point I wanted add about the social side of
axial line drawing. Tom Dine talks about different views of the city
from car height and people height. Ben Croxford has pointed out that
perhaps these may be irrelevant when looking at city navigation,
suggesting that since so much of the eye-height is cluttered with cars,
buses, lamp-posts and so on, perhaps we look at building top level
instead to give us clues about the configuration.
Again, best wishes,
Alasdair
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