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Dear Alasdair, thank you, you message makes things a little clearer for me. I started by asking 'what is the axial line' and Alan Penn gave me an answer straight away, which you amplified. My problem was that I was looking for an answer to a question more like 'what is the axial line all about'. Alan's answer was a good procedural definition, it told me how to make the line, but not why I would want to draw it. As you say, that sort of definition is probably not mathematical, it is about what the line is there to represent. I am a bit surprised to see you write that "perhaps there is some underlying social feature that they capture" ; I had naïvely thought that this was what space syntax was all about (although I could never quite find it in the books.) So when you say that there are millions of possible maps of the Tate, you are talking about mathematically different maps aren't you? Not maps of different sorts of things. What I meant was something like the different sorts of maps of London which are printed: road maps, historical maps, theatre maps, sight-seeing maps etc. Different purpose maps, not different content maps. Did I make a reasonable stab at the different purposes for space-syntax maps? As I wrote before, there do not seem to be that many different types of purpose for axial maps, do there? regards, Tom Dine PS. You over-estimate me: my aside about Popper wasn't drole - I really didn't understand your point ! [log in to unmask] Chassay+Last Architects Primrose Hill London