Hi Bin,



Yes you can repost the combined answers and replies to the list, wanted to keep the stream of emails down for everyone, since I was mostly asking for further clarification.



On the basis of your persistence on single variables, quantitative at that, I feel I should be asking another question. Does it make sense to want to approach an idea about mental maps on the basis of a single quantitative variable? I think it might always be a combination of factors that creates a single impression. This idea then is in need of its own concepts and it seems doubtful to assume that existing quantitative measures might feed into it immediately.



I feel still somewhat at a loss as to what you are trying to understand by understanding the generation of the mental map, as you mainly explained to me what you think you could do with scaling if it were of constitutive importance methodologically. Understanding how a mental map is generated seems either commonsensical or something more readily achieved for individuals. How you go from there to a collective mental maps I don't really see. It almost seems a contradiction to me even.



I also wonder whether it helps to put the space syntax example in if it has no real relation to it. Scaling seems a generic property and may therefore also 'hide' in the axial plans, but for me personally both the dotted pattern and the space syntax one do not convince me I'm as a viewer affected by scaling. I couldn't quite work out what you think you are showing with the pictures and think it might possibly help to use the actual physical artefacts as examples rather than these more abstract schemata. Nonetheless, at the same time, the more concrete you get, the further away from a collective perception (if there is such a thing?) one seems to get also. It brings it back to the individual.



I think regarding the example of streets, you probably need another, specifically appropriate concept of it (neither axial nor named) to argue for relevance to perception. Unless there is a strong theoretical argument why named or axial streets are appropriate for making the jump from an individual to collective mental maps. I realise this is not about space syntax, but I do wonder whether this questioning doesn't again get caught in similar social theoretical caveats as space syntax.



If your question simply was: could scaling play a role in the generating of mental maps, then I think I'm still in need of a better explanation as to how. This how will only make sense with strong theoretical arguments for the units or concepts you select to demonstrate its existence in the city landscape on.



Good luck!



Benjamin



Sent from my Windows Phone

________________________________

From: Bin Jiang<mailto:[log in to unmask]>

Sent: ‎21/‎12/‎2012 03:03

To: [log in to unmask]<mailto:[log in to unmask]>

Subject: Re: The image of the city



Alan, and all,



I just had a good sleeping, so I can continue discussions with my fresh mind; see comments below.

On 12/20/2012 11:15 PM, Penn, Alan wrote:

OK - let me try something for the sake of argument  (with no real empirical justification of course:-).



Scaling phenomena tend to refer to those relationships between two variables where either one or both are considered linear on a logarithmic scale - so for instance the largest something and the second largest are an order of magnitude different in size as are the second and third largest, etc.

Yes, often scaling refers to allometry, e.g., relationship of body size to shape. In this regard, Phil Steadman and Mike Batty did some interesting work. It also refers to somethings with a power law distribution, in which case, one single variable rather than two variables in the former case. For example, in terms of street connectivity, there are far more less-connected streets than well-connected streets; in terms of building heights, there are far more low buildings than high buildings. The traditional definition of scaling is restricted to a power law distribution only, but my paper (http://arxiv.org/abs/1209.1112) relaxed this definition to include lognormal, exponential and their associations such as power law with exponential cutoff. My relaxed definition is pretty simple: scaling is a recurring structure of far more small things than large one. One simply uses head/tail breaks (http://arxiv.org/abs/1209.2801) to partition things (relying on one single variable) into multiple hierarchical levels.



It seems reasonable that the experiencing subject might notice order of magnitude differences between different situations in the world and so possibly learn associations between pairs of variables  of this kind.

As a reminder, and as mentioned above, I was talking about one single variable, rather than allometry, since perception of a single variable things (e.g., street connectivity or building height) is simpler than perception of two variables relationship.

It is perhaps less obvious that they would notice differences between normally distributed variables?

Yes, my point was if things (or more precisely city artifacts) are normally distributed (lack of the scaling), one can hardly form the image of the city.

So let us consider space syntax 'intelligibility'  - the correlation between local and global measures of the graph. If one or both of the measures are highly skewed (and both tend to be) then the correlation may be learnable if it exists.

According to my experience, local measures (like connectivity) tend to be highly skewed, but not global measures.

This perhaps offers a mechanism through which part of Lynch's concept of legibility might be realised and where 'scaling' would be useful characteristic of the underlying variables. It is just a thought.

Yes, you are right if you were talking about one single variable. Both Lynch's imageability and legibility can be quantified with respect to "scaling". For example, I would say imageability or legibility of a dead city is zero (c.f. Figure 4 of this paper http://arxiv.org/ftp/arxiv/papers/1209/1209.1112.pdf)

 The problem might be that scaling phenomena tend to be ordered purely on the dimension of interest- largest, second, third etc. and not in the subject's experiential order which must be according to the order of connections in the network. Perhaps with bivariate correlations and in the long run the association to be learned des not depend on the experiential order?

As a kind reminder, I was talking things or order of things with a single variable.



Alan



Bin - I think it would be worth reviewing the following papers which may be relevant to your argument:

This is one comment I received from someone else early. I did not integrate the interesting work, since I was talking about one single variable things. And importantly, my paper was NOT about space syntax in particular. I am sorry for creating this impression that this paper is about space syntax, since axial lines were used in the case studies. As I explicitly and deliberately mentioned just at the beginning of the case studies (http://arxiv.org/abs/1209.1112), axial lines were used as a proxy for city artifacts that demonstrate the scaling property. I could have used streets (either named streets or natural streets) for the case studies.



Many thanks Alan for the stimulating questions. Feel free to get back to me if any doubts.



Cheers.



Bin





Kim, YO and Penn, A (2004) Linking the spatial syntax of cognitive maps to the spatial syntax of the environment.<http://discovery.ucl.ac.uk/278/> ENVIRONMENT AND BEHAVIOR , 36 (4) 483 - 504. 10.1177/0013916503261384<http://dx.doi.org/10.1177/0013916503261384>.



(Also Young KIm'a PhD thesis which lends support for feature recognition related to scale.)



Carvalho R, Penn A (2004) . Scaling and universality in the micro-structure of urban space.PHYSICA A vol. 332, 539-547.

10.1016/j.physa.2003.10.024<http://dx.doi.org/10.1016/j.physa.2003.10.024>



Hillier, B. and Iida, S. (2005) Network and psychological effects in urban movement. In: Cohn, A.G. and Mark, D.M., (eds.) Proceedings of Spatial Information Theory: International Conference, COSIT 2005,Ellicottsville, N.Y., U.S.A.,September 14-18, 2005. (pp. pp. 475-490). Springer-Verlag: Berlin, Germany  http://eprints.ucl.ac.uk/1232/



Also Nick Dalton's PhD thesis on point intelligibility and recognisable urban areas.





On 20 Dec 2012, at 17:23, David Seamon <[log in to unmask]<mailto:[log in to unmask]>>

 wrote:



Bin,



I looked at this new link but, from what I can tell, the article is the same as the one at the earlier link.



I have to say I don't understand what you're arguing. You really don't offer a convincing justification for why this scalar focus is so important (note your justification is a brief two sentences that really aren't clear in what they mean!). As I said to you in the last email, I really don't think one's "conscious" image of a place is that crucial in knowing that place or traversing that place.



Phenomenologically, what is needed is a thorough developmental study of how people, experientially, come to know a new place and how an unrelated set of environmental elements come to cohere in some organized understanding of place. But, still, below all this, is the power of body-subject, which you provide no context for whatsoever.



I am sorry but I am really not sure what you are arguing makes sense. And I especially don't see your jump to using the axial maps and the red "lines" as somehow the scalar mechanism. I agree that, in Lynch's research, paths were the dominant elements for most people, and the paths usually "imaged" were the most integrated pathways. But I still think that is "after-the-fact" knowledge in relation to what successful traversal of a place is experientially (and thus phenomenologically).



I hope you'll read my GEOGRAPHY OF THE LIFEWORLD, because it was my first effort to point out the considerable weaknesses of any cognitive approach to spatial behavior and environmental conception. The book is available in its entirety at my university website. The link is:



http://www.arch.ksu.edu/seamon/books_intro.htm



Sorry not to be more positive about your work. I just think you should be careful and not spend a lot of time on a "theory" that may not be accurate.



David Seamon



----- Original Message -----

From: "Bin Jiang" <[log in to unmask]><mailto:[log in to unmask]>

To: [log in to unmask]<mailto:[log in to unmask]>

Sent: Thursday, December 20, 2012 9:56:17 AM

Subject: [SPACESYNTAX] The image of the city



Hi, I thought this paper might be of interest to some of you:

http://arxiv.org/abs/1212.3703



With this, I am humbly looking forward to your comments and criticisms

in particular.



Happy holidays to you all!



Bin















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Bin Jiang

Division of Geomatics, KTH Research School

Department of Technology and Built Environment

University of Gävle, SE-801 76 Gävle, Sweden

Phone: +46-26-64 8901    Fax: +46-26-64 8758

Email: [log in to unmask]<mailto:[log in to unmask]>  Web: http://fromto.hig.se/~bjg/

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European Associate Editor

Computers, Environment and Urban Systems: An International Journal



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