As a side track to this, Alan, how do you feel about this in the light of the basic units of general space syntax? For me, admittedly, it is problematic to have convex spaces, nodes, axial lines, segments, which have a spatial, geometrical and perhaps mathematical (if you like) precision and elegance, but the why of those, on a human and social (including the temporality and constitution of such configuration) level, is rarely questioned beyond a kind of "must be logic" argument and then explored through correlations (of which I must admit there are many and astounding ones, which therefore rightfully inform further questioning). Nonetheless, this why element has led me to rethink the whole human-space relation to conceptualise analytical units which answer to the why. This social accuracy may lack the precision, objectivity, and spatial elegance of space syntax, but to me appears a contribution to understanding through incorporating the why and exploring configurative constitution from a human (social and spatial being) perspective. Here, I am just wondering what your stance is on the basic units of space syntax, in the context of your critique in this specific discussion.
Thanks,
Benjamin
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________________________________
From: Penn, Alan<mailto:[log in to unmask]>
Sent: 26/12/2012 17:02
To: [log in to unmask]<mailto:[log in to unmask]>
Subject: Re: resend from yesterday
Yes, take a tree and add some links would probably do it, but mathematical structures are more precisely defined. Associativity + commutativity + idempotency gives a partial ordering and a lower or upper bounds.
My question was "why the hierarchy?" What I hear is that this is a base assumption, not to be questioned or justified. I suspect that this is the problem
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On 26 Dec 2012, at 15:26, "Bin Jiang" <[log in to unmask]> wrote:
> Alan,
>
> As far as I understand, semi-lattice is created by adding a few random links. This is very similar to adding a few random links into a regular graph leading to a small world graph. It is in this sense that I was impressed by Alexander's deep insight into the problem; see my remarks in this paper (p. 4441), http://fromto.hig.se/~bjg/flowcapacityPHYSA.pdf
>
> Maybe I have not fully understood your question yet. According to my reading or understanding of Alexander's theory of centers, he stressed that hierarchical order, recursively defined. The first three of the 15 geometric properties (levels of scale, strong centers, and boundaries) are something about the hierarchy.
>
> Cheers.
>
> Bin
> On 12/26/2012 3:55 PM, Penn, Alan wrote:
>> Bin,
>>
>> I know that they are both hierarchies. My question was why? The part of a Pattern Language that always convinced me that he had got it wrong was his focus on hierarchical order - larger elements has smaller elements, recursively, something that seems completely anti urban as well as rather anti social.
>>
>> By the way the semi-lattice and the tree are both precisely defined structures in mathematical terms, which if I remember correctly is what Alexander was talking about. A semilattice is associative, commutative and idempotent which induces a partial ordering. What I remember Alexander liked about the semilattice was the partial ordering: while for a tree an element could only be in one subset, in a semilattice an element could be in the overlap between a number of different subsets. This is certainly an attractive property.
>>
>> Alan
>>
>>
>> On 26 Dec 2012, at 12:07, Bin Jiang <[log in to unmask]> wrote:
>>
>>> Alan, let me try to explain why hierarchical order on behalf of Alexander.
>>>
>>> A city is not tree, but a semi-lattice, which I interpret as a network. However, both a tree and a network share the hierarchical order; I had this view expressed in this short paper (p. 8 below figure 2): http://arxiv.org/abs/1212.0940. Still a bit odd to you...?
>>>
>>> Bin
>>> On 12/26/2012 11:22 AM, Penn, Alan wrote:
>>>> Hear, hear! I wonder why Alexander is so into hierarchical order? He famously spotted that the city was not a tree on account of hierarchy, but then reinserted order in the form of the semi lattice... By the time of Pattern Language hierarchy seemed to have taken over entirely. It always seemed a bit odd to me...
>>>>
>>>> Alan
>>>>
>>>> Sent from my iPad
>>>>
>>>> On 26 Dec 2012, at 01:55, "David Seamon" <[log in to unmask]> wrote:
>>>>
>>>>> Bin,
>>>>>
>>>>> One last comment. If I were you, I would not set too much store in Salingaros's work. I realize he is a mathematician, but my sense is that he constructs his "objective" equations and scalings on the basis of personal prejudices. He has written a number of "over the top" commentaries on modernist and deconstructivist architecture that are mostly opinionated, subjective tirades. For some reason, Alexander has been taken in by his work and in fact there is a highly questionable quantitative ranking of the "best architecture in the world" as an appendix drawing on Salingaros's "degree of life" index in the first volume of Alexander's NATURE OF ORDER (p. 469).
>>>>>
>>>>> Salingaros claims to have come up with a quantitative means for measuring the "degree of life" in a building. From what I can see, his approach is a priori biased against any modernist work, thus the no. 1 building with the most "degree of life" is--wait for it!--the Alhambra, with the Taj Mahal no. 2, and the Dome of the Rock, no. 3. As one might guess, modernist work scores much lower, and the first modernist work to appear on the list is, oddly, Piano's Pompidou Centre at no. 17 (Fallingwater is no. 19, the Sidney Opera House no. 20, and the Seagram Building no. 21). The bottom three buildings on the list of 24 are Saarinen's TWA terminal, Kahn's Salk Institute, and Corbu's Ronchamp chapel.
>>>>>
>>>>> To me, this whole business of attempting to measure the ineffability of wholeness and environmental robustness is silly and impossible. I don't know why Alexander included this work in vol. 1, but sometimes his good sense gets lost.
>>>>>
>>>>> David Seamon
>
>
> --
> --------------------------------------------------------
> 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] Web: http://fromto.hig.se/~bjg/
> --------------------------------------------------------
> European Associate Editor
> Computers, Environment and Urban Systems: An International Journal
>
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>
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