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Started by droqen, May 14, 2023, 06:54:31 AM

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Semilattice (left)
Tree (right)

Oh, cool. Christopher Alexander is describing some early concept of the relationship between patterns. Patterns do not nest neatly within one another as in a tree (right), but overlapping messily as in a semilattice (left).


He gives nine examples of cases of city planning which are fundamentally tree-like. Here is one such, but they are all worth reading for the same thing that they all are: trees.

P. 8, line breaks added
QuoteCommunitas is explicitly organized as a tree: it is first divided into four concentric major zones, . . . Each of them is further subdivided:
the commercial centre is represented as a great cylindrical skyscraper, containing five layers. . .
The university is divided into eight sectors. . .
The third concentric ring is divided into neighbourhoods of 4000 people each. . . apartment blocks, each of these containing individual dwelling units.
. . . the open country is divided into three segments: forest preserves, agriculture, and vacation lands.
The overall organization is a tree.


I should say "It's lists again!"
I have been thinking about lists quite a bit lately. I haven't been able to describe what I don't like about lists until now. Of course it would be Alexander who gets me through this weird bump. I don't like lists when the elements are discrete.

Elements in lists should overlap. That's something I should study a bit more. I need to gather lists I love vs lists I hate.


Quote[In] today's social structure . . . If we ask a man[sic] to name his friends and then ask them in turn to name their friends, they will all name different people . . . There are virtually no closed groups of people in modern society. . . . the systems of friends and acquaintances form a semilattice, not a tree


Alexander suggests that individual houses on long streets may more strongly reflect the reality that you do not know your neighbours, and that a city like Greenbelt with its "subsidiary groups of houses built around parking lots" places focus on, or emphasizes, "the most irrelevant" groups. I suppose that he means these little 'subsidiary groups of houses': they are built for a reality that does not exist.


Quote. . . the tree is comparable to the compulsive desire for neatness and order . . . The semilattice . . . is the structure of a complex fabric; it is the structure of living things, of great paintings and symphonies.

It must be emphasized, lest the orderly mind shrink in horror . . . that the idea of overlap, ambiguity, multiplicity of aspect and the semilattice are not less orderly than the rigid tree, but more so. They represent a thicker, tougher, more subtle and more complex view of structure.

This conception of order is so clearly the root of the title of The Nature of Order, though here I find the argument vaguely uncompelling, because what is order in the first place?

Rather than order or orderliness, an abstract concept which as a goal is mobile (here as in "moving the goalposts"), let us talk about completeness, an abstract concept which as a goal is stable -- complete as in a complete graph, an image that has haunted me for a long time:

"A complete graph is a graph in which each pair of graph vertices is connected by an edge."

When the complete graph was presented to me long ago I thought there could be nothing so foolish, so pointless; what even is the point of graph theory if not for the differing relationships between nodes (above nodes are called vertices--I'm not clear on the difference)? That is, if every node is equally connected to every other node, nothing remains to be said.

However, the complete graph presents an abstract ideal: rather than making slippery claims to the orderliness of the semilattice versus the tree we can say that the semilattice allows us to get closer to completeness than does the tree--and while a complete graph is impossible to realize in most cases, especially large cases*, we ought still look in that direction in order to produce a "thicker, tougher" structure.

*regarding large cases:
P. 2-3
Quote. . . let us think abstractly for a moment. . . Instead of talking about the real sets of millions of real particles which occur in the city**, let us consider a simpler structure made of just half a dozen elements. Label these elements 1,2,3,4,5,6. . . . Suppose we now pick out certain [subsets]: [123], [34], [45], [234], [345], [12345], [3456].

**particles, or rather larger things made up of particles:
P. 2
Quote. . . the newsrack, the newspapers on it, the money going from people's pockets to the dime slot, the people who stop at the light and read papers, the traffic light, the electric impulses which make the lights changes, . . . the sidewalk which the people stand on . . .

I think that the above quotes work to illustrate the magnitude of impossibility of achieving 'real' completeness, but I can certainly say that the constraints of the tree work against it at some point. There are things that the tree structure is good for (very good for!); in order to do work on anything collectively the pieces must be sufficiently separate so as to allow divisions in social structure (oh, it's Conway's law, but in converse! to produce a given design, an organization of the same structure follows). Alexander writes something about this that I want to dwell on...

Quote. . . since certain groups have been emphasized by the physical units of the physical structure, why are just these the most irrelevant ones?

I suppose that I must believe in noncompleteness after all, in importance... I know I'm talking in circles here. Certain connections are strong and real. The complete graph is not, in fact, natural. I must reconnect with that old revulsion.



He says it better here:

P. 10
QuoteWhenever we have a tree structure, it means that within this structure no piece of any unit is ever connected other units, except through the medium of that unit as a whole.

. . . It is a little as though the members of a family were not free to make friends outside the family, except the family as a whole made a friendship.

P. 9
Quote. . . the Columbia plan [and] the Stein plan . . . [suggest] a hierarchy of stronger and stronger closed social groups, ranging from the whole city down to the family, each formed by associational ties of different strength.


He talks about play and playgrounds in a way that speaks to me...

P. 13
QuoteConsider the separation of pedestrians from moving vehicles, a tree concept . . . At a very crude level of thought this is obviously a good idea. Yet the urban taxi can function only because pedestrians and vehicles are not strictly separated.
. . .
Another favourite concept . . . is the separation of recreation from everything else. This has crystallized in our real cities in the form of playgrounds. . . .  The playground, asphalted and fenced in, is . . . pictorial acknowledgement of the fact that 'play' exists as an isolated concept in our minds. It has nothing to do with the life of play itself.
. . .
Play itself, the play that children practise, goes on somewhere different every day. [indoors, then in a friendly gas station, then down by the river, then in a derelict building, then...] Each of these play activities, and the objects it requires, forms a system.


P. 14
QuotePlay takes place in a thousand places it fills the interstices of adult life. As the play, children become full of their surroundings. How can children become full of their surroundings in a fenced enclosure! They cannot.


I find myself editing Christopher Alexander now and then -- sometimes his opinions get him a little cringe, which isn't something very useful or interesting to me. As an example he writes that tree structures for urban planning are "born of the mania every simple-minded person has for putting things with the same name into the same basket." Like, I can feel the dude's frustration here, but he's being a bit rude, and I don't think it's productive.

In my mind I translate his thought into something that I want to live on in my head and my heart:

P. 15
QuoteDoes a concert hall ask to be next to an opera house? . . . The only reason that [various performing arts have been gathered, in some cities, to form just one core] is that the concept of performing arts links them to one another. But . . . the idea of a single hierarchy of urban cores [does] not illuminate the relations between art and city life.

[Tree structures are] born of the mania every . . . person has for putting things with the same name into the same basket.

I'd like to remind myself to think about this when I do it though -- especially when recommending Christopher Alexander or his writing to others, or maybe when talking about any kind of nonfiction. I like reading his frustration; it shows a passion; but then I feel the need to edit it out to integrate it within my own mind. I'd rather not do that. I mean, id rather not forget about the passionate frustration. But I also don't want to dwell on it, because it distracts me from the knowledge.

Hard problem.


God damn this essay ends hard. Let's see, the thing I want to take away from this is that Alexander and I agree that the problem, the 'problem'(?), is that people--and therefore designers--categorize and form trees in their mind readily. In this essay he lays out a problem, not a solution. I believe that in The Nature of Order, Book Two, The Process of Creating Life, he truly lays out a solution. Wow. A life's work.


P. 16

Quote. . . why is it that so many designers have conceived cities as trees when the natural structure in every case is a semilattice? Have they done so deliberately. . . Or have they done it because they cannot help it, because they are trapped by a mental habit, perhaps even trapped by the way the mind works . . .

P. 17

QuoteI shall try to convince you that it is for this second reason . . . because designers, limited as they must be by the capacity of the mind to form intuitively accessible structures, cannot achieve the complexity of the semilattice in a single mental act.


Here then is the fundamental problem with top-down design, with holding any object in your mind: you can do it, but it will be of a form that is comfortable in the mind, before it is a form that is good in reality, before it serves the real problem.

The mind has limitations, and art, creating art, allows us to produce works containing complexities that (perhaps) could not, in principle, ever fully exist as a whole mental object.

The mind too is a medium, is form.
Content can never be without form.