Reflections on a Tree

Semilattice Example

Ward shared with me the other day work he has been doing to create semilattices in the wiki. One was for a talk on pattern languages that he did for an architectural group called PUARL . One of the primary objectives of this meeting was to explore the future of pattern languages:

>These varied disciplines and their cooperation and more and more collaboration are held together by the belief in the improvement of society and the environment through research in and application of the methodology of patterns and pattern language as a way of improving buildings, the urban structure and the environment, as well as creating positive societal change and, in general, opening up new ways of thinking and humanizing the world.

In Christopher Alexander's seminal piece, A City is not a Tree , he explores the structural difference between what he calls an artificial city and a natural city. Natural cities have evolved organically and feed the human spirit, artificial cities have controlled design and lack vitality.

This piece seeks to explain why.

He argues that artificial cities are designed in a hierarchical tree structure, while the patterns of natural cities are more fluid and can be described with semilattice models.

He describes a series of examples of planned communities around the world that lack the richness of organic, natural cities. Each of these are trees structures where parts are cleanly defined, but isolated from other.

He ends his first section with this example:

>The most beautiful example of all I have kept until last, because it symbolizes the problem perfectly. It appears in Hilberseimer's book _The Nature of Cities_. >He describes the fact that certain Roman towns had their origin as military camps, and then shows a picture of a modern military encampment as a kind of archetypal form for the city. >It is not possible to have a structure which is a clearer tree. The symbol is apt, for, of course, the organization of the army was designed precisely in order to create discipline and rigidity.

Richness of experience, he surmises, comes from overlapping parts that allow for chance interactions and deeper, more complex systems.

Logical conjunction ("and")

_In the context of Boolean logic, they are filled with a myriad of conjunctive "and" statements, not just disjunctive "or" statements. _

In a sense, with Alexander is talking about is the existence of what biologist call ecotones . Ecotones are areas where two ecosystems overlap, such as a river's estuary. This overlap forces a tension that creates new opportunities for creation.

This idea of creative tension fits nicely within Jean Piaget's concepts of learning , where "accomodation" to new ideas forces revisions in one's schema, something that could be called Dialectical Synthesis.

_Richness, Creativity and Learning_

Typical Org Chart Structure

The organizational structure of most companies and schools can be described by a hierarchical tree.

I wonder how we might be more intentional about moving our companies and schools from an tree-based command and control structure (with its militaristic heritage) to ones that are more organic and holistic, allowing for more ecotones of thought that can be mapped as semilattices?