Christopher Alexander

"The City is not a Tree'

In his attack (or rebuttal) on the concept of the city being a tree, as proposed by Aldo van Eyck, Christopher Alexander presents and defends the view that a city should be more like a semilattice. To develop his argument he first sets up his offensive by means of defining or explaining the elements that make up this "semilattice". Systems that overlap (comprised of elements and sets of elements) occur in "natural" cities and are what is missing from "artificial" cities.

It seems that Alexander is inferring that cities that occur naturally, or at least are derived from exploring the means by which natural cities are developed, are the only successful representations of what a city should be. A city is grouping of systems (varying in complexity) whose relationships to one another are those of interdependence - elements form sets that form systems that rely on one another to provide meaningful spaces. If an element of this semilattice system form were to be removed and replaced by something that had no place or significance in relationship to any of the other elements, the system would fail, according to Alexander. The entire city is simply a large semilattice comprised of many systems that form the whole, but it is only through overlap that this is possible. He generously provides about a dozen examples of a tree as represented by the lay of a city or community that do not have overlap and are thus not a semilattice (figures one through ten). Curiously, a specific example of a city or community that does have overlap and is then a semilattice is not provided, because to be able to visualize the occurrence of more that one set of elements is too complex for the minds eye of designers (except for mathematicians like him).

In cities that Christopher Alexander considers to be "trees", the spaces are rigid and deliberately disjointed and separated form each other. This, he claims, is because it is simple and, in his opinion, designers are unable to visualize in their mind the complexity of the semilattice in a single mental act. He feels that the mind is determined to reduce groups, systems, relationships, etc. into elements that do not overlap but are separated, of course so that we may color in between the lines… He claims that when we design or think in terms of trees we are "trading the humanity and richness of the living city for a conceptual simplicity which benefits only designers, planner, administrators, and developers". His "axiom" of a semilattice goes like this: "A collection of sets forms a semilattice if and only if, when two overlapping sets belong to the collection, the set of elements common to both also belongs to the collection." His axiom of a tree read: "A collection of sets forms a tree if and only if, for any two sets that belong to the collection, either one is wholly contained in the other, or else they are wholly disjoint." It seems to me that any thing that is and or will be designed will be a tree because, for example, a project (say the ARCH 410 project) has a site that is a specific location. This location is contained within a district, which is contained in a city with is contained in a stated, which is contained in a region of the United Stated, which is contained in North America, which is contained in the Northern Hemisphere, which is contained by the planet earth, which is contained by… Referring to page 142 of the reading (not from memory), he speaks about a university [perhaps it could be Tech] that has grown with a city naturally and the diagram obviously describes what he refers to as a semilattice. The natural city that has overlap is successful because of the relationships that occur between the elements, set, systems, and so on, as described in the example on page 130 of the intersection that has the traffic light and the newspaper rack, etc. It is my belief that grid or no grid; "tree" or no "tree"; "semilattice" or no "semilattice", it is these relationships that make a place (city, park, building plan, you name it) successful.