I went down a set theory rabbit hole this morning.
Charles Stein (in his book Light of Hermes) was discussing infinine divisibilty and transfinitive sets. This reminded me of the weird math we Gen-Xers learned as kids. We were taught set theory in like 2nd grade. We were learning rudimentary Boolean logic. I’m convinced that this is why all designers of my generation are always making Venn diagrams. I found a cool book in the political history of new math — the origin of all the set theory curricula. That inspired a long and odd post on my bizarre relationship with math.
So lately I’ve working on a top secret project concerning product management practices, especially Teresa Torres’s “opportunity solution trees”. I am interested in what product management tends to exclude, and what service design might be able to reintroduce. And suddenly the word “tree” jumped out at me, and I recalled this old Christopher Alexander paper “A City is Not a Tree”. And I thought — Wow, maybe opportunities and solutions are also not a tree! And maybe these tree structures are the kind of thing that makes silo-ization inevitable in organizations. And of course, silos fragment services and introduce discontinuites, gaps, inconsistencies and all the other stuff of bad experience.
So I start reading “A City is Not a Tree”… and here is how it starts:
The tree of my title is not a green tree with leaves. It is the name of an abstract structure. I shall contrast it with another, more complex abstract structure called a semilattice. In order to relate these abstract structures to the nature of the city, I must first make a simple distinction.
I want to call those cities which have arisen more or less spontaneously over many, many years natural cities. And I shall call those cities and parts of cities which have been deliberately created by designers and planners artificial cities.
Siena, Liverpool, Kyoto, Manhattan are examples of natural cities. Levittown, Chandigarh and the British New Towns are examples of artificial cities.
It is more and more widely recognized today that there is some essential ingredient missing from artificial cities. When compared with ancient cities that have acquired the patina of life, our modern attempts to create cities artificially are, from a human point of view, entirely unsuccessful.
Both the tree and the semilattice are ways of thinking about how a large collection of many small systems goes to make up a large and complex system. More generally, they are both names for structures of sets.
In order to define such structures, let me first define the concept of a set. A set is a collection of elements which for some reason we think of as belonging together. Since, as designers, we are concerned with the physical living city and its physical backbone, we must naturally restrict ourselves to considering sets which are collections of material elements such as people, blades of grass, cars, molecules, houses, gardens, water pipes, the water molecules in them etc.
When the elements of a set belong together because they co-operate or work together somehow, we call the set of elements a system.
I think what I’m trying to say is this:



