Notes on the genesis of wholes

Interior of one of the buildings at the Eishin School near Tokyo, by Christopher Alexander and associates.

“In the last two decades, physicists and other scientists and philosophers of science have begun to discover that a wholeness-based view of the world is essential to proper understanding of the purely physical universe....The conception, experimental techniques, and even the way to modify our essentially Cartesian view, so that it can admit self, “I”, and feeling — are extraordinarily difficult. Yet they are necessary for the progress of science. They are necessary, too, for the progress of architecture.”
— Christopher Alexander, “Some sober reflections on the nature of architecture in our time,”

As I noted in the introduction, Jacobs and Alexander are complementary in a very useful way, namely, while their work has considerable overlap, each of them focuses more deeply on aspects of cities that the other does not. Each of them also takes up different parts of the professions that deal with cities, and finds them wanting.

If Jane Jacobs was always primarily concerned with the actions of planners and how well they succeeded or failed in making better cities, it could be said that Christopher Alexander was always primarily concerned with architecture and urban design, and how well those professional fields succeeded or failed in making successful environments from a broader human point of view. In the same way, Alexander was more directly focused on the formal structure of human environments — the “architecture” in a more general sense — and how these forms arise, at least in part, from human design. (Indeed, this concern with the details of environmental structure is captured in the name of Alexander’s long-time research office, the Center for Environmental Structure.)

Certainly, both authors were concerned with the successes and (too common) failures of architecture and planning. As I noted in the introduction, Jacobs was no stranger to the concerns of architecture, having served previously as a staff writer at Architectural Forum before taking on The Death and Life of Great American Cities. But it was Alexander who, in Notes on the Synthesis of Form — his first book, in 1964 — described how environmental architectures were often created through history, in what he termed an “unself-conscious process.” He went on to describe how this form-creation had changed in the modern era, taking on more “self-conscious” but still rather inadequate aspects, with important and sometimes destructive implications for the design professions. (I will have more to say about this important set of observations later in this section.)

There were other notable differences in their backgrounds. While Jacobs was an independent journalist and polymath, Alexander was a Cambridge, England educated mathematician, physicist and architect, who went on to develop many of his seminal ideas in the Cambridge, Massachusetts of the late 1950s. That was an academic environment populated by the likes of the architectural pioneer Walter Gropius, and the cognitive psychology pioneer George A. Miller, both of whom Alexander knew at the time. For Alexander, cognitive psychology in particular offered crucial insights into how we perceive our environments and shape their forms, for better or worse.

Half a century after the beginning of his career, Alexander’s dramatic and sometimes controversial contributions to the field had not abated. In 2003 he began publishing the first of his four-volume magnum opus, The Nature of Order: An Essay on the Art of Building and the Nature of the Universe. It too was concerned with the problem of form, or the particularly well-adapted variety of it that Alexander called “order”. Central to his understanding of this kind of order was the phenomenon he called “wholeness” — a concept I will discuss in more detail in this chapter.

The grand title of this last major work, and equally grand and dense text, fueled a perception in some quarters that Alexander’s career somewhere derailed from his earlier, rigorous scientific path, into an impenetrable world of mysticism, solipsism or worse.

But the truth is more interesting, and more promising. Alexander’s career is in fact a straight line from the Cambridge (UK) physics student of the 1950s, dealing with precisely the same topic throughout: the relation of parts to wholes — the ancient topic of mereology in philosophy — and the search for useful new design tools to aid in their genesis and transformation. Along the way Alexander surprised even himself with the increasing philosophical complexity of his conclusions — but he never deviated from the scientific methods that brought him there.

Furthermore, his career has revealed as much about the modern history of planning and architecture, and the philosophical issues scarcely yet confronted, let alone resolved, as it does about one individual’s remarkably diverse, idiosyncratic, but (as I will argue) coherent corpus.

Alexander, the first PhD student in architecture at Harvard, made a dramatic impact as an influential new thinker with his PhD dissertation (later became his first book, Notes on the Synthesis of Form). Its considerable influence extended far beyond the world of architecture and planning: it was said to be a required reading for researchers in computer science throughout the 1960s, and reportedly influenced major software innovations of the 1970s including object-oriented programming. It was no less an influential text for the generation of architectural theorists that included Lionel March and Horst Rittel.

Like the remarkable polymath Herbert Simon’s classic paper of that era, "The Architecture of Complexity", Notes took up anew the age-old philosophical question of the relationship between parts and wholes (again, mereology) but in a specific modern form. Both Alexander and Simon wanted to know the precise mathematical structure of that relationship, and of its development and transformation over time. Alexander was interested more specifically in the designer’s challenge. As he formulated it then: how does a designer synthesize a coherent and successful form out of the elements of a design program?

Like Simon, Alexander made the basic structural observation that parts tend to relate to wholes in hierarchies, roughly speaking. The phrase ‘roughly speaking’ turned out to be key: there are subtle but significant areas of overlap and redundancy, and in that fact there is something profoundly important. These overlaps may seem accidental or trivial, but they are not: they are essential attributes of what we would today recognize as network structures, and they occur in very particular ways. Alexander quickly recognized, perhaps even more than Simon, that these areas were somehow of fundamental importance.

That insight was the salient point of his widely cited 1965 paper on the failures of that era’s new towns — and by extension, modern urban planning as a whole — "A City is Not A Tree". The tree he referred to was a mathematical kind of structure, a neat hierarchical system of nested sets and subsets.

Whenever we have a tree structure, it means that within this structure no piece of any unit is ever connected to other units, except through the medium of that unit as a whole. The enormity of this restriction is difficult to grasp. It is a little as though the members of a family were not free to make friends outside the family, except when the family as a whole made a friendship.

He contrasted that structure with a semilattice, a more complex kind of structure with overlap, ambiguity and mutual interaction. This characteristic was a key aspect of the architecture of complexity.

The city is full of these overlapping and ambiguous systems, Alexander noted, and they are responsible for a great deal of its complexity and richness:

It must be emphasized, lest the orderly mind shrink in horror from anything that is not clearly articulated and categorized in tree form, 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.

Figure II.1.1. A ‘tree’, or hierarchy, segregates its elements into neatly branching categories, or sets. Entirely self-contained neighborhoods might be examples of ‘tree’ structures within cities.

Figure II.1.2. A ‘semilattice’, or network, has overlapping sets. While it may seem messier, it is actually a more complex kind of structure, with more internal connectivity — and more like many natural structures, including cities. This example shows the overlapping uses between the city and the university in Cambridge, England.

And yet, as he showed, much of modern planning exhibited this tree-like structure. He argued that the rational mind inevitably defaults to these neater, more easily managed categories of thought.

It is for this reason — because the mind’s first function is to reduce the ambiguity and overlap in a confusing situation and because, to this end, it is endowed with a basic intolerance for ambiguity — that structures like the city, which do require overlapping sets within them, are nevertheless persistently conceived as trees.

But the result of this can be devastating:

…the city is not, cannot and must not be a tree. The city is a receptacle for life. If the receptacle severs the overlap of the strands of life within it, because it is a tree, it will be like a bowl full of razor blades on edge, ready to cut up whatever is entrusted to it. In such a receptacle life will be cut to pieces.

"A City is Not a Tree" quickly took on the status of a landmark critique, joining the ranks of Jacobs’ The Death and Life of Great American Cities in shaping that era’s seminal criticisms of modernist planning. With other critical texts of that era, it helped to put a brake on the rush of new towns and ‘urban renewal’, and set the stage for a more circumspect, asset-based approach to planning.

Yet 50 years later, we can ask whether the implications of this seminal work were ever fully realized. Today a new generation of planners and architects seems to have forgotten — or never learned — Alexander’s elegant mathematical analysis. New towns following the old model are springing up around the world, notably in the developing world, and new infill projects are proposed for rapidly growing cities. There is a greater emphasis on mixed-use and interaction, but not much difference in the fundamental planning methodologies or results. As Jacobs noted in 1961, the urban professions have still not made the progress of other fields, particularly the biological sciences.

Alexander next asked, if the mind inevitably tries to force complex systems into neat hierarchies, then how can designers counteract this trend? Are there methods available to overcome this limitation?

Alexander noted several hopeful sources. One was in the structure of natural languages. An entire complex system, with all its overlap, can be represented by a word or phrase, which can be inter-linked to other words through grammatical rules. While following basic hierarchical rules of structure, natural language nonetheless does permit tremendous ambiguity, overlap and interactivity. Poetry, for example, is an obvious example of language that is rich in overlap and density of interrelations.

Another inspiration came from computer science. Alexander had developed his original work in the synthesis of form using computer programs, and he made an intriguing observation. Amid the unwieldy thicket of data he was generating, he saw recurrent patterns of the same elements, or the same kind of solutions. If these patterns could be abstracted, they could perhaps be re-combined in usable ways, preserving the essential network structures of the patterns. Such a ‘language’ itself could, like a natural language, contain overlap and network connectivity.

Figure II.1.3. The network structure of some of the patterns within the book A Pattern Language.

This was an enormous revelation for Alexander, and it opened his eyes to yet another revelation. He began to recognize that human beings had already been using something like a ‘pattern language’ in their traditional building cultures. The apparently humble structures of vernacular building were in fact extremely robust and capable of producing exceedingly complex results. Something like this pattern structure seemed to be deeply rooted in the nature of the interactions between humans and their environment. It might even be rooted in the very nature of things.

In a deeper sense, Alexander was once again wrestling with the topic of mereology, or how parts relate to wholes. Do the parts simply “add up” to the wholes? Clearly not. Are they related in some linear, sequential sense? On the contrary, they have an inter-connected web-like pattern, and this seems to be essential to their quality of wholeness. (It is also the secret to the robustness of language.)

Pattern languages were, in a real sense, a method of manipulating wholes and their parts, without disturbing the contextual structure, the “tissue” of wholeness in which they were embedded. Whereas other methods of design tended to ignore the contextual wholeness and “invent from zero,” the method of pattern languages was to accept the context as an essential aspect of the problem, and to model its most salient parts.

Alexander developed this concept of a ‘pattern language’ through a series of tests, and found it worked sufficiently well to develop a major compendium of patterns. He began to envision a resource that any ordinary person could use to produce reasonably good vernacular buildings, in place of the unsatisfying standardized buildings that comprised the vast majority of the built environment.

Alexander and his colleagues compiled an initial set of 253 patterns, and, in 1977, published them in the book A Pattern Language. The book became an immediate and perennial bestseller, and a major influence on yet another generation of architects and planners. As I will discuss later in this section, there was much more to come.