Christopher Alexander

A small tree that was kept in the yard of the Eishin School near Tokyo, Japan, designed by Christopher Alexander and associates.

“The core of all living process is step-by-step adaptation — the modification and evolution which happen gradually in response to information about the extent to which an emerging structure supports and embellishes the whole.”
— Christopher Alexander, The Nature of Order

It’s likely that no architect illustrates — or indeed, develops — these ideas better than Christopher Alexander. As we discussed previously, his first book, Notes on the Synthesis of Form, was hailed at the time as a landmark treatise in design theory. It launched him on his life’s work in mereology, his own modern exploration of the relation between parts and wholes, and the structure of wholes — and thus, “wholeness” itself, as a structurally comprehensible phenomenon.

At the time the subject was the elements of a design problem, and how they may be solved through solution configurations that he called diagrams (and later, patterns). The context was the dawning of the cybernetic age, and the manifest problem of complexity in human technology — and in nature itself. (As mentioned before, the cybernetic pioneer Herbert Simon had two years earlier written his landmark paper on the same topic, “The Architecture of Complexity.”)

But the ultimate subject was none other than Aristotle’s hylomorphism, updated for technological modernity. Essentially Alexander asks, do parts simply “make” wholes, in some additive or compositional sense? Clearly not: the whole is somehow greater than the sum of the parts. Moreover, the whole in a sense makes the parts as much as the reverse. (This is particularly true for biological processes. We would not say that the leaves “make” the tree — on the contrary, it’s clear that through a process of differentiation, the tree makes the leaves!)

Where things get particularly sticky is in the way the parts and wholes propagate out to other parts of the environment, and come back to interact in unexpected ways — a manifestly complex affair. How can this complexity be distilled down usefully to a salient “diagram,” without losing some essential connectivity? For designers and technologists, how can we decompose this complexity — not to assume it is merely a reductive aggregation, but rather, so as to manage it effectively?

As I discussed in Section II, what Alexander observed was that the sets of diagrams — which as noted, he later termed “patterns” — were not perfectly nested into tree-like hierarchies. On the contrary, they contained subtle but important characteristics of “semi-lattices,” or redundant networks — a property he called “overlap.” This relatively small feature, easy to overlook, is not an accidental defect, but a critical property of natural systems — particularly living systems. Somehow, we needed to be sure our processes of diagramming and generating — our processes of using human abstractions — engaged this structural quality.

The consequences of failing to do so could be seen when looking at structures like cities — as Alexander showed in “A City is Not a Tree.” He showed that cities also display this critical property of overlap, or “semi-lattice structure”. But planned cities often lack the property — which, Alexander argued, accounts for their higher rates of failure and dysfunction. He did so through a brilliant set of simple examples and analyses of catastrophic failures of modern “planned” cities — thereby providing a comprehensible structural explanation for a critical modern failure. The paper was widely hailed as a landmark, but its core message was sadly ignored by most urban designers.

But this insight had important implications for design at many levels — and an important implication for Platonic idealism. One could “nearly decompose” a design problem (to use Herbert Simon’s apt phrase) to useful effect, but one could never go so far as to reduce the problem to a purely elemental scheme without losing some essential vital attributes of the system. As Gödel showed, there can be no perfect blueprint of reality.

Further work on patterns

Alexander then asked the next question: how can we create a design tool or method that explicitly incorporates these overlaps, and generates these network-like attributes? As we now know, his answer was a “pattern language” — a structure of design elements that has hierarchical properties, but also network properties and the potential for overlap and ambiguity. The reference to language is more than an analogy, since languages also have the same combination of hierarchy-like overall form with the capacity for overlap, networks of meaning, and even intentional ambiguity. Indeed, this is what marks the distinction between a mere list of facts, or grammatical statement of the ordinary, and the power of literature or poetry. But something like this happens in ordinary circumstances too, Alexander argued, in the creation of ordinary environments and the ordering of ordinary events of human life.

This kind of ordering, he argued, did proceed routinely in human affairs as a matter of instinct. But in our modern (and neo-Hellenic) effort to be rational, we could too easily strip away this complex level of order, and leave ourselves greatly impoverished. Moreover, we could experience potentially catastrophic failures in our designs, no matter how well-intended, resulting in an increasingly unsustainable condition for technology and for civilization. Alexander’s design theory was beginning to take on the outlines of a critique of technological modernity itself.

Mereology, wholeness and quality

But Alexander wanted to go deeper — into the workings of life itself, and its processes of creating form. What could we learn from the new scientific insights into these processes? What could we learn about how living systems achieve complexity, sustainability, even great beauty — doing so with prodigious quantities and at prodigious scales, through the marvelous working s of self-organization? What are the implications for modern human technology? The new insights of science were offering tantalizing new clues.

As we saw in section II, Alexander concluded that living systems do not use anything like a “little blueprint” or set of Platonic forms. Rather, they use coded processes to generate form, and these function rather like step-wise recipes. Though these processes can become dizzyingly complex in their iterative compounding, at heart they are relatively simple algorithms and can be understood in a fully rational way.

But second, these processes are transformational, and cannot be “run in reverse” in most cases (except as a simplifying abstraction, which inevitably loses important parts of the story). The transformations introduce progressive differentiation through the breaking of the symmetrical states that existed previously (e.g. a round egg splits and becomes a linear structure). And as this process unfolds, all of the parts are, to varying degrees, mutually adapting to one another — including parts that are not within the same originating cluster. This creates (to often small but important degrees) the quality of “overlap,” and the network of inter-connections that is characteristic of complex systems.

The process can be seen clearly in embryogenesis, where the whole organism is going through a continuous transformation that preserves the whole, but also articulates new structures (Figure One). And the process is clearly coded according to simple chemical operations at the molecular scale — but operations that quickly become vastly complex and interactive at larger scales.

Figure III.3.1: Comparison of bat and mouse limb embryogenesis — a process of stepwise differentiation of wholes with new parts — but always preserving and extending the whole.

One can also see the same kind of process in non-living systems. For example, I previously described the simple process of a small droplet of milk striking a thin sheet of milk, in a famous series of photographs by Harold Edgerton. For this discussion I will present the images once again (Figure III.3.2). At any step of the process, there is a coherent whole with coherent parts (which indeed look strikingly like the articulation of arms and hands in embryogenesis). At each step, there is a comprehensible dynamic operating to transform those wholes and parts — at its heart, a relatively simple dynamic. But at each step, the wholes differentiate and articulate in new and often very surprising ways, giving rise to astonishing variety — even in a simple example like the milk drop.

FIGURE III.3.2: Edgerton's famous series of photographs of a milk drop as it strikes a thin sheet of milk on a sheet

Again, there is a progressive differentiation, following a symmetry-breaking. There is a mutual interaction of all of the milk particles, with various forces they exert upon one another (most notably, the forces of surface tension). These forces can overlap across distinct regions, so that the motion of one droplet can pull on its neighbor through the surface tension of its arm. All of these generative processes result in distinct structural patterns, and can be identified as such. A “genetic recipe” could be created for generating just such a structure, and by varying the patterns of the initial setup (the thickness of the milk plane, say) one could vary the patterns that result.

Indeed, Alexander noted that such morphogenetic processes often give rise to the same characteristic sets geometries, whether in biology or in other natural systems: strong centers, boundaries, alternating repetition, levels of scale, local symmetries, and so on. These in turn can be tied to the detailed mechanics of the transformations, and the transformations of sets of “centers” or localized fields. This was a hylomorphism taken to a much more articulated level of description.

For Alexander, it was clear from new biological research that the processes that give rise to life are themselves natural, and can also produce structures that have equally life-like characteristics. More astounding, he concluded from this, and from his own empirical examples, that we can assess “degrees of life” in a given structure, including a human environment and, moreover, that this is no mere analogy, but a factual description of the characteristics of a given structure. (This is a controversial idea in some quarters, but seen from a new structuralist lens, it need not be: life is a kind of structural process, and it can and does occur in “precursor” forms.)

At an urban scale, a very similar kind of process could be seen at work. I previously shouwd the gradual transformation of the Piazza San Marco in Venice, which involves the same kind of transformation of wholes, the same kinds of articulations of new centers and the same kinds of differentiations of space into more articulated sub-spaces.

Philosophical implications:
The Place of value and the place of the quantitative

For Alexander, the structuralist, value can now be understood as the structure of what is living and thriving, and what promotes and enhances that structure. In this sense, what is valuable can be thought of as a kind of structural fitness to the a priori problem of living and thriving.

This will vary between individuals who are in competition, perhaps; they may certainly experience different value in the same outcome if it happens to benefit one but not the other, say, if a young woman chooses between two male suitors. (This example shows how Alexander can perfectly well accommodate diversity while retaining a sharable definition of value, countering a persistent claim of some critics of a pathetic fallacy or, worse, a “value foundationalism.”) But, nonetheless, this value can be understood rationally as a kind of structure (in the example, the structure of courtship and family). Where individuals are cooperating, it can most certainly be shared.

But what is valuable is not exactly the same thing as what is qualitative. I may value or not value redness, but in either case I experience it as a quality. So what is this quality? What accounts for the qualitative dimension of things?

We know that in the case of redness, there is a wave pattern in the light energy emitting from a source, in the range of about 650 millionths of a meter from one wave peak to the next. If we change that frequency, the light consistently stops being red. (If we shrink the wave peaks to about 460 millionths of a meter, the light becomes “blue.”) In a sense this is “all there is” to redness, but in another sense, it is only the beginning of what redness truly is.

For we can now begin to see that redness is a complex, emergent, but ultimately non-mysterious property, from the whole structural system that comprises me, my brain, my eye, the light source, the “red” object and its tendency to absorb non-red colors, and so on. The quality of redness can really only be explained as a systemic property of the whole system, that inextricably includes my body and all the other structures. It follows that to try to decompose the system into a set of simple parts is to miss the essential dynamics of the system — and its small but important connections to external components, too.

Moreover, we miss the capacity of the system to produce what we experience as “meaning,” as the following example will illustrate. In a condition where some structural element of the system is not working in the same way — for those who have a very complex change in the color-processing structure of their brains as a result of a stroke, say — “redness” is not present. One could say, “Oh yes, ‘red’ is present, you just don’t perceive it.” But that is not actually true. What you have come to call ‘red” as an abstraction is still present, — but not the emergent property of redness. This would be a little like saying, “Oh yes, the color “gruengepled” also exists at 5 millionths of a meter, you just don’t perceive it, nor does anyone else.” This would not be false so much as it would simply be meaningless. We are simply not interested in this structure, because it does not comprise a salient whole that is related to our experience. We do not call it a color, and if we describe it at all, it is for much more secondary reasons. For example, we might discover some property in the laboratory, far from ordinary experience, in which case we might name the frequency for its discoverer, but we would be very unlikely to describe it as anything so salient as a “color.”

Again, to describe it as a color would be, quite literally, meaningless. And yet, we now see that describing redness as a color is certainly, by contrast, meaningful. In this way, Alexander brings us back to a comprehensible structuralist theory of meaning.

What is meaningful to us is very close to what “matters” to us as living structures, that is, what we encounter and consider important as organisms, in our a priori participation in the world (notwithstanding our ability to discern a partly decomposable structure to these phenomena). Indeed, “matter” is nothing other than what “matters to us,” what is the matter, what is in the way, what is “material” to us. The abstractions we use are all secondary, and forever derivative of this a priori condition.

As Whitehead argued coherently and persuasively (in Modes of Thought, 1938), it is this sense of importance that is the logical antecedent of what we regard as “fact.” And it is a kind of trick of the mind, or more precisely, an abstraction, to suppose the reverse is true. Abstractions are, of course, highly useful, but as abstraction, this is (again as Whitehead so effectively pointed out) an omission of part of the truth.

Again, there is surely a comprehensible biological basis to all this. Going back to the example of redness, there may be (and surely are) other structural phenomena going on, of which we may be unaware (for example, the way certain perceptual processes work, the shifts in color perception with certain adjacencies, and so on). But the important point is, we are able to take in all these (comprehensible but complex) structural conditions, and experience an emergent quality. This is very likely closely associated with the need for living systems to make rapid determinations of large fields of stimuli.

Thus I can very quickly perceive the redness of a fire raging near me, at the same time that I can perceive a blue sky in the other direction that offers escape. I can no less quickly detect the alarming smell of burning wood, which must go through a series of highly complex and subtle processes on the way to my brain. Indeed I routinely make exceedingly complex (in fact vastly complex) syntheses of what is going on structurally, and experience these complex inputs as qualitative feelings. I can then act as an organism in a way that is most likely to preserve and enhance my own structure.

Thus we also have a structuralist theory of quality, and of feeling, rooted not only in biological needs, but in the complex structure of biological wholes. I may feel well or ill, happy or sad, based upon vast numbers of complex internal and external inputs, structurally transformed. But my feeling and the quality of the things I perceive, are not simple atomic states, but vast fields of wholes, whose structure is vastly intricate, rich, and varied.

Moreover, based upon my definition of choices through the agency of thinking and language and its vast transformational powers, I can then take actions to alter them and do so with my fellows, thereby creating the very dynamic of culture and of life. But I must do so with skill and care, so as not to make categorical errors, or misuse the capacity of abstraction to tease out these useful structural insights.

If I do this with care, I find that the structures I make have a biological suitability to them that is extremely gratifying to me. I find their aesthetic character to be beautiful. I find that they gratify important biological and cultural needs which are, to varying degrees, both innate and malleable. There is a deep capacity for cultural creativity.

Again, this is seen as a natural structure at heart, though it is astonishingly vast. But this structural essence in no way reduces what it is to feel or to experience these powerful structural processes of life. It only means that we can also come to know these processes, in our capacity to “see,” isomorphically, their essentially structural, and at the same time interconnected and (to us as organisms) meaningful aspects.

An example from music can make the point very well. I find Bach’s Prelude Number 1 from “The Well-Tempered Clavier” to be quite beautiful, and indeed I can find a particular passage with a sudden A flat note particularly beautiful and emotionally powerful. But if I pull that A flat out of the song, it has no power by itself whatsoever. It is not an independent element that can be added to others to produce a simple cumulative compositional effect;, rather, its power comes from its place in a field of relationships. The symmetry of these relationships to parts of my own brain and to the parts of my life is deeply pleasing and beautiful.

This one small example engages the Pythagorean ratios of the musical vibrations; the physics of hearing; the high level of neuroprocessing in my brain; the evolutionary function of my perception of sound; the cultural tempering of my perception of music (including the tempering of the scale, itself a profound structural innovation); the structuring of my own appreciation for music and for this piece in particular; and so on. In just this example, we begin to see the vast complexity of everyday experience.

The universe is thus shot through with meaning, and it is shot through with structure. It is alive, and at the same time, it is structural. There is no conflict.

We will discuss the implications for designers in more detail below. But one implication is dramatic: characteristics of the built environment do carry relative value for individuals — and that value can, to varying degrees, be shared. The beautiful (like the good and the true) is not so much in the eye of the beholder, as it is in the complex structural resonance between an individual and the world around. This is a comprehensible state of affairs — one with important implications for designers.