We cannot enter a world for which we have no language.

— David Whyte

 

I climb out onto the very far end of a tree branch and only then do I worry about how the hell I’m going to get back down.

— Christopher Alexander

 

Christopher Alexander is a Janus-headed scholar.

In one direction he apprehends the world with an analytical mind: focused, linearly logical, comfortable with mathematical formulations and modeling. This mode produced such works as Notes on the Synthesis of Form, BART, and A City Is Not a Tree. Alexander’s writing style—straight prose—aims for explanation and demonstration. Blunt sentences plod steadily, bullheadedly, forward.

In the other direction the gaze is intuitive, receptive, phenomenological, embodied, open-ended. We read works such as The Timeless Way, The Foreshadowing of 21st Century Art, and Book Four of The Nature of Order. His writing style becomes personal, discursive, evocative, long-winded, circling around a topic from multiple angles, with an overabundance of examples. The aim is to embrace the diffuse, mysterious, latent, mystical.

To merely observe that Alexander is endowed with both an analytical and intuitive mind would be trivial. Less trivial would be to notice: first, Alexander’s predilection for exploring edges of understanding where we do not yet have established language or adequate tooling; second, his peculiar epistemology. Alexander makes sense of the not-yet-known by tightly zigzagging between analysis and intuition. The zigzag is sometimes a cooperative horizontal back and forth where the same situation is looked at one way and then the other; sometimes we find longitudinal zigzags. Very much a ballistic scholar, Alexander moves ever forward but in a way which remains backward compatible. He will investigate a topic as far as possible and then abandon it until the day fresh insights compel him to pick it up again. It is not surprising, for example, to see that a late (2009) essay on harmony seeking computation picks up and further develops early (1964) work on the perception of symmetries.

To reflect on Alexander’s signature way of working, I refer to a number of his works, but also draw from personal conversations that I had with him during the 1990s when I was helping with early drafts of Book Two and Four of The Nature of Order. My role as first reader was to be adamantly dim-witted, never feigning to understand what I really didn’t, insisting on discussion until the formulations of newly hatched ideas were clear.

Always Out On a Limb

Perhaps we are most innovative when we are desperate—our backs to the wall, left in the lurch by inadequate tools. Here are three examples, out of many, where Alexander, out on a limb, felt it was do or die: Notes on the Synthesis of Form, Harmony Seeking Computations, and The Mirror-of-the-Self Test.

Notes is Alexander’s PhD thesis, an analysis of a traditional Indian village. He reported having been utterly flummoxed by his research task. He readily confessed that he never understood Mother India in general, nor, in particular, the village where he was doing field work, the villagers, their shenanigans, motives, and decisions. He remembers returning to America and watching the manuscript of his thesis being passed around from person to person, department to department. Nobody knew what to do with it. It didn’t belong in any established academic box.

He opens Notes with a reference to Plato. I quote it here in full since it is germane to his lifelong endeavor to make sense of things.

First, the taking in of scattered particulars under one Idea, so that everyone understands what is being talked about. . . . Second, the separation of the Idea into parts, by dividing it at the joints, as nature directs, not breaking any limb in half as a bad carver might. (Preface Material, Notes on the Synthesis of Form, 1964)

Now I myself, Phaedrus, am I lover of these processes of division and bringing together, as aids of speech and thought; and if I think any other man can see these things that can naturally be collected into one and divided into many, him I follow after and walk in his footsteps as if he were a god. (Plato Phaedrus, 265D)

Alexander’s entire legacy could be considered a single long riff on the carving knife of Phaedrus: the requirements of intuiting the whole and following the natural joints, the action of the whole on the parts, and the action of the parts on the whole.

In his thesis, Alexander relates how he struggled with the processes of decomposition by creating mathematically determined sets and subsets along strong and weak links. However, unlike the Thanksgiving patriarch wielding a carving knife over a modest sized and conveniently immobile turkey, Alexander must come to terms with an entire town and its life over time. He intuitively senses that the Indian setup is far superior to anything in the West, and far, far superior to anything he had heard about in school. Without the help of vocabulary that would be developed later by others, he innovatively thinks about the evolving built environment as a complex adaptive system: distributed intelligence, redundancy of information, stability and change through fast and slow feedback loops, corrective design by misfits.

Harmony-Seeking Computations

In 2009, forty-five years later, Alexander is still taking inspiration from Plato’s Phaedrus. Harmony-Seeking Computations: A Science of Non-Classical Dynamics based on the Progressive Evolution of the Larger Whole lays out another new form of computation aimed at understanding harmony within a system. The desperation is not that of a student feeling the pressure of a university requirement, but of a man now old. The years have passed, his time is almost up, and the mystery of it all continues to elude and tantalize him.

In Harmony, Alexander argues that current explanations of phenomena in complex systems, although now far better understood, still fall short. He takes the example of V flight formations in real geese and those in computer boid simulations. He says the boid rules (collision avoidance, velocity matching, flock centering) go an impressively long way toward simulating general flocking behavior, but rules of this sort do not do as well at generating a persistently stable V formation. Two other rules are required: leader turn taking and flying the sweet spot which is the line of the vortex cylinder of the bird in front.

This, he argues, is not a simple bottom-up emergence since it has a three-level structure. The real geese compute in a way that makes their body (a local CENTER) work to create a second level element which is the POSITIVE SPACE shown in the drawing below. These second level elements form the third level diagonal structures of which the V-formation is formed. Therefore, we are witnessing the action of a three-level structure.

The above drawing is Alexander's own. I paraphrase his explanation of it (from the paper): The shaded space between adjacent geese is a positive shape, composed by one bird’s left wing, the other bird’s right wing, and the two bodies. Two birds can discover that there is an optimum ride when the left wingtip of one bird is in line with the right wingtip of the one ahead, generating the rectangle in space. At that spacing the vortices cancel, minimising turbulence. This relies on the positive and definite shape of the space between the geese which strengthens the stability of the dynamic configurations. We cannot model this properly without a harmony-seeking transformation based on the structure of the whole V as a guiding field, because the computation needed to generate the V is a computation that explicitly relates the individual to the whole. The real issue is that the emergence usually attributed to the geese (viewed as mechanisms) is not as mechanistic as some would like to think. To produce the V‑formation, the geese themselves perform a harmony-seeking computation: they act to relate themselves to the larger whole and to help that larger whole.

Returning to the pragmatic questions of the built environment, Alexander then argues that because conventional mathematics is unfamiliar with computations of the sort needed in complex systems, we ignore the highly sophisticated but natural calculations done by unselfconscious vernacular builders. Alexander illustrates with the simple act of the rancher who places new fence posts roughly equal-distance. The rancher is actually calculating with fine precision because he takes into account the tree, the boulder, the dip in the land. It is not just a question of feeling, but also a question of structural congruence between an existing structure and an injected structure. The structure of the whole is the rancher’s guiding field. When well done, human effort extends and enhances the natural structure and beauty of the landscape.

Harmony suggests that the desirable close-knit geometric adaptation between existing and injected structures has not been a major focus of scientific study because it eludes simple algorithmic formulations. There is a need to develop language and tools for three-level harmony seeking computations.

Harmony points to possibilities about cosmological mereology that are not necessarily easy to grasp. The example of geese flight formation is accessible, as is the rancher’s fence. His other examples are perhaps less so. His descriptions of the interactions between cloud and blue sky or between tree branch and surrounding air require us to see space as not empty but itself a three-dimensional system, a dynamic object, that has its own shape and behaviour. He writes:

I mean to propose that there is a certain class of mathematical structures, in space itself, that has features that, for spatial and computational reasons alone, gradually appear in space, not because of something that is caused by forces, but because of the geometry of space itself. (Harmony-Seeking Computations, 2009, p. 36)

Alexander may turn out to be dead wrong about “the geometry of space itself.” He may be guilty of misusing, so to speak, the necessarily reductionist aspects of computer simulations. However, by going far out on a limb and forcing these questions, he will, at least, have been wrong in interesting ways. More we cannot ask. The greatest of the great scholars turn out to be wrong, but when they are wrong in ways that prod further consideration, we all benefit.

The Mirror-of-the-Self Test

As a third example of working on the edge, consider a moment when the desperation was financial. Alexander became obsessed with Sufi prayer carpets. Absolutely obsessed. He described himself as a frenzied acquisitive madman. The carpets could be bought, but they were expensive. Dealers would allow potential buyers to take a rug home for a week before committing to a purchase. He couldn’t afford to buy all the carpets. He had to choose. How?

He devised the mirror-of-the-self test.

The mirror-of-the-self test entails taking any two comparable objects—two carpets, two paintings, two tables, two floorplans, two coffee mugs—and asking yourself, not which one you like best, but which one most closely represents you, the real you, you with all your feelings and thoughts. If you came back in your next life, say, as a coffee mug, which one would be the better reincarnation of you?

Many people roll their eyes when hearing about this exercise, give it a miss, and move on. However, it seems to work. Take two objects in any category, do the test, then query the connoisseurs who have spent years in study of that category. The test answer will, by and large, get you closer to expertise. It’s a short cut to competent evaluation.

Alexander speaks here about comparing two carpets:

I believe that almost everyone, after careful thought, will choose the left-hand example. Even though the two are of roughly equal importance, and of comparable age, I believe most people will conclude that the left-hand one is more profound: that one feels more calm looking at it; that one could look at it, day after day, for more years, that it fills one more successfully, with a calm and peaceful feeling. All this is what I mean by saying that, objectively, the left-hand carpet is the greater—and the more whole, of the two. (A Foreshadowing of 21st Century Art, 1993, p. 29-30)

The mirror-of-the-self test invents an epistemology using the body as a computational device. Is this so strange? Maybe not. Clearly, we think and feel not just with a few ounces of gray matter between our ears but with our entire bodies. If we go see a film and identify with the protagonist, we will be reading emotional cues from within our own physical selves. But from film hero to Sufi prayer rug? Is that not a bridge too far?

We live in a structured universe. We ourselves are structured. Our art work—be it film, acting, woven rugs, or building—is structured participation in our structured world. Can we not, through intuition and introspection, plumb the depths of interiority to find analog resonances of structure? In any case, if sufficient testing confirms this innovative mirror-of-self methodology, it must be telling us something significant about what to value and how to evaluate it.

The Zigzag

Let us now examine the back and forth between the two modes of apprehending. Early work provides two conveniently short examples of moving from analysis to intuition.

Community and Privacy: Towards a New Architecture of Humanism, co-authored with Serge Chermayeff, 1963. This project investigated the human needs for both community and privacy and how to provide for that. The authors laid out the forces at play and then compared various design options and tradeoffs. They concluded with a design winner: clusters of court houses. Project completed.

But, then, Alexander leans back relaxing into a softer receptive mode to reflect on what they had accomplished. Out of the corner of his intuitive eye, he perceives a heretofore unanticipated and unseen layer of connecting tissues between areas of community and privacy. He realizes that the integrity of the spaces depended on smaller joint elements—screen, buffer, filter, transfer point, lock, junction—and it was these joints which actually provided the hierarchical structure. For Alexander, this postscript observation about connecting tissue and hierarchy becomes the most significant result of the project.

BART, a 1964 project in San Francisco for the Bay Area Rapid Transit, deployed system analysis. At that time, Alexander thought he had it nailed with 390 systems requirements for a ticket booth. Twenty years later, the BART project came back under discussion when Alexander was being interviewed by biographer Steven Grabow (1983). Alexander’s revised position was that designers do not control their creations. Systems have to come to terms with themselves and also with the forces that they themselves generate—in this case, traveler sociability. Arbitrary sets of requirements alone won’t accomplish the job.

For an example of moving from an intuitive gaze to analysis, consider the birthing process of A Pattern Language (APL). In the early 70s the National Institutes of Health put out a Request for Proposal to investigate the relationship (if there was one) between the built environment and human well-being. The proposal submitted by Alexander and his team stated that they had absolutely no idea of how to go about such an investigation but that they found it an intriguing question and would like to give it a go. The “go” turned out to be a receptive, unfocused walkabout. If something caught their eye because it seemed relevant to well-being, they stopped for a focused look. “Ah,” one of them might notice, “people seem to like to hang out on deep balconies where they can sit, have coffee, and wave to neighbors. Balconies that are just narrow ledges are never used, abandoned to junk and drying clothes.” From that observation, they drilled down, thought it through, and wrote up the noted configuration as SIX-FOOT BALCONY. These configurations (or patterns) were eventually compiled in the well-known and popular book, APL.

People now working with patterns sometimes mistakenly assume that they should work analytically and first identify the forces or design constraints that must be reconciled through a pattern. The Alexandrian approach was not that, but, rather, that of the explorer in unmapped territory, strolling about, noticing what was already there, making an assembly of notations—a labelling system and first parsing—which might, someday, become a taxonomy. The methodology was that of natural history: notice, examine, write up a note.

In his later career Alexander came to think of himself as a sleuth. A workaholic if there ever was one, he rarely took breaks. He would draw and paint, but that was a form of serious study not recreation. If he did give himself a bit of time off, he would pick up a who-dun-it.

“Is there any point to which you would wish to draw my attention?”

“To the curious incident of the dog in the night-time.”

“The dog did nothing in the night-time.”

“That was the curious incident,” remarked Sherlock Holmes.

—Silver Blaze, Arthur Conan Doyle

The hallmark of the creative detective is abductive reasoning. Abduction is guessing. It has nothing to do with the analytical skills of either deduction (from general to specific) or induction (from specific to general). These skills are closed with regard to prior assumptions and data: they cannot produce new ideas. New ideas come only from abduction. Sherlock Holmes notices that the dog did not bark in the night. Through abduction, a guess, a leap of the mind, comes the possibility that the dog might have known, and known quite well, whoever broke into the building that night. A working hypothesis is born.

At the very end of two thousand pages of detective work into, literally, the nature of order, our sense of sentience in the universe, of the numinous behind a veil, the existence of God, Alexander concludes The Nature of Order with himself cast as Sherlock Holmes:

As Sherlock Holmes said, if you have examined every possible alternative, and you have gradually eliminated all the alternatives but one, then that one—no matter how fantastic—must be the truth. (The Nature of Order, Book Four, 2004, p. 344)

I have put forward a portrait of Alexander as a driven investigator, always exploring at the fringe of knowledge. No modes of apprehension, no heuristic metaphors, no epistemologies were off the table, and he invented a few of his own. He did not disallow the analogue in favor of the digital or vice versa. It is not exactly that each mode, like yin and yang, contains a latency that becomes the other, but rather that there is an alchemy of learning from having looked at something with an analytical eye which then provokes a question handled intuitively, or, the other way round, that something gleaned from an intuitive query gives rise to analysis. Alexander’s insistent zigzag became itself a womb / a lever / a transformative matrix producing a creative recursive flow and feedback between his introspective self and extrospective examination. This yielded a constant cohering, refining, and complexifying of his project.

Alexander’s Advice

Since advice is an integral part of Alexander’s dual visioned legacy, a few words from that perspective are called for.

How do we embrace wholeness, potential, connectedness? Alexander had thought that with the publication, in the 1970s, of the trilogy, The Oregon Experiment, Timeless Way, and A Pattern Language, that the world had been given everything needed to get on with creating a better-built environment. He was sorely disappointed. His readership couldn’t see the forest for the trees. Buildings constructed with APL in hand were funky, incoherent, lacking in profundity. Skills of intuition, insightfulness into the real nature of things, were weak.

He asked himself: What additional information is necessary? He disappears and returns, years later, with The Nature of Order. The new publication takes things further. For example, in a well-executed pattern language, there will be, at a meta-level, geometric properties. Each pattern informs the next smaller scaled pattern and the next larger one, but the ratios have to be right, not too close, not too distant: this results in LEVELS OF SCALE. Each pattern is a focal point in space: a CENTER, itself with a THICK BOUNDARY. And so on. Long explanations of intuiting wholeness and latent structures are offered.

When trying to help people perceive wholes, Alexander would essentially devise ways to have them relax. We need to unwind and soften our gaze. Our concepts and words misguide us, pushing us toward a fragmented view. He commented that we basically had to do away with current education. Children and the intellectually disabled did better on the wholeness perception tests than Ivy League students. As for techniques for himself, he would sometimes leave his desk, draw a bath, and reflect in a tub of hot water.

His advice provides pointers but the learner is left to practice—as in seeing wholeness with this photo of A tree, a road, a bicycle, and a cyclist.

Summarizing from pages 92–93 of Book One of NO: Learning to see wholeness is difficult. The centers here, when we look for wholeness, are not ‘road,’ ‘bike’, ‘tree.’ We need to make our minds blank and unfocused. Then we see the big swath of space over grass and road, the cotton wool top of the tree, the trunk and the ring of space around it. We shall not understand how the world works unless we pay attention to the structure of wholeness as it is.

Alexander’s advice is sharper when it comes to more analytical tasks. Above all is the constant admonition: For Heaven’s Sake, we are but Pooh Bears of Little Brain. Accept and pay attention to our limitations. Set things up so that we are working within our capacities.

For example, A City is Not a Tree lays out his argument that the life and vitality of a city depend on a complex structure of overlapping subsets, but that we typically and wrongly design a city as a tree structure because that is all our little Pooh brains can handle. Alexander patiently works out the cognitive difficulty of thinking in terms of overlapping subsets with an embarrassingly simplistic example. Given an orange, a watermelon, a football, and a tennis ball, we can group them as fruit and sports balls or as small spheres and large oblong objects. We can visualize individual groupings in a tree structure, but not overlapping subsets—precisely because they overlap. It is beyond us to visualize four sets simultaneously in one simple move. We have to decompose and then re-compose. We have royally screwed up our cities because we can’t readily apply Plato’s carving knife along the natural joints.

Much of Alexander’s pragmatic how-to material counters current architectural tooling and practices. Building contracts should not be based on complete A to Z blueprints and CAD drawings where all values are pre-assigned. Better a step-by step unfolding process where each stage has its own coherence and a manageable number of decisions. If, for example, you are standing on a building site where windows will look out over a valley and you have walls partially in place, you can effortlessly place those windows exactly where they need to be for maximum effect. If, however, you must, early in the process, place the windows on a blueprint while sitting at a desk a hundred miles from the site, it is hit or miss. If a client wants a generous entrance, do not put down arbitrary measurements but, rather, let the desire for generosity float until measurements are absolutely necessary, and, by that time, more relevant contextual information will be in place. Basically, postpone decisions until the construction context requires them.

Take inspiration from traditional building practices which put decisions at the right level—meaning the level where the multiplicity of design constraints is naturally best understood. Consider, for example, design by misfit described in Notes. The power to initiate change resides with those who personally experience the misfit. If you, as owner of a home, recognize that the best improvement expenditure to be a small brick patio just outside the kitchen door, so be it, you put it in. If your brick laying skills aren’t quite up to the job, that’s no problem, you can retouch and get it right. If, however, you are renting from an absentee landlord, the improvement is unlikely to happen. Design by misfit affords great system robustness. Small changes bring in necessary evolution while the overall system retains necessary stability.

Traditional building also suggests humility. Patterns, just to take that aspect, result from many people, over many years, in many different situations, trying, failing, experimenting again and again. Many of the fresh new patterns that people currently publish are trivial. Of course they are. It’s too difficult. And a good pattern is never lopsided. All forces must be reconciled. There is no point in super-efficient wind turbines if it makes the rest of the habitat unpleasant. This is Alexander’s main comment to the sustainability crowd.

I once asked him if he could make one change, and only one change, to the way building was done, what would that be. He replied that he would limit materials to those naturally found within a regional radius, as done in vernacular building. He would not bet on builders to do the right thing; he would rather bet on the power of the materials themselves—because of their inherent constraints—to command a certain coherence in texture and structure, and to retain a certain wholeness through a natural marriage to the land.

Alexander’s life work provokes discussions, conferences, publications, listservs. Although I have no proof, it seems to me that Alexander’s readership falls into two camps. Each camp selects out of Alexander’s extensive writings those pieces which bolster its preferred mode.

Those of us whose comfort zone is more qualitative and intuitive enjoy and employ a richer and arguably more precise language which deliberately includes the personal, the embodied, and which animates the sensations of life within the built environment. We tolerate ambiguity, multiplicity, and contradictions, but easily miss out on the economy of perceptive effort that comes with abstraction and algebraization. We tend to be less handy with power tools based on computerization.

Those of us with a leaning toward quantification and analytical work adapt easily to substantial instruments of simulation and modeling but are subject to the heavy price tag that comes with reductionism and over automatization. Unlike the iconic Zen butcher who never has to sharpen his carving knife because he cuts where the meat isn’t, our feelingless tools allow us to slice the wrong way. We then fail with composition and the synthesis of form.

We need all our skills and each other. That which can be rendered into mathematics cannot be readily rendered into empathy and vice versa.

The contention in this essay has been that Alexander’s unusual and continued ability to explore the fringes of understanding resides in the feedback loops of his dual regard and tireless zigzagging. The wellspring of his creativity is his Janus headedness.

References

Alexander, Christopher. Notes on the Synthesis of Form. Cambridge, MA: Harvard University Press, 1964.

Alexander, Christopher. “BART: The Bay Area Takes a Million Dollar Ride.” Architecture Forum 124 (1965): 36–61.

Alexander, Christopher, M. Cox, H. Abdelhalim, E. Hazzard, I Kural, and M. Schukert. The Grass Roots Housing Process. Berkeley, CA: Center for Environmental Structure, 1973.

Alexander, Christopher, M. Silverstein, S. Angel, S. Ishikawa. and D. Abrams. The Oregon Experiment. New York: Oxford University Press, 1975.

Alexander, Christopher, S. Ishikawa, and M. Silverstein. A Pattern Language. New York: Oxford University Press, 1977.

Alexander, Christopher. A Foreshadowing of 21^st Century Art. New York: Oxford University Press, 1993.

Alexander, Christopher. The Timeless Way of Building. New York: Oxford University Press, 1979.

Alexander, Christopher. The Nature of Order, vol. 1: The Phenomenon of Life. Berkeley, CA: Center for Environmental Structure, 2001.

Alexander, Christopher. The Nature of Order, vol. 2: The Process of Creating Life. Berkeley, CA: Center for Environmental Structure, 2002.

Alexander, Christopher. The Nature of Order, vol. 4: The Luminous Ground. Berkeley, CA: Center for Environmental Structure, 2004.

Alexander, Christopher. Sustainability and Morphogenesis: The Birth of a Living World. Berkely, CA: Center for Environmental Structure, 2004.

Alexander, Christopher. “Harmony-Seeking Computations: A Science of Non-Classical Dynamics based on the Progressive Evolution of the Larger Whole.” 2009. (An extended version of a 2005 Keynote address at the University of York, England; available on livingneighborhoods.com.)

Alexander, Christopher. A City is Not a Tree. Portland, OR: Sustasis Foundation, 2015.

Chermayeff, Serge, and C. Alexander. Community and Privacy: Toward a New Architecture of Humanism. New York: Pelican Original, 1963.

Gabriel, Richard P., and Julian Quillien. “A Search for Beauty/ A Struggle with Complexity: Christopher Alexander.” Urban Science 3, no. 1, Special Issue: New Applications and Development of Christopher Alexander’s The Nature of Order (2019): 1-32. https://doi.org/10.3390/urbansci3010030.

Grabow, Stephen. Christopher Alexander: The Evolution of a New Paradigm in Architecture. London: Routledge & Kegan Paul, 1983.