Apr 25, 2021
The fundamental structure-preserving transform

(Notes from A Search for Beauty / A Struggle with Complexity: Christopher Alexander by Richard P Gabriel and Jenny Quillien, with indented passages by Christopher Alexander.)

Jane Jacobs' place ballet is about the ability of an urban hardscape to accommodate multiple choreographies acted out simultaneously. A single-use prop, say a fancy street bench where one can only sit, does us little good. We're better off with a low wide wall that can operate in multiple subsets: protect a bed of tulips, let grandpa sit in the sun, invite little Johnny to pretend he's on a tightrope, mark a boundary for neighborhood gangs, and accommodate a teenager who needs to put down schoolbooks to text a friend.

Building traditions rooted in soil and history have a demonstrable superiority in dealing with organized complexity: distributed intelligence across a network, redundancy of information, multiple means of embedding information throughout the network, deep knowledge of variables such as local geography, weather patterns, multiple cultural demands, effective and economical use of local materials. Such a natural and un-self-conscious process entails gentle abstraction by generalization. Forms are local, buildable, purposeful, economic. Form does not follow function as in an abstract edict; function follows the concrete potentiality in the available forms. A field is cleared of rocks and the rocks offer their particular affordances for building, right there in situ. All interconnected within a complex whole. Modern professionals — with no choice but a self-conscious process which divorces them from such rich reality and limits them to arbitrary simplifications (often made far from the actual building site and inhabitants) — are condemned to failure. The number of likely mistakes is astronomical compared to the generated building where manageable phases unfold in sequence.

A tree of 20 elements maximally has 19 non-overlapping subsets, but a semi-lattice makes room for over a million. If it were 50 elements instead of 20, the number would start 'one quadrillion...' It is beyond us to visualize four overlapping sets simultaneously in one simple move. We have to decompose then re-compose.

There is a central quality which is the root criterion of life and spirit in a man, a town, a building, or a wilderness. This quality is objective and precise, but it cannot be named.

The great traditional buildings of the past, the villages and tents and temples in which man feels at home, have always been made by people who were very close to the center of this way. It is not possible to make great buildings, or great towns, beautiful places, places where you feel yourself, places where you feel alive, except by following this way. And, as you will see, this way will lead anyone who looks for it to buildings which are themselves as ancient in their form, as the trees and hills, and as our faces are.

The first place I think of when I try to tell someone about this quality is a corner of an English country garden where a peach tree grows against a wall. The wall runs east to west; the peach tree grows flat against the southern side. The sun shines on the tree and, as it warms the bricks behind the tree, the warm bricks themselves warm the peaches on the tree. It has a slightly dozy quality. The tree, carefully tied to grow flat against the wall; warming the bricks; the peaches growing in the sun; the wild grass growing around the roots of the tree, in the angle where the earth and roots and wall all meet.

The quality without a name is a subtle kind of freedom from inner contradictions.

This quality in buildings and in towns cannot be made, but only generated, indirectly, by the ordinary actions of the people, just as a flower cannot be made, but only generated from the seed.

  • an architect-builder is in charge
  • each site has its own builder’s yard for materials and tools
  • common land between houses and the array of lots is handled by the community itself in groups small enough for face-to-face meetings
  • families design their own homes
  • construction is based on a standard process, not on standard components.


  • Organic Order is achieved when there is a perfect balance between the needs of the parts and the needs of the whole: planning and construction will be guided by a process which allows the whole to emerge gradually from local acts
  • Participation: all decisions about what and how to build will be in the hands of the users
  • Piecemeal Growth: the construction undertaken in each budgetary period will be weighted overwhelmingly toward small projects
  • Patterns: all design and construction will be guided by a collection of communally adopted patterns
  • Diagnosis: the well being of the whole will be protected by an annual diagnosis which explains, in detail, which spaces are alive and which ones are dead
  • Coordination: the slow emergence of organic order in the whole will be assured by a funding process which regulates the stream of individual projects.


A center is something distinct which appears within the larger whole as a distinct and noticeable part. A center's distinctness makes it separate out from its surroundings and makes it cohere. It is from the arrangements of these coherent parts that other coherent parts appear.

A fundamental differentiating process for the man-made

At any given moment in a process, we have a certain partially evolved state of a structure. This state is described by the wholeness: the system of centers, and their relative nesting and degrees of life.

We pay attention as profoundly as possible to this wholeness — its global, large-scale order, both actual and latent.

We try to identify the sense in which this structure is weakest as a whole, weakest in its coherence as a whole, most deeply lacking in feeling.

We look for the latent centers in the whole. These are not those centers which are robust and exist strongly already; rather, they are centers which are dimly present in a weak form, but which seem to us to contribute to or cause the current absence of life in the whole.

We then choose one of these latent centers to work on. It may be a large center, or middle-sized, or small.

We use one or more of the fifteen structure-preserving transformations, singly or in combination, to differentiate and strengthen the structure in its wholeness.

As a result of the differentiation which occurs, new centers are born. The extent of the fifteen properties which accompany creation of new centers will also take place.

In particular we shall have increased the strength of certain larger centers; we shall also have increased the strength of parallel centers; and we shall also have increased the strength of smaller centers. As a whole, the structure will now, as a result of this differentiation, be stronger and have more coherence and definition as a living structure.

We test to make sure that this is actually so, and that the presumed increase of life has actually taken place.

We also test that what we have done is the simplest differentiation possible, to accomplish this goal in respect of the center that is under development.

When complete, we go back to the beginning of the cycle, and apply the same process again.

The fifteen properties

  • Levels of Scale: There are centers of all sizes, which support or help each other. Small jumps (2:1 or 4:1) are best.

  • Strong Centers: A strong center is one toward which other centers point. The eye rests on it, one keeps coming back to it, going away from it, coming back to it. In short, the entire design sets up a vector field so that every point has the property that from that point the center is in a certain direction.

  • Boundaries: A boundary separates a center from other centers; it focuses attention on the center; a boundary is itself made of centers.

  • Alternating Repetition: Strong centers repeated with alternating centers; not simple repeating; a pattern with variation.

  • Positive Space: A center that moves outward from itself, seemingly oozing life rather than collapsing on itself. We may see it like ripening corn, each kernel swelling until it meets the others, each one having its own positive shape caused by its growth as a cell from the inside.

  • Good Shape: A center is somehow beautiful by itself. It has high degrees of internal symmetries, a well-marked center (but not in the middle). The spaces it creates next to it are positive; it is very strongly distinct from what surrounds it and is relatively compact. It exhibits a feeling of being closed and complete. It is reinforced by other centers of good shape; it is made of centers of good shape.

  • Local Symmetries: Living things, though often symmetrical, rarely have perfect symmetry. Indeed, perfect symmetry is often a mark of death in things rather than life. Overall symmetry in a system, by itself, is not a strong source of life or wholeness. In any complex whole in the world, there are nearly always complex, asymmetrical forces at work—matters of location, and context, and function—which require that symmetry be broken.

  • Deep Interlock and Ambiguity: Centers are sometimes “hooked” into their surroundings. It is sometimes difficult to disentangle a center from its surroundings through actual interlock or through an ambiguous zone which belongs both to the center and to its surroundings.

  • Contrast: Works of art which have great life often have surprisingly intense contrast in them — far more than one remembers, more than one imagines would be helpful or even possible to sustain.

  • Gradients: Almost anything which has real life has a certain softness. Qualities vary, slowly, subtly, gradually, across the extent of each thing. Gradients occur. One quality changes slowly across space, and becomes another. Almost always the strengthened field-like character of the center is caused, in part, by the fact that an organization of smaller centers creates gradients which point to some new and larger virtual center. Sometimes the arrows and gradients set up in the field give the center its primary strength.

  • Roughness: Things which have real life always have a certain ease, a morphological roughness. It is not a residue of technically inferior culture, or the result of handcraft or inaccuracy. It is an essential structural feature which they have and without which a thing cannot be whole. Often the border of an ancient carpet is “irregular” where it goes round the corner — that is, the design breaks, the corner seems “patched together”. This does not happen through carelessness orinaccuracy. On the contrary, it happens because the weaver is paying close attention to the positive and negative, to the alternating repetition of the border, to the good shape of each compartment of the wave and each bit of open space—and makes an effort all along the border to be sure these are “just right”. To keep all of them just right along the length of the border, some loose and makeshift composition must be done at the corner.

  • Echoes: Smaller elements and centers, from which the larger centers are made, are all members of the same family, they contain echoes of one another, there are deep internal similarities between them which tie them together to form a single unity.

  • The Void: In the most profound centers which have perfect wholeness, there is at the heart a void, which is like water, in infinite depth—surrounded by and contrasted with the clutter of the stuff and fabric all around it. The need for the void arises in all centers. A cup or a bowl rests, as a living center, on the quiet of the space in the bowl itself, its stillness.

  • Simplicity and Inner Calm: A certain slowness, majesty, quietness. This quality comes about when everything unnecessary is removed. All centers that are not actively supporting other centers are stripped out, cut out, excised. What is left, when boiled away, is the structure in a state of inner calm. It is essential that the great beauty and intricacy of ornament go only just far enough to bring this calm into being, and not so far that it destroys it. Everything is still, silent.

  • Not Separateness: We experience a living whole as being at one with the world, and not separate from it. This is, finally, perhaps the most important property of all. The other fourteen ways in which centers come to life will make a center which is compact, beautiful, determined, subtle—but, without this fifteenth property, still often somehow strangely separate, cut off from what lies around it, lonely, awkward in its loneliness, too brittle, too sharp, perhaps too well delineated—above all too egocentric, because it shouts “Look at me, look at me, look how beautiful I am.”

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