“Fright is something one can never get over. When a warrior is caught in such a tight spot he would simply turn his back to the ally without thinking twice. A warrior cannot indulge thus he cannot die of fright. A warrior allows the ally to come only when he is good and ready. When he is strong enough to grapple with the ally he opens up his gap and lurches out, grabs the ally, keeps him pinned down and maintains his stare on him for exactly the time he has to, then he moves his eyes away and releases the ally and lets him go. A warrior, my little friend, is the master at all times.”
Carlos Castaneda

A Separate Reality

Christopher Alexander – Fundamental Property 11: Roughness

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This is one of the patterns that resonate deeply with me. It makes me feel at ease, relaxed, it gives me permission to do what I feel needs to be done without having to know in advance how everything will come together. It invites me to trust my choices and to trust that tending to well to what is before me now is the best thing I can do “in the grand scheme of things.”

“Things which have real life always have a certain ease, a morphological roughness. This is not an accidental property. It is not a residue of technically inferior culture, or the result of hand-craft or inaccuracy. It is an essential structural feature without which a thing cannot be whole.

The Persian bowl … is covered by mall designs (sinekli) made of two blows and two strokes … They are rough, in the sense that the size of the individual brush strokes, their exact spacing, and the exact shape and length of stroke all vary from one to the next …

It is intuitively clear that this subtle variation is partly responsible for the charm and harmony of this bowl … we probably attribute this charm to the fact that the bowl is handmade … trace of human hand … we know therefore that it is personal, full of human error.

This interpretation is fallacious., and has entirely the wrong emphasis. The reason that this roughness in the design contributes so greatly to the wholeness of the bowl is that a perfect triangular grid of the kind used here, cannot be made to fill a spherical surface properly …

Indeed, throughout the design the subtle variation of the brush strokes and their spacing, are done in such a way … each one is placed, by eye, just exactly where it needs to be … When the painter painted the strokes, he could do this almost without thinking … it is this which makes the bowl so perfect …

Often the border of ancient carpet is ‘irregular’ where it goes round the corner, that is the design breaks, and the corner seems ‘patched together.’ This does not happen through carelessness or inaccuracy. On the contrary, it happens because the weaver is paying close attention to the the positive and negative, to the alternating repetition of the border, to the good shape of each compartment …  To keep all of them just right along the length of the border, some loose and makeshift composition must be done at the corner.

If the weaver wanted to calculate or plot our a so called ‘perfect’ solution to the corner … these would all be determined mechanistically by outside considerations, i.e., by the grid of the border … The corner design would then dominate the design in a way which would destroy the weaver’s ability to do what is just right at each point. The life of the design would be destroyed.

… The seemingly rough arrangement is more precise because it comes from a much more careful guarding of the essential centers in the design.

… Roughness can never be consciously or deliberately created. Then it is merely contrived. To make a thing live, its roughness must be the product of endlessness, the product of no will … Roughness is always the product of abandon – it is created whenever a person is truly free, and doing only what is essential

… Roughness does not seek to superimpose an arbitrary order over a design, but instead lets the larger order be relaxed, modified according to the demands and constraints which happen locally in different parts of the design.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

 

 

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Some good clay advice: stop for just a moment

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Beautiful work and heart. Hearing about narratives in his works made me look inside and wonder what would my narratives be? I (still) cannot see them … I felt naked.

via Iulia 🙂

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Christopher Alexander – Fundamental Property 10: Gradients

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“… Gradients must arise in the world when the world is in harmony with itself simply because conditions vary. Qualities vary, so centers which are adapted to them respond by varying in size, spacing, intensity and character. Daylight varies from the top floor of an urban building to the bottom floor: both windows and ceiling heights will probably have to vary to adapt to these conditions …

… These gradients will also form centers because the field-like character which is needed to make every strong center is precisely that oriented, changing conditions which ‘points’ towards the center of the center …

Buildings and artifacts without gradients are more mechanical. They have less life to them, because there is no slow variation which reveals the inner wholeness …

… although gradients are commonplace in nature … and in much traditional folk art, they are nearly non-existent in much of the modern environment. That is, I think, because the naive forms of standardization, mass production … and regulation of sizes … all work against the formation of gradients, and almost do not allow them to occur.

… In the towers of the Golden Gate Bridge there is a fine gradation of cell size, member size, ad plate thickness, from the top of the tower, to the bottom, to economize on steel, and place the most material where it is needed most by stresses.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

see also: Paul Krafel: Gradients and Edges

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Christopher Alexander – Fundamental Property 9: Contrast

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“… Life cannot occur without differentiation. Unity can only be created from distinctness. This means that every center is made from discernible opposites, and intensified when the not-center, against which it is opposed, is clarified, and itself becomes a center … in order for the thing to be truly whole, the contrast has to be pronounced … the most important contrasts do not merely show variety of form … but represent true opposites, which essentially annihilate each other when they are superimposed … awareness of silence created by a hand-clap …

In the case of the Shaker classroom … the two bands of wood above shoulder level, because of contrast, form a definite center which would not be there or felt strongly – if the wood were pale … The center which is so formed helps the room to become one, unified …

In the glaring lobby staircase … the contrast – between dark stair and bright window – does not unify … It is not contrast created in order to help centers become alive. IT is either a mistake, or an eye-catching device.

I use this rule to help people understand the fifteen properties: ‘Draw diagrams … sketch something, which has the property in it. But it is not enough to catch the property as you believe it is defined. To succeed, you must make a thing which has the property, and which gains deeper feeling because of the presence of the property. Only when you have managed that, can you be sure that the meaning of the property has not eluded you.’ … only when you … make the thing have deeper feeling, can you say you have grasped the property.

… contrast is also practically necessary: the shop in the neighborhood is different from the houses next to it. The front door is different from the back door … The light i the bedroom is different from the light in the passage. In case after case evidence suggests that the sharp extended and visible differences between things which are different allows each center to make its proper nature. It permits more intensive attention to individual functions. And it creates a feeling of distinction which relaxes people, because it acknowledges and permits different dimensions of experience.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

I’ve done a bit of editing to demonstrate the simulation for the Shaker Schoolroom:

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Christopher Alexander – Fundamental Property 8: Deep Interlock and Ambiguity

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Images selected by me inspired by the ones shown in the book.

“In a surprisingly large number of cases, living structures contain some form of interlock: situations where centers are ‘hooked’ into their surroundings. This has the effect of making it difficult to disentangle the center from its surroundings.

… a similar unification is accomplished through the creation of spatial ambiguity … a common example … is the house with a gallery or arcade round it … the space in the gallery belongs to the outside world and yet simultaneously belongs to the building.”

Profound interlock in Inca stonework

Dovetail as an example of deep interlock

Tile-work and brick in the 16th centur Tabriz Mosque

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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Christopher Alexander – Fundamental Property 7: Local Symmetries

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“… Where a living center forms, it is often necessary to have some local symmetry.

… Living things, though often symmetrical, rarely have perfect symmetry. Indeed, perfect symmetry is often a mark of death in things, rather than life. I believe the lack of clarity on the subject has arisen because of a failure to distinguish overall symmetry from local symmetries.

… The Rorschach ink-blot, for instance, is a rather weak whole; it has relatively little life as a structure; its centers are poorly developed. The one large symmetry it has, by itself, gets you very little.

… over simplified symmetry in a building is mot often naive and even brutal … Albert Speer’s design for Zeppelinfeld … is [an] example …

In general, a large symmetry of the simplified neoclassicist type rarely contributes to the life of a thing, because in any complex whole in the world, there are nearly always complex, asymmetrical forces at work – matter of location, and context, and function – which require that symmetry be broken.

We see this clearly in the Alhambra … a marvel of living wholeness. It has no overall symmetry at all, but an amazing number of minor symmetries, which hold within limited pieces of the design, leaving the whole to be organic, flexible, adapted to the site.

… the real binding force which symmetry contributes to the formation of life is … in the binding together and local symmetry of smaller centers within the whole.

… an experiment I did … at Harvard Center for Cognitive Studies … I compared a number of black and white paper strips, and measured their coherence as felt, experienced, perceived, remembered, by different subjects.

… The experiments were performed with 35 black-and-white strips seen on a neutral gray background. Each strip was 7 squares long, and was composed of 3 black squares and 4 white squares, arranged in different arrangements …

First, we established that the relative coherence of the different patterns … is not an idiosyncratic subjective feature of the patterns seen differently by different people. It is an objective measure of cognitive processing, roughly the same for everyone.

Second, we were then able to identify the structural feature of these patterns which caused this perceived ‘coherence.’ It turned out that [it] … depends on the number of local symmetries present in the pattern. However since most of the symmetries are hidden, this feature is far from obvious …

… For three of four years after completing the experiment, I worked almost continuously to find some structural feature of the 35 black and white patterns which would explain the rank order of coherence of the different patterns …

… it was quite unclear how to unite the idea of symmetry with the idea of large lumps. It was this that finally gave me the key, when I realized that both overall symmetries and large lumps actually contain more local symmetries inside them.

.. the strips which are most coherent experimentally also have the highest number of subsymmetries to within a high degree of correlation … The number of local symmetries the pattern contains essentially predicts how ‘good’ it is.

… It is as if the symmetrical segments act as a kind of glue … which holds the space together. The more glue there is, the more the space is one, solid, unified, coherent. And … for the glue to be effective, it seems that many of the symmetrical segments must overlap.

… the local symmetries … though hidden from view … essentially control the way the pattern is seen and the way it works.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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Christopher Alexander – Fundamental Property 6: Good Shape

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Reading this section while thinking about creating the excerpt made me tense. I feel this property is tricky because it is so obvious and yet also so subtle and hard to pin down. When I create these excerpts I choose to share parts which feel clear and resonate for me (in the hope that my sense of clarity adds something to the being-ness of excerpt). This one was sticky. It was challenging for me (the first time around, the second time easier) and I expect it may be challenging for you. It demands that we look examine our likes (and dislikes). It is confrontational in that it dares to suggest that we’ve learned to like futuristic chairs; that they are empirically bad; and that if we want to learn to make living structures we are going to have to acknowledge this, reflect on these likes and we are going to have to unlearn them, to see past them, to restore a deeper, more subtle form of seeing. It is a tough ask.

The Copenhagen Police Headquarters was the only image specific enough to seek out and find on my own, the others felt too subtle and I could not find substitutes that felt good enough for me, so I scanned them from the book.

“When I began looking for living structures … I became aware of a special quality that I began to think of as good shape, but could not very easily explain it, or define it …

It took me a long time to see that good shape itself is also related to the centers … a shape we see as good it a shape which it itself, as a shape, made up from multiple coherent centers …

It it easiest to understand good shape as a recursive rule … the elements of any good shape are always good shapes themselves …

… the simplest and most elementary good shapes are from elementary figures … the good shape, no matter how complex, is built up from the simplest elementary figures. The teapot stand can be seen to be built up from the illustrated simple shapes, each of which has good shape …

On the other hand, the amorphous mass of the futuristic chair cannot be understood as being composed of elementary shapes at all.

… what seems like complex centers are made of simple centers which are also alive – and it is these centers above all which give the complex ones their life …

… The good shape is an attribute of the whole configuration, not of the parts; but it comes about when the whole is made of parts that are themselves whole in this rather simple geometric sense …

All in all, in my experience, in the build-up of a good shape the following elements are the most common: square, line, segment, arrowhead hook, triangle, row of dots, circle, rosette, diamond, S-shape, half-circle, star, steps, cross, waves, spiral …

All of this is subtle when we try to apply it. Take the circle, for instance … [it] has great problems. The space next to it is not easily made positive, not easily made into centers – and the circle, when used in a design can easily then not be good shape at all. We see such an example in the courtyard of the Copenhagen Police Headquarters: a ridiculous plan, which is trivial because the space next to the circle is formless, and therefore meaningless.

The high degree of sophistication needed to make a circle have good shape is seen in the fabulous Ottoman velvet … where the two systems of circles are drawn slightly distorted so that the moon shapes, the space between the circles, and the small circles and large circles all work as centers.

Although it may seem surprising to someone raised in the mechanist-functionalist tradition, good shape … is not only making things more beautiful; it also makes them work more profoundly, more effectively.

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

 

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Christopher Alexander – Fundamental Property 5: Positive Space

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“What I call positive space occurs when every bit of space swells outward, it substantial in itself, is ever the leftover from an adjacent space. We may see it like a ripening corn, each kernel swelling until it meets the others …

An almost archetypal example of this positive and coherent state of space may be seen in the 17th century Nolli plan of Rome. In this plan each bit of every street is positive, the building masses are positive, the public interiors are positive. There is virtually no part of the whole which does not have definite and positive shape. This has come about, I think, because of these spaces … has been shaped over time by people who cared about it, and it has therefore taken a definite, cared for shape with meaning and purpose …

In the present Western view … we tend to see buildings floating in empty space … the buildings … have their own definite physical shape – but the space which they are floating in is shapeless, making the buildings almost meaningless in their isolation. This has a devastating effect: it makes our social space itself – the glue and playground of our common public world – incoherent, almost non-existent …

Here in the famous Kizaemon tea bowl, now preserved in Japan … its beauty lies in the fact that not only does the bowl have a beautiful shape in itself, but that also the space next to the bowl has a beautiful shape. One might even say that the beauty of the bowl is created by the fact that the space next to it is beautiful.

… In Matisse’s cut-out blue nude, every part of the space is positive …

The definition of positive space is straightforward: every single part of space has positive shape as a center. There are no amorphous meaningless leftovers. every shape is a strong center, and every space is made up in such a way that it only has strong centers in its space, nothing else besides.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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Christopher Alexander – Fundamental Property 4: Repetition

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Once again, except for the dull office building facade (scanned from the book), the images are selected by me.

“… Centers intensify other centers by repeating. The rhythm of the repeating centers, slowly, like the beat of a drum, intensifies the field effect.

… Most things are made from repetition at some level: repetition of atoms, molecules, waves, cells, volumes, roofs, trusses, windows, bricks, columns, tiles, entrances and so on. But the repetition which occurs in things which have life is a very special kind of repetition … where the rhythm of the centers that repeat is underlined, and intensified, by an alternating rhythm interlocked with the first and where a second system of centers also repeats, in parallel. The second system of centers then intensifies the first system, by providing a kind of counterpoint, or opposing beat.

… Somehow the sense of order in a thing comes from the fact that elements are repeated … often the calmest life arises when a thing, like a basket, is made entirely out of one kind of smaller element repeating.

… repetition tends to be inexact; it is then the subtle variation which comes with the repetition that is satisfying and life giving. This happens because the elements are not identical, but modified each according to its position in the whole …

But there is a deeper aspect of the repetition. This concerns the fundamental character of the repetition and the way that elements are repeated: there is profound and satisfying repetition of living centers, and there is banal repetition of elements …

… the facade of a modern office building … Here the alternation is brutal, banal … what repeats is one dimensional: there is no alternation to speak of, no living centers … no vital secondary centers …

… in Brunelleschi’s Foundling Hospital, the round medallions alternate within the columns and column bays. We see the columns repeating … the arches repeating … space of bays repeating … triangular space between adjacent arches repeating … ceramic roundels in these triangles repeating … Each of these things … is a profoundly formed and living center. The result is beautifully harmonious and has life.

… it seems that what is really happening is not repetition, but oscillation … In the Ottoman velvet … the oscillation … has reached tremendous and profound subtlety.. The waves with the ‘lips’ oscillate. The triple circles oscillate. The space between circles and lips oscillates. The overall effect is a profound unity.

… The life comes about only when the alternating wholes are beautifully and subtly proportioned and differentiated.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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Christopher Alexander – Fundamental Property 3: Boundaries

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My attempt to find suitable images to use in these excerpts is a demanding practice. This time I separated the task of looking for images from writing the excerpt itself. At first I felt that these images were easier to find than those for the previous posts. But then when I came to assemble the excerpt and looked at the examples in the book, I again saw differences. Though the example I have chosen to include in the excerpt are valid, they are usually not as good as the ones in the book. Noticing these differences is a profound learning experience for me.

” … living centers are often – nearly always – formed and strengthened by boundaries …The Norwegian storehouse is replete with boundaries at every scale …

The purpose of a boundary which surrounds a center is two-fold. First, it focuses attention on the center and thus helps to produce the center. It does this by forming the field of force which creates and intensifies the center which is bounded. Second, it unites the center which is being bounded with the world beyond the boundary. For this to happen, the boundary must at the same time be distinct from the center being bounded, must keep this center distinct and separate from the world beyond it, and yet also have the capacity of uniting that center with the world beyond the boundary. In both ways, the center that is bounded becomes more intense.

… the boundary needs to be of the same order of magnitude as the center which is being bounded. If the boundary is very much smaller than the thing being bounded, it can’t do much to hold in or form the center … An effective boundary for the river Seine consists of roads, walls, paths quays, trees, something almost as massive as the river itself. It general it it necessary to think of boundaries as very large.

When taken seriously this rule has a very big effect on the way things are organized … the lips as the boundary of the mouth are similar in size to the mouth; an arcade … the same order of size as the building … marsh as boundary of a lake … capital and base as boundary of the column …

The door as a center is intensified by placing a beautiful frame of centers around that door. The smaller centers in the boundary are also intensified, reciprocally, by the larger center which they surround

… to establish the interlock and connection, coupled with separation … the boundary itself is also formed of centers … in the [Persian] manuscript … the boundary is formed out of large centers, sometimes almost as large as the field, but made in such a way that they unite the thing bounded with the world beyond … Essentially they form centers, or systems of alternating centers, which look both ways …

… Taken by itself, the boundary rule seems simple. But the rule does not merely refer to the outer boundary of the thing. If we apply the rule repeatedly, it says that every part, at every level, has a boundary which is a thing in its own right. This includes the boundaries themselves. They too have boundaries, each of which is a thing in its own right. What seems like one rule, then, is a pervasive structural feature of enormous depth, which is in effect applied dozens or hundreds of times, at different scales throughout the thing.

… it is possible for a thing to follow this rule and still lack an outer boundary around the whole, because that outer boundary (present or not) is merely one of ninety-nine other boundaries which do exist within the whole, at different scales … The limited idea of a main boundary by itself completely fails to convey the shimmering sense that is created when a hing has boundaries within boundaries, which are boundaries of boundaries, and that all together permeate its structure.

The castle of Gwalior: the whole building front is made of boundaries, and boundaries of boundaries.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

This additional example came up in my searching … I keep staring at it and getting lost in it … almost transported into a dream-like state:

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Christopher Alexander – Fundamental Property 2: Strong Centers

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For this excerpt I was able to find compatible images, so the images you see are not the ones shown in the book.

“… I began to  notice that, next to the property of levels of scale, possibly the most important feature of a thing which is alive is that we find that the various wholes which exist at different levels appear not merely as centers or ‘wholes” or ‘blobs,’ but actually as strong centers.

… As we look at the mosque of Kariouan … we see many mutually reinforcing centers. The great courtyard, the large dome, the smaller dome, the individual battlements, the steps, the entrance, the individual arches, even the segments on the roof … the sequence of three domes, each one higher than the other, leading up to the main dome as a pinnacle. The entire structure builds up to the main dome …

 

… The imperial inner city of Beijing … is a layered system of nested domains which lead, one by one, to the inner city, and then to the inner sanctum of the inner city … the deep center arises at the heart of the inner city, because of the field effect generated by the nesting.

… In contemporary buildings, it is often hard to create this hierarchy of centers, perhaps above all because – in practical terms – we don’t know what to put at the center … What function could there be at the center that is important enough to  make the building have a series of levels …? … What were once powerful centers – the fire, the marriage bed, the table – no longer have this power, because individually and as families are not centered in ourselves. The emotional confusion of the present-day family reveals itself in the lack of power in these centers of the house.

But when a house is organized with clearer centers … it becomes immediately more potent, even in its ability to harness unknown and undeveloped tendencies of centering in the life people live there together.

… The tip of each roof in the trulli at Alberobello is a strong center which is formed, not merely by the little knob, but by the way the whole roof of focused towards the tip, the way the tip if painted white, and the way this then culminates as a core of a center that is formed.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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Damien Rice (Soirée de Poche)

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he seems to be in a delicate place and resonating wish so much power and clarity.

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Christopher Alexander – Fundamental Property 1: Levels of Scale

n

I spent a couple of hours trying to find alternative images to those in the book. The concrete one was easy to find, the rest not … so I  gave up trying. The images in the book (especially the living ones) are too subtle to easily replace. So I opted to scan a few samples (this chapter, and the next 14 are filled with many more visual examples). I have picked out a bare minimum to support the core idea.

“The first things I noticed when I began to study objects which have life, was that they all contain different scales. … the centers these objects are made of tend to have a beautiful range of sizes, and that these sizes exist at a series of of well-marked levels, with definite jumps between them.

… If you capture any two things, one with more life and one with less, it is very likely that the one with more life will have better levels of scale in it … consider the following pairs of doors  … both … have parts of different sizes … but the door on the right has a variety of sizes which is more dramatically differentiated, more ‘extended’ along the range of scale than the door on the left. It has three sizes of panels, it has a gradation of scale from the bottom to the top.

… In the right-hand door, we experience the levels more deeply …  First, there actually are more levels … [and] the degree to which the centers help each other … the actual life of each center comes about because it is enlivened by the size and position of the next larger center which lies near it, and by the size and position of the next smaller center which lies near it.

In the left hand door the detail is there – but the details isn’t doing anything to create life in the larget centers, and is therefore almost meaningless.

It is also extremely important that to have levels of scale within a structure, the jumps between different scales must not be too great … if we look at the concrete wall in the picture below … the wall [is] a center … we also see small individual centers (bolt or boltholes) … [they] are too far apart in scale to be coherent with each other.

… To intensify a given center, we need to make another center perhaps half or a quarter the size of the first. If the smaller one is less than one-tenth of the larger one it is les likely to help in in its intenstity.

… In the tilework at Meshed, we see this principle carried from the giant tower-like structures through many intermediate levels, all the way down to the tiles themselves. There are distinct wholes, or centers, visible at every level in between the two.

… the small centers intensify the large ones … the large centers also intensify the small ones …”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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Japanese Words for “Space”

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Thinking of Christopher Alexander and his Japanese Tea House sequence as I was reading this:

“a space in Japanese culture is understood by how it shapes relationships … a room is always filled with invisible structures, regardless of its occupants

… For example, traditional tea houses have doors that are narrow and low. This forces guests to lower their head and, historically, for samurai to leave their swords outside by the door.

… Building spaces that deepen relationships (wa), generate new knowledge (ba), connect to the world around us (tokoro), and allow moments of quiet and integration (ma) can enrich our experience of the world and that of those around us.”

source

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Drawing Centers

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As I mentioned before I took some time to draw centers … and it was a fascinating practice. I tried to capture some of it, though to fully experience it I invite you to do it on your own.

Milford Graves (<– link will open in a new tab in case you wish to listen while reading) guided me through this exercise 🙂

This is the source (from the book) I started with:I had already spent time reading about the pattern and following Alexander’s guidance in how to look at it (seeking centers, local symmetry, etc.)  … and I gave it a first try:

I then went at it a second time and paused to scan each step on the way. It starts with a dot on a piece of paper that starts to unfold and increase with life:

I did step 2 already in my first try, but step 3 was a big aha moment for me. In my first try I went directly to the “black hearts” that are attached to the small protrusions, but I did not know how to size them properly so that there would be room for the thickness of the white heart itself. When I looked at the image some more the 4 diagonal lines suddenly popped out … and they made the next steps simple and steady and peaceful:

The diagonals created clear fields from which the hearts appeared. That transition in step 3 became like a switch that came on and stayed on. I found simplicity and clarity in the black spaces. Instead of trying to draw the white spaces that I was seeing by default I switched to seeking the black spaces.

I was being held and guided by the black spaces, yet something in me wanted to “do the hearts” … but I stuck with the black

… until it felt necessary to draw the top heart as it lead into the evolution of the pattern at the top

… and the top part appeared with ease, easier than my first attempt to “draw it” … and closer to the original.

… the rest of the hearts followed naturally and swept down … and then it felt that a base was needed … and the spaces that formed between the base and the heart-flower already started to glow with the horizontally oriented patters of the base … and again black guided:

… two small black triangles … and fill it all in:

I’ve pulled together the source and my two attempts for comparison:

The second attempt was easier and more peaceful and I now know and remember it in a very different way – not so much as an image but rather as a sequence of steps in which centers come into being. I feel that if I spent more time and more iterations with it, I could refine the sequence … a recipe, narrative, story … a pattern that underlies the visual image. I may already be able to draw it again without having to look at the source image.

The second attempt is also closer to the source, better balanced, fuller, more stable. This is especially clear if you look at the top and bottom patterns. In the first attempt I tried to draw the actual white shapes (at the top and bottom) which is very tricky because my eyes registered one thing “the white space” but because it has thickness two lines need to be drawn to create that space. In the second attempt I created the black spaces and the white-spaces were simply left over.

In both attempts I did not get the proportions of the heart-flower correct: the hearts were too big in relation to the actual center.

I decided to go ahead and try the second pattern (for the first time). When I first looked at it, there seemed to be a spacing challenge. Then I realized that the top pattern (which I had already learned) created the overall rhythm … and so I started with it:

and then started traveling down … again following a clear path of black spaces.

… and that’s when those wrong proportions of the heart-flower really surfaced. Step 20 should have brough me way further down. I had to correct, in step 21,  by stretching what should have been squares into longer rectangles.

This is just one example of many, how a slight change in one element resonates strongly through the entire wholeness. Millimeters differences can have a drastic effect on this image which is ~9cm by 7 cm. This also demonstrated the idea of “character” – like in the four images of Matisse – despite variations caused by my perception and drawing, the overall pattern (if I got the centers right) persists.

Here the sequence started to become less clear to me. I feel that I still have not discovered the right sequence of centers for this second pattern … still black spaces guided me well:

… and once again the original for reference

… this felt fundamental … like learning to walk …

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Milford Graves

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this delightful creature came to me via Fred Wilson

I just went swimmig through these two albums:

reminded me of my encounters with Ariel Shibolet in Israel … right around my time with Shahar

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Christopher Alexander – 15 Fundamental Properties

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There is a bit of an anxiety in me as I arrive at this excerpt. It is rooted in knowing that in publishing it I am making a kind of commitment about the next 15 excerpts. And since this is my second reading, I know how daunting a task this can be. So I am curious how this is going to unfold.

“… I began to notice that objects and buildings which have life all have certain identifiable structural characteristics. The same geometric features keep showing up in them, again and again. Initially I began writing these characteristics down informally, and I began to ‘keep watch’ on them.

What I did was straightforward and empirical. I simply looked at thousands and thousands of example, comparing those which had more life with those that had less life. Whenever I looked at two examples, I could determine which one had greater ‘life’ or greater wholeness, by asking which of them generated a greater wholeness in me. Thus I did not impose on myself the modesty of judgement typical in a pluralistic society …

I asked myself this question: Can we find any structural features which tend to be present in the examples which have more life. and tend to be missing in the ones which have less life?

… This is what I did. For twenty years, I spent two or three hours a day looking at pairs of things – building, tiles, stones, windows, carpets, figures, carvings of flowers, paths, seats, furniture, streets, paintings, fountains, doorways, arches …

I managed to identify fifteen structural features which appear again and again in things which do have life. These are:

  1. Levels of scale
  2. Strong centers
  3. Boundaries
  4. Alternating repetition
  5. Positive space
  6. Good shape
  7. Local symmetries
  8. Deep interlock and ambiguity
  9. Contrast
  10. Gradients
  11. Roughness
  12. Echoes
  13. The void
  14. Simplicity and inner calm
  15. Not-separateness

At first, I observed  these features without understanding what they were. That is, I understood each of them … as something which was present, often or very often, in a living system – to such an extent that one might almost say that each one was a predictor of whether a thing would have life or not … [but] I did not understand why …

I came to understand that they work, they make things have life, because they are the ways in which centers can help each other in space.

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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Christopher Alexander – Centers & Life … and Robert Pirsig

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This excerpt has, for me, a unique flavor. It is brief. I originally intended to skip it, but decided to come back to it. It will probably come across as abstract. I did not find a way to capture the essence of the next few sections which contain examples that illustrate the point Alexander is trying to make (which is why I was leaning towards skipping it).

This point is also special for me because in it (details below) Alexander references the work of Robert Pirsig. This is the only work that I’ve encountered that acknowledges Pirsig’s work which has inspired me so much.

“Armed with the ideas that each center is a multi-levelled field-like phenomenon made of other centers, let us now come back to the idea that each center has its degree of life[*footnote referencing Pirsig].

… I want to now extend this idea and apply it separately and individually to every distinct center in the wholeness of a thing …

… the degree of life of each center in a given wholeness depends on the degree of life of all the other centers in the wholeness.”

Robert Pirsig footnote:

“The idea that every center has its life make the ‘life’ of the centers teh ultimate primitive of this theory. This is perhaps comparable to Robert Pirsig’s idea that Quality, not Substance, is the ultimate primitive. As Pirsig puts it, ‘Quality is supposed to be just a vague fringe word that tells what we think about objects … The idea that quality can create objects seems very wrong … but the idea that values create objects gets less and less weird as you get used to it.’ … I am saying something similar about that which animates the living centers.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

The following section includes an image (though not this one) of this space in the Alhambra:

… followed by a detailed inquiry into the pattern that is un the lower half of the picture – the texture beneath the arched openings. I attempted to play around with recreating in sketching one of the elements that make up the pattern and was blown away by 1) allowing myself to sketch, shifting my attention away from precision and towards centers and 2) the seeing and subtlety that are required to recreate it, even when it already exists before my eyes as a reference. It is amazing how very small variations project so strongly into the wholeness that is created. The more time I spent with it the more I realized how much more there it to see … my “success” or “failure” was not so much a function of my drawing abilities (close to none) but of my ability to perceive.

I am now playing with sketching a more elaborate pattern from one of a Turkish rug mentioned in one of the next sections.

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Christopher Alexander – Recursive Centers

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“What exactly is a center? …

The crux of the matter is this: a center is a kind of entity which can only be defined in terms of other centers. The idea of a center cannot be defined in terms of any other primitive entities except centers.

We are used to a view where we try to explain one kind of entity by showing it to be constructed of other different kinds of entities. An organism is made of cells, an atom of electrons, and so on … If we ask what the centers are made of, we come up against a brick wall. Here we have a question so fundamental that it cannot be explained or understood, as a composite of any other more fundamental kind of entity … centers are only made of other centers.

… In mathematics, such a concept is called recursive. Grasping this idea, and grasping the fact that this bit of understanding is a positive step forward, and not problematic is key to understanding wholeness.

… What then is a center? A center is not a primitive element. Centers are already composite. Yet they are the most primitive element available. They are bits of wholeness which appear as structures within the wholeness … It is … a field of organized force in an object or part of an object which makes that object or part exhibit centrality.

… This circularity … is the essential feature of the situation.”

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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Christopher Alexander – Living Structure created by Centers

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Once again, the illustration is my attemp to replicate an illustration from the book.

“mutual helping among the centers … causes … life

… the terrace is made of structural bays – each made by four columns – each roughly square … Each of these bays it itself a center … The columns are centers too. And on each column, on each of its corners, there is a chamfer. The chamfer is once again a center in its own right.

Each of the four-column bays is helped to be alive by these tiny chamfers on the columns at the corners of the bay … each bay becomes more of a center, and is more alive, because of the chamfer. Suppose, for example, that the column had been square, without the little octagonal chamfer on the corners. Then … each column would slightly eat into the space of the bay, thus disturbing the wholeness of the bay. Instead, the four chamfers help, geometrically, to increase the unity and wholeness of the space in the bay … chamfers … two or three inches across, strengthen and intensify the structural bay …13 feet across.

… this helping relation … does not occur automatically … the columns could have been given a shape which does not help … “

Christopher Alexander – The Nature of Order – Book 1: The Phenomenon of Life

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