tat tvam asi

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:

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 …

image via Wallpaper Cave

“We may consider any configuration in the world, a building, a street, a room full of people, a forest. Each has its wholeness. By that I mean that there are visible within that thing, a huge number of entities, at different scales … and that the totality of these entities with the way they are nested constitute the wholeness of the thing. We may think of these entities as parts (as they may sometimes seem to us) or as local wholes or sub-wholes. But, as I have illustrated in the case of the sheet of paper and the dot, these parts and entities are rarely pre-existing. They are more often themselves created by the wholeness. This apparent paradox is a fundamental issue in the nature of wholeness: the wholeness is made of parts, the parts are created by the wholeness. To understand wholeness we must have a conception in which ‘parts’ and wholes work in this holistic way.

… I have learned to call them … ‘centers.’ What this means is that each one of these entities has, as its defining mark, the fact that it appears to exist as a local center within a larger whole.

There is a mathematical reason for thinking of the coherent entities in the world as centers not as wholes. If I want to be accurate about a whole it is natural for me to ask where that whole starts and stops. Suppose, for example, I am talking about a fishpond, and want to call it a whole. To be accurate about it in a mathematical theory, I want to be able to draw a precious boundary around this whole, and say for each point in space whether it is part of this set of points or not. But this is very hard to do. Obviously the water is part of the fishpond. What about the concrete it is made of ..? the air which is just about the pond? … the pipes bringing in the water? These are uncomfortable questions … The pond does exist. Our trouble is that we don’t know how to define it exactly. But the trouble comes from referring to it as a ‘whole.’ That kind of terminology seems to make it necessary for me to draw an exact boundary … That is the mistake.

When I call a pond a center, the situation changes … the fuzziness of edges becomes less problematic. The reason is that the pond, as an entity, is focused towards its center. It creates a field of centeredness. But, obviously, this effect falls off … the organization of the pond is caused by a field effect in which the various elements work together to produce this phenomenon of a center. This is true physically … and it is also true mentally in my perception of that pond … The same is true for window, door, walls, or arch. None of them can be exactly bounded. They are all entities which have a fuzzy edge, and whose existence lies in the fact that they exist as centers in the portion of the world which they inhabit.

… if I call it a center, it already tells me something extra … it makes me aware of the larger pattern of things, and the way this particular element … fits into that pattern.“

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