Local parts exist chiefly in relation to the whole, and their behavior and character and structure are determined by the larger whole in which they exist and which they create.

Wholeness, in any part of space, is defined as:

  • the structure defined by all the various coherent entities that exist in that part of space, and
  • the way these entities are nested in and overlap each other

The whole is unbroken and undivided.

Wholeness is not merely a way of focusing on the gestalt of the thing, but is instead a real structure, an actual “thing” in itself. It is a structure which exists in the world that includes what we intuitively perceive as the gestalt, the overview, the broad nature of a thing. It is the source of the coherence which exists in any part of the world.

A crucial feature of the wholeness is that it is neutral: it simply exists. Determination of its details may be made by neutral methods, yet at the same time […] the relative harmony of “life” of a given building may be understood […] without reference to opinion, prejudice or philosophy, merely as a consequence of the wholeness which exists.

I have not yet emphasized the enormous power of the wholeness, W. This structure catches the overall character in a way which is almost mysterious, but goes to the heart of many things not easily explained. This happens because it is an overall field-like structure, a global, overall effect. It is distinct, completely distinct, from the elements or “parts” which appear in that wholeness; it is unusual in our experience, yet catches what we have often thought of as the artistic intuition about the whole.

The degree of life which exists at that place and time also comes from the wholeness, and only from the wholeness. The neutral wholeness spawns characteristics which are far from neutral — characteristics which indeed go to the very origin of right and wrong.

Life comes from the particular details of the ways the centers in the wholeness cohere to form a unity, the ways they interact, and interlock, and influence each other. The academic and difficult task of grasping the nature of this wholeness will pay us back, by giving us the origin of life.

  • -> Center
  • -> Holism, Gestalt psychology
  • -> [whole-part-configuration (image schema)]

Whole-part vs. center-periphery

Wholeness is a structure of great subtlety which is induced in the whole. It cannot easily be predicted from the parts, and it is useless to think of it as a relationship “among the parts”. The wholeness is an autonomous and global structure, which is induced by the details of the configuration. It is a real physical and mathematical structure in space — but it is created indirectly, by symmetries and other relationships which are induced by the geometry.

Is there a spectrum on which a whole-part-configuration schema can be closer to a container schema, where parts are mostly described with boundaries, or closer to a center-periphery schema, where parts are mostly described as centers?

Present-day conventional wisdom (perhaps Cartesian and mechanistic in origin) tells us that everything is made of parts. In particular, people believe today that every whole is made of parts. The key aspect of this belief is the idea that the parts come “before” the whole: in short, the parts exist as elements of some kind, which are then brought into relationship with one another, or combined, and a center is “created” out of these parts and their combinations as a result.

Software: this has modularization and composability written all over it.

When we understand what wholeness is really like as a structure, we see that in most cases it is the wholeness which creates its parts. The center is not made from parts. Rather, it would be more true to say that most of the parts are created by the wholeness. They settle out from the wholeness, and are created by all of it. […] This is fundamentally different from the idea that wholes are made up from elements or built from parts.

Alexander’s (almost) formal definition

I propose a view of physical reality which is dominated by the existence of this one particular structure, W, the wholeness. In any given region of space, some subregions have higher intensity as centers, others have less. Many subregions have weak intensity or none at all. The overall configuration of the nested centers, together with their relative intensities, comprise a single structure. I define this structure as “the” wholeness of that region. This structure exists everywhere in the world. It exists in nature; it exists in buildings; it exists in works of art. It is a fundamental structure in space which not only encompasses the wholeness or gestalt of the thing; it also encompasses the obvious parts, or elements, from which this thing is made.

From the chapter notes:

The idea of representing any given pattern as a system of selected coherent sets also appears in the foundations of topology. A particular topology is defined by the way in which the coherent sets are nested. But in this case, the definition of “coherent set” is much more restricted and less interesting. The fundamental ida expressed in this book is that the levels of coherence of different sets of centers may be continuously variable, and defined by much more subtle criteria.

Concepts presently available to us in mathematics are not yet powerful enough to let us grasp this structure fully. For this reason many of the techniques, tests, and methods which I describe in this book are cognitive. The empirical methods which are described in this book (chapter 9) are the best I have been able to develop to get to grips with the structure.

Mathematical features responsible for strength of centers

  • Symmetry
  • Connectedness
  • Convexity
  • Homogeneity
  • Boundaries
  • Sharp change of features

[These] are all functions of the configuration as a whole. The centers which make up any given wholeness do not exist independently, but appear as elements which are generated by the configuration as a whole. It is the large-scale features of the configuration which produce the local centers and allow the local centers to ‘settle out’.

Examples from other disciplines

In biology, it is the larger configuration that determines the destiny of the growing material, not its local or internal structure (for instance when transplanting cells from one part of the body to another, different kind of tissue).

For neurophysiology Alexander refers to a 1950s paper. There has been some progress since then. Some of the theories of how the brain works that Lakoff mentions in his talks about embodiment and embodied cognition seem relevant.

In medicine, it is difficult to draw a definite boundary around an organ such as a lung, even though it can clearly be seen as its own entity. It is inseparable from its environment.

#book/The Nature of Order/1 The Phenomenon of Life/3 Wholeness and the theory of centers#

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