A modified physics
In physics, the effort has always been to take the geometry of a material system and to derive from it, predictions about the dynamic behavior, forces, and casual interactions — impacts, effects, consequences, of a mechanical kind — which follow from a particular configuration. That is the nature of physics.
In art and building, we have a different set of problems. Again we have geometry, but here we seek especially to derive from it, to predict from it, the harmony, gracefulness, and quality of life, which different geometries may have. That raises a different set of questions from those raised in physics.
Further, still, in the study of living systems — ecosystems and organisms — we have yet a third set of problems. Here we have geometric structures, and we seek to derive from their geometry both the behavior of the systems (in that regards it is like physics) and the health or degree of life and coherence of the systems (in that regard it is like art and architecture).
In what follows, now, I am taking the view that all three cases are to be included in a single view of matter — and that all these questions, all three kinds of questions, are to be raised. We seek an embracing picture of space and matter in which all these issues can be understood together. Thus, a view of matter-space which gives us understanding of causal effect; of degree of harmony and degree of life; and of the two together, where degree of life and harmony work together with causal effects to form the underpinning of an organism or of a living ecosystem. We seek a view of space and matter which can lead us, successfully, to all these effects together.
[…] Our picture of the matter-space of the universe must be modified in a way that is consistent with the insights of 20th-century physics. But to fill out the picture as I have suggested, the matter-space must have certain additional features, not provided for by contemporary physics, which allow us to see the wholeness as it occurs in space, thus forming an extension of the present picture.
The existence of centers and wholeness
The first new feature which is needed is simply recognition of the existence of wholeness — a pervasive multi-level structure created by centers throughout space, together with the idea that different centers have different degrees of life and centeredness. The centers are created by local symmetries, boundaries, hierarchies of other centers, positive space… all the geometric properties of Book 1, chapter 5. That is, of course, the origin of wholeness as it is defined in Book 1, chapter 3 and 4. It is this which provides the source of degrees of life in material structures.
In an unpublished paper, I have argued that the wholeness, as a structure, is essentially similar to a topology. It is a measure erected on space according to the coherence and life of the different sets and subsets, thus establishing a structure not unlike a topology, but (unlike topology) dealing with value rather than spatial contortion and connectivity. Christoper Alexander, “An Unexpected Structure Underlying Physical Reality”, submitted to Physics Essays.
As a focus of attention, this emphasis on wholeness with variations in centers caused by their differing degrees of life, is new and not, at present, part of the structures taken into account by physicists. It is possible that this structure requires no new features for the matter-space continuum. The existence of wholeness and centers follows, at least to a first approximation, merely from the local symmetry structure of space, and may (in principle) be calculated just from the space alone, and the differences of material which occur in it.
It is likely that a more sophisticated calculation will also be needed to show the bootstrap recursive character of the field of centers, and the way that each center is dependent for its life on the life of other centers. Again this will, in all likelihood, not require new mathematics of the space itself. My guess is that this will turn out to be manageable within the present view of Euclidean space. What will be novel will be the way the mathematical self-bootstrapping nature of the field works, not the conception of space. I should be surprised if it needs anything beyond the normal well-understood Euclidean geometry of three-dimensions as a substratum. It is likely (but am not sure) that the calculations which show how each region in space has a different degree of life can be made to follow from the mathematics of the space itself, and can — in principle — be managed perfectly well within our present view of space. See Book 1, appendix 4.
It is also possible that even for such a system (wholeness and centers and symmetries) an entirely new conception of space may be required, one, for instance, that consists of nested platelets of local symmetry — and that this structure is not merely superimposed on the continuum we know today, but itself becomes the model of space, one which replaces the present conception of space altogether.
This is similar to a suggestion made by David Finkelstein, about viewing the world not as a continuum but as a simplicial complex. See “All is Flux”, in B. J. Hiley and F. David Peat, Quantum Implications (London: Routledge and Kegan Paul, 1987), 293. Also, see David Peat’s remark, in discussing Penrose’s work, that space might be seen, in the future, not as continuous, but as a nested structure of sets having only functional properties. F. David Peat, Einstein’s Moon (Chicago: Contemporary Books, 1990), 133-46.
Whether innovations are needed or not in the system of space itself, in any case there are certainly other features of the theory of centers which do seem to need modification in our conception of the matter-space. Let us take them one by one.
Value of life as part of space itself
The possibility exists that we might be able to derive the degree of centeredness of each region, by calculating some function of the local symmetries. But whether that is realized or not, the conception of matter-space I have described presents us with something unknown in present-day physics: a conception of matter-space in which each spatial region, at every scale, has a relative value, and a relative degree of life.
This is a new idea. The conception of space with degrees of value inherent in it (whether we can calculate it or not), is something very different from the value-neutral view that is deeply entrenched in the present-day physicist’s view of matter-space.
The 20th-century matter-space is steadfastly neutral. The neutrality of value of the different regions in space, is fundamental to its machinelike character, and to the way we think about it. If we succeed in getting a new view which gives each region of space, at every scale, a different value, and we thus have a kind of matter-space which has value attached to every region, and to every point, this then becomes — qualitatively — an entirely new kind of space. It gives us a substratum to our picture of the world which is new, not the same as the present value-neutral view. Whether the value of each region can be calculated from local symmetries, or whether it is observed empirically, still the result — a space in which every region has its own (different) value — is an entirely new kind of thing.
Time asymmetry: Structure-preserving transformations as the origin of the laws of physics and biology
One of the most unsatisfactory aspects of Cartesian physics has been the so-called symmetry of time: the fact that classical equations do not, for the most part, distinguish between forwards and backwards. Like a clock mechanism, the mechanistic universe can run backwards or forwards equally well. Onsager and Prigogine struggled to create a thermodynamics of becoming, within the classical world picture, and succeeded. However, our world picture would be far more satisfactory if there is an overall and natural sense in which ‘forwards’ and ‘backwards’ are essentially different.
The world picture which I have been describing provides such an asymmetry in a natural way. In the physics contemplated for a world-picture based on wholeness and its transformations, all laws will (I believe) fall out as natural consequences of the principle of unfolding wholeness (Book 2, chapter 1). That principle will say, only, that the next step after a given configuration will be the one which does most to preserve and extend the structure (structure being defined by the wholeness), and I conjecture that it will be possible to show that all physical laws turn out to be special cases of this principle.
In crystal growth this will allow us to see how snow crystals form, as they truly form (not merely the fuzzy approximations presently available which form something vaguely the right shape), and will explain why the deeper symmetries, not presently explained, occur. In the unfolding of an embryo, this rule will imply that the whole moves to a next state in which the structure of the previous state is strengthened and extended and enlarged. In the electron and the two-slit experiment, it will imply that the probability distribution of the electron throughout space near the slit is given by a function assigning high value to those zones which have the most structure-preserving effect on the configuration as a whole.
The important thing is that for the first time the possibility occurs of a natural way of understanding time-asymmetric laws as the foundation of all physical processes.
The personal quality of space
Another feature of centers, as they appear in the theory I have presented, extends the 20th-century view of matter-space in a more surprising way. I have suggested that each living center, to the degree that it has life, reflects (for each of us) our individual self. Living centers are, in this sense, highly personal. A personal link with our own self is connected to each region of space, in that degree to which that region of the space has life or is centered. Thus, not only value becomes associated with each region of matter-space, but something personal and self-like — feeling — also appears in space. And this, then, of necessity, would be part of physics.
The idea that matter-space, matter itself, might be personal or linked to the human self in any way at all, is utterly different from anything in the 20th-century physicist’s picture of space. Indeed, it violates the most basic attribute of space as it was conceived in the 20th century — namely, that it is (and it used to be held that it must be) inert, impersonal, not connected with the self, remote from the self, and without any personal quality that could link it to the self.
Here, for the first time, we are entering the possibility of a view of matter which, in its extent, character, and quality, is personal and self-like in its nature. This is a new kind of matter-space altogether. Something very new and something which, if it ever becomes widely accepted as true, will revolutionize our picture of the universe.
The objection could be raised that this is not new at all, indeed that one of the major revolutions of modern physics was the recognition that object and observer are entangled, and indeed it is true that this has been, since the time of Heisenberg, a major feature of 20th-century physics. The observer effect is dealt with in nearly all accounts of quantum physics. But what the observer entanglement meant was something vastly more restricted than what I mean here. Perhaps it gave a hint of a possible personal connection between matter and self. But it came nowhere near asserting the personal character of matter as its essential quality.
The Ultimate I
To reconcile the vision of matter with the experience of personal relatedness we feel when in touch with living structure, I have, in addition, introduced the conception that living centers open some kind of window or tunnel to a ground and to an ultimate I which constitutes this ground.
Here we have a kind of picture in which all matter-space is linked to a single blinding unity, but with the added assumption that different regions of the matter-space are linked more or less to it, according to their structure; and that as the matter-space becomes organized it becomes more and more strongly linked to this ultimate ground which lies beneath it, or inside it, or throughout it. With this conception, we arrive at something entirely different from present conceptions, something really weird, unlike any present conception of matter-space at all. For this, it seems to me, we have, up until now, had virtually no model at all. This is a conception which almost baffles our imagination, and here we are, truly, in a mental territory of an entirely new kind, with an entirely new conception of the material universe.
Yet I believe that for this conception, too, there are sound arguments, and that the views I have put forward in this book (in the mid-book appendix and in chapter 6) give us sound, if not ironclad, reasons for thinking that it might be so, and almost must be so.
All in all, what seems to be required is a conception of the universe in which the matter-space is understood as roughly the same extended continuum which is conceived in present-day physics (with or without strings and granular small-scale structure), but this matter-space continuum is now modified in its behavior so that:
We recognize the relative existence of value in different regions of space,
The value is personal and space is conceived as having some connection to our personal lives,
Space itself is viewed as having connections, or windows, to some undifferentiated plenum of light, or unity, or mind which lies beyond the space and is possibly even in another dimension, but is nevertheless connected to it at every point in the continuum.
Although this suggestion introduces only a fairly small change — the possibility of seeing, judging, and calculating degree of centeredness for every region of space — this could still be understood as an extension of current physics. It would incorporate most present-day physics as it is. However, it would add essential new features for making it capable of allowing our world-picture to include both contemporary physics and the crucial issues of value, feeling, and mystical experience. It could do this in a way that is consistent and continuous with the mechanical facts which are familiar and well explained by the present view of matter. It is conceivable, too, that this picture might have the capacity to contribute substantial insights to the biologists’ longstanding search to find a coherent and deep view of what life really is when it arises in organic nature. It would, furthermore, provide a new basis for discussion of the profound question: Why does consciousness occur in some living systems?