The progression in the previous note to a more dynamic interactive relationship with the surface on which the elements of significance are configured appears to reach close to a stage at which chaos theory insights emerged. The Belousov-Zhabotinsky chemical reactions result in the spontaneous emergence of patterning in the film of fluid in which they take place. From this arose some of the insights into the principles of self-organization. Perhaps a more evocative example is the standing wave Chladni patterns generated by vibrating a sheet of metal covered in sand (Waller, 1961).

1. Value self-organization

To what extent does a configuration of human values emerge into individual or collective awareness through an analogous process of self-organization based on behavioural interaction? The behaviour of an individual or group would then be understood as governed by some kind of epistemic value space to which descriptors could not be attached. But the original (possibly uniform) space(time) becomes textured or featured as the consequence of global interactions through which a particular pattern of behavioural attractors emerges. Chladni pattern formation illustrates how a space can be configured in different ways as a result of different triggering vibrations. Unlike such physical examples, the clustering of significance in value space is qualitative rather than quantitative. As with the mandala, physical locations on any map are associated with qualitative values (hence the symbolic importance of compass points and their associated god-related qualities in such mandalas).

2. Local vs Global

At the first Artificial Life Workshop (Los Alamos, 1987) Craig Reynolds presented a computer simulation of bird flocking based on 3 simple rules conditioning an otherwise unconstrained set of "boids" (Langton, 1989). Each boid was required to:

1. Maintain a minimum of distance from other objects, including other boids;

2. Match velocities with neighbouring boids;

3. Move toward the perceived centre of mass of boids in the neighbourhood.

These rules are all local, applying to individual boids, and yet their effect is that of flocking dynamics of striking realism and elegance. Flocking is here an emergent global phenomenon. It is interesting to reflect on the extent to which the three rules capture the essence of the standard 3-value set (Liberty (1), Equality (2), and Fraternity (3)) basic to French society.

Of special interest is the way in which the component elements emerging during such self-organization are both mutually constraining and mutually sustaining. Each is a vital local part of the global pattern within the bounded space. A different pattern can be engendered within the same space and with the same value "stuff" -- but the significance is distributed into different clusters, whether differently located, of a different size, or of a different number.

3. Catalysis of self-organization

But how is the emergence of a particular pattern catalyzed? There are perhaps clues in the way in which during the pre-organized phase the potential or proto-components are "tested" against each other. A breakthrough for Brian Arthur was the recognition that a rich mixture of positive and negative feedbacks cannot but help produce patterns (Waldrop, p. 36). Comprehension of the significance of an emerging value acquires maturity to the extent that both its unique contribution and its limitations are tested in relation to other potential attractors. For individuals, whether through personal experience or in formal social roles, repeated exposure to the merits and hidden weaknesses of a valued principle, refine what emerges. Drama makes much of coming to recognize the importance of a value through a succession of failures to updold it. The differences in patterning of a set of values may result from the frequency of exposure to such value-response reversals.

4. Global structuring of value sets

The discussion above offers a way of thinking about the different value sets which have emerged from different social groups over the past decades (or centuries). Whilst a value label, such as "equality", may appear in a 3-value (liberty/equality/fraternity), 5-value or 10-value set, the significance it carries in each case is different. In the 3-value set it carries a third of all valued significance, whereas in the 10-value set it contains a tenth. In the latter case it encourages a narrower and more precise connotation compared to the more profoundly abstract connotation called for by the former. But any such conclusion raises the question of the completeness of the value set captured by such cases and the adequacy of the variety captured by any further articulation.

From such a perspective it is clearly far less appropriate to attempt to focus on any particular pattern of values. The Tibetan Buddhists claim that 725 basic mandala patterns have been developed (Trungpa, p. 79)). Of much greater relevance is to recognize the process whereby different kinds of contextual circumstances can evoke such different patterns from the value space. It is somewhat like having a cake which people will choose to cut up in different ways according to different circumstances (big pieces, little pieces, segments, without-cherry, etc).

Another way to look at such patterning is in terms of the "pathways" that may emerge between different value locations. Just as a pattern of mountain valleys may severely condition the nature of relationships between otherwise proximate zones, particular values may also affect (or be dependent on) each other to a greater or lesser degree.

There is of course a further step in the progression towards more appropriate mapping surfaces emphasizing a global quality. The limitations of 2-dimensional surface maps in relation to the Earth as a globe are obvious. It might be asked why it is appropriate to assume that a value set can be adequately represented on a 2-dimensional surface -- once the daring step beyond a checklist is taken. A spherical surface resolves the questions raised about the outer boundary of any matrix or mandala by holding the information on a surface that is finite but unbounded (Judge, 1980). Unexplored, mysterious zones on that surface can then be located rather than designed off the map. Like a window on a building, matrix patterns can too easily be oriented to give a carefully chosen view that is far from comprehensive. There is almost no constraint on creative editing of checklists.

Such a spherical surface makes it easier to discuss the need to configure the "pulls" between the different attractors. This raises the issue of whether self-organization can be deliberately catalyzed or facilitated without contradicting the meaning of self-organization. The argument here is that the kind of self-organization possible is to some degree dependent on the contextual framework. Any shared understanding of that framework will partially determine the range of possible patterns that can emerge. It could be argued that patterns on a self-bounding spherical surface are of greater potential significance than those on an artificially bounded planar surface.

Consensus on the form of a surface thus influences the richness of the patterns that may emerge. There is also little difficulty in reaching consensus on the approximate sphericity of the Earth however much there is potential disagreement on the perspectives from any portion of that surface.