It is useful to summarize the approach outlined in the previous note, in relation to what follows, in terms of a distinction between levels.

1. Word level

At this level, as illustrated by Figure 1 (constructive values) and Figure 2 (destructive values),  the concern is with the actual form of words used, notably in the case of negative values as commonly used in problem names. There is a need to take account of grammatical variants and usages and to clarify and group some forms (eg fear/afraid). The approach is essentially driven by usage.

2. Polarity level

At this level, as illustrated by Figure 3, the concern is to cluster synonyms from the previous level and to distinguish alternative meanings. Antonymic relations are confronted, notably to highlight paradoxical qualities (constructive value of negative terms and destructive value of positive). The approach is essentially controlled by the semantics of the English language as exemplified by Roget's Thesaurus. The basic ordering is adapted to the widely accepted sequence in Roget.

3. Set level

At this level, discussed in the following note, ways are sought to cluster the above polarities into a structured pattern, as illustrated by Figure 4. The focus is on experimental exploration of several patterns of semantic clusters of different complexity. The challenge is to find ways to make the set of polarities meaningful as a whole. There is a sense of a variable "geometry" of set structure whereby patterns of meanings can be folded or unfolded according to the users tolerance of complexity.

4. Selfconstraining value set

At this level there is concern with how any set of values can be seen as self-constraining or self-organizing. There is a shift from value sets as linear or tabular arrays to exploration of the possibility of mappings onto various approximations to a sphere as implying an integrated whole. There is recognition that the spherical surface can be divided up into a larger or smaller number of zones. There is also recognition that there is an interlocking effect that reflects necessary interrelationships between distinct values. The challenge is to discover how the spherical array get "tensed" and "tuned" by an appropriate disposition of polarities.

Given the evident failure of value systems based on value checklists and value matrices, there is a case for exploring spherically mapped values. These offer new, and intuitively appealing, ways of exemplifying: a sense of holism and whole; a sense of integration and interlocking; mutual visibility; a possibility of complexification and decomplexification; a sense of checks and balances that uses differences rather than being undermined by them.

A spherical array highlights how limiting is a simplistic linear array of values that effectively denies many interrelations between its elements. The current challenges of governance are associated with acting in the light of a meaningful set of values and relating them to practical policy concerns. In effect a spherical array is closely related to the pattern of government ministries or departments and suggests how they might usefully be related. A spherical array lends itself to complexification or decomplexification in the light of the number of ministerial "portfolios" active in a given government or implied by set of agencies. In a simple, probably characteristic of the smaller countries, fewer ministerial portfolios would probably be justified.

The many attempts to reduce the set of values to 5 to 10 should be seen as a decomplexification which conceals variety required for practical policy making. By contrast, a useroriented process approach is required to display and work with value information. They key lies in being able to "concertina" the value set according to need. Information needs to be held so as to permit this.

5. Alternative spherical mappings

Beyond the single spherical mapping, there is a need to explore more systematically the possibility of alternative mappings and their possible complementarity. The concern is to elaborate a methodology that challenges any tendency to lock into a particular pattern, excluding the possibility that other patterns may usefully carry alternative sets of meanings. Polyhedral nets provide a useful transitional structure between matrices and spherical mappings. Of interest is the indication of alternative meanings for a word as an overlay on any such structure

6. Ordered set of complementary mappings

Pursuing the logic of this structural mapping, at this level there is the possibility of recognizing the existence of an ordered set of complementary mappings. Structurally this is exemplified by the periodic table of basic polyhedral structures.

7. Bridge building

The whole exercise is confronted by a heritage of ambiguity and confusion in the use of words to denote values. The information needs to be held so that these challenges can be explored, without expecting immediate and simplistic solutions. The challenge is to find ways of tuning the value array and there may be a variety of ways to do so, each with their uses. Some may be especially appealing to different cultures, as is the case in music.

In conventional approaches difficulties arise because of the confusion between the word and the semantic connotations. Words have to be used to communicate but are never sufficient to carry the complexes of meanings to which they point. Efforts to produce sets of 5 to 10 words to carry understandings of basic values essential to world governance, sustainable development and peace on Earth are therefore doomed as exercises in tokenism, political symbolism and academic sympathetic magic.

A bridge has to be built between:

• the word level through which problems and values are identified in all their rich variety and multiplicity;
• the semantic clusters which reduce that variety, grouping synonyms and related notions, and transcending the paradoxes of the positive features of negative values and the negative features of positive values;
• the functionally integrated sets of these semantic clusters which correspond to operational responses to the complexity of dealing with the world through sustainable strategies (ministries);
• the representations of these sets that facilitate comprehension of the complexity that they subsume as conceptual scaffolds.

It is by using lists as such conceptual scaffolds, and by assuming that the words in them successfully carry universally the meanings which some may be able to associate with them, that confusion arises and is reinforced.