The next stage in the procedure was to explore ways of further regrouping the information to bring out a more meaningful and comprehensible pattern. The question was how to cluster and reorder the 220 polarities, illustrated by Figure 3, of Section V into a smaller number of categories. Having ordered the information from Sections VC and VD into polarities (namely using a factor of two) in the absence of any other guidelines, it was decided to further divide the data set by factors of three and five. This was based on studies of patterning which indicate that new patterns only emerge when a new prime number factor is used to divide up the data (McClain, 1976).
2. 3-fold categories
In the course of imposing these constraints, the opportunity was taken to associate polarities which (in Section VP) might be considered too similar to be usefully distinguished. This exercise resulted in 45 three-fold categories (see Figure 4), the 224 polarities having been "condensed" to 135 by associating those that were similar. The possibility of using this condensed set of polarities as the basis for Section VP to group the entries in Sections VC and VD was considered and rejected in favour of using the extended set which corresponded more closely to the original Roget pattern. The 45 triplet categories are presented in Section VT with cross-references to the polarities in Section VP which they group. Where several polarities cross-referenced within an entry in Section VT bear the same qualifier code "a", "b" or "c", these could be combined in any condensed set of polarities.
The names given to the entries in Section VT (Figure 4) are merely indicative of a "transcendent" complex of value polarities. The significance of a word used to label such an entry should not be confused with the significance of the same word in Section VP or Section VC.
3. 5-fold categories
In an attempt to explore the results of further ordering the information the factor five constraint was imposed on the 45 categories. The resulting categories are presented in a 5 x 9 matrix as Figure 4. This gives an overview of the Section VP polarities grouped into triplets (by matrix cell (with the elements coded "a", "b" or "c"), with each triplet cell forming part of a five-fold group (a column) and a nine-fold group (a row). Totals for each portion of Figure 4 are given in Figure 5. The 45 value types are listed in Figure 6 in order of the total number of cross-references (via Section VP) to Sections VC and VD in the 1991 edition.
The arbitrary guidelines governing this classification experiment would have required that a factor seven constraint be used instead of allowing the data to form nine-fold groups. This possibility was explored, but it was decided that the nine-fold group raised the possibility of comparison with a more complex classification system currently being used experimentally to group international organizations and the world problems (from this volume). That is the code matrix used for the companion series the Yearbook of International Organizations (Vol 3: Global Action Networks).
4. Alternative coding systems
Consideration was given to coding the negative value operators associatex with world problem names in two distinct ways:
(a) in terms of polarities (via Roget links)
(b) in terms of matrices
Actual problem titles (not necessarily the main one) are clustered under individual value polarities. In further work the polarities could be clustered under a variety of matrix patterns as quite separate exercises.
5. Ambiguities arising from multiple connotations
Clearly ambiguities are rife. It is not to be expected that any results will be strikingly satisfactory. There is much confusion and overlap in usage. Many distinctions are not clearly established or maintained. Since links have to be made to problem entries based on documents, excessive rigidity in terminology would appear contrived and counterproductive. Roget is considered as a major guideline but cannot be considered the final pattern to be sought, and hopefully further clarification will emerged sometime in the future.
It is possible that the ambiguities associated with each negative qualifier can be considered as "secondary harmonics" associated with the structure of a given matrix, namely as alternative meanings or associations from other locations in the matrix that have a significant relationship to that given prime significance.
6. Experimental manipulation of negative operators
Negative qualifiers (or drivers) were held in a single file and coded according to each matrix system in 3 separate fields. They were also held as negative values in the values file, and were crossreferenced to the appropriate value polarities that cluster them.
The negative qualifiers were also related (via Roget) to various value polarities. The aim was to code the qualifiers uniquely for each matrix system, namely overriding the ambiguities implied by the multiple associations provided by Roget. In this way each negative qualifier was given a principal sense through each matrix system.
7. Mapping value systems onto 3-dimensional structures
Following the experiment in coding and patterning Earth Summit issues (see Section TZ), the matrix as a 2dimensional representation was considered inherently inadequate as a way of holding understanding of an integrated system in which patterns of checks and balances based on disagreements need to be used to provide integrity to the system as a whole if it is to cohere at all.
The 5x12 matrix was therefore treated as mappable onto a 3dimensional structure composed of 120 polarities aligned in 10 interlocking circles of 12 polarities each. It is hypothesized that the areas defined and bounded by the interlocks are associated with the principle issue areas with which problems are associated.
It is mappings of polarities of this kind which it is suggested may eventually provide higher orders of consensus in which agreement is based on ordered patterns of disagreement. However this form of agreement constitutes a fundamental challenge to comprehension. Conventional modes of comprehension necessitate the kinds of polarization whose configuration delineates this higher form of consensus. The polarization cannot be avoided and is essential to any "realistic" relationship to problems with which people are confronted.
8. Tuning value systems
Metaphorically value classification exercises may perhaps best be understood as an efforts design and tune a conceptual instrument. As an exercise in classification this means seeking the best distribution of significance across a matrix, bearing in mind the associative pulls exerted to different locations. The phrase which reputedly triggered the Buddha's enlightenment is woerth bearing in mind in this respect. If the strings on an instrument are not tightenough, then it cannot be played, but if they are too tight, then they break. Recalling Gregory Bateson's insight, destroying the pattern which connects destroys all quality. The exercise is an effort to explore the nature of that pattern at a level of complexity adequate enough to carry the richness of problems and values recognized in society.
9. Global patterning
In other studies, exploring the possibility of more comprehensible classification systems highlighting global patterns of significance within sets of data, the importance of seeking ways to project the data onto new patterns has been stressed (Judge, 1980). In particular the need to bypass the misleading limitations of a matrix have been emphasized in order to reinforce non-linear relationships within patterns. One possibility considered was that of projecting the data onto a tensegrity structure (of which examples are given elsewhere). Such structures have the unusual property of existing in three dimensions as a result of a dynamic balance between tension elements (cords) and compression elements (struts). What makes such structures unique is that the struts do not touch one another and there are no privileged struts, especially at the centre (where there are in fact no structural elements at all). It is such properties which usefully encode the possibility of non-linear relationships between the value categories. Of special interest is the possibility of projecting value polarities onto struts.
The particular model presented to highlight these possibilities for further investigation has been selected because it has 90 struts. Speculating that it may be fruitful to distinguish between a conscious (explicit) and an unconscious (implicit) form of the 45 value dimensions, the two sets of 45 could be projected onto such a model.
The distinction between two such sets is itself modelled by the impossibility of viewing more than half such a global structure from any one perspective. Other properties of interest are the three-fold and five- fold groupings of polar elements within the model as well as many symmetry effects which contribute to the integrity of the model. It is the use of such properties to stabilize and render comprehensible interpretation of the complex relationships between values that merits attention.
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