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Beyond Method: engaging opposition in psycho-social organization (Part #7)

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1. In order to generate such an integrated multi-set grouping of operational statements it is of course vital to have a rich variety of source material an possible content. Such material was collected for an earlier paper (18) and tentatively ordered there according to the number of elements in the sets in question. The contents of that paper are given here as Annex 1, as an indication of the variety of material. As pointed out in that paper, this ordering permitted useful comparisons between sets in different schemes having an equal number of elements.

2. Such material can only be useful if care is taken to treat the morphological characteristics as independent of the special properties of the substrate with which a given set is particularly concerned. This point has been clearly by Rene Thom in his study of morphogenesis:

'L'indépendance du substrat: L'idée essentielle de notre théorie, à savoir qu'une certaine compréhension des processus morphogénétiques est possible sans avoir recours aux propriétés spéciales au substrat des formes, ou à la nature des forces agissantes, pourra sembler difficile à admettre, surtout de Is part d'expérimentateurs habitués à tailler dans le vif, et continuellement en lutte avec une réalité qui leur résiste. L'idée cependant n'est pas nouvelle, et on Ia trouve, formulée presque explicitement, dans le traité classique de d'Arcy Thompson On Growth and Form; mais les idées de ce grand visionnaire étaient trop an avance sur leur temps pour s'imposer; exprimées souvent d'une manière trop naivement géométrique, il leur manquait d'ailleurs une justification mathématique et dynamique que seules les recherches récentes pourront leur donner ... On m'objectera qu'ici j'ai comparé l'incomparable, an mettant sur Ie même plan un processus biologique d'une part, et un processus de la nature inanimée d'autre part. Précisément, cette comparaison fera sentir un point important, dont peu de gens sont conscients: à savoir que la morphogenèse en nature inanimée est moins bien connue at tout aussi peu comprise que la morphogenèse des êtres vivants; cette dernière a attiré l'attention des biologistes depuis plusieurs siècles ...

Le dédain des physico-chimistes pour ce genre de questions s'explique aisément: c'est qu'il s'agit là de phénomènes extrêmement instables, difficilement reproductibles, et rebelles à toute mathématisation: en effet, Ie propre de toute forms, de toute morphologie est de s'exprimer par une discontinuité des propriétés du milieu: or, rien ne met plus mal à l'aise un mathématicien qu'une discontinuité, car tout modéle quantitatif utilisable repose sur l'emploi de fonctions analytiques, donc continues.' (19, pp 10-12, emphasis added)

The point is also made in relation to one of documents included in the material collected:

'This study will develop the hypothesis that the "lattice logic" which de Nicolas perceives in the Rg Veda was grounded on a proto-science of number and tone. The numbers Rgvedic man cared about define alternate tunings for the musical scale. The hymns describe the numbers poetically, distinguish "sets" by classes of gods and demons, and portray tonal and arithmetical relations with graphic sexual and spatial metaphor. Vedic concerns were with those invariances which became the focus of attention in Greek tuning theory. Because the poets limited themselves to integers, or natural numbers, and consistently used the smallest integers possible in every tonal context, they made it possible for us to rediscover their constructions by the methods of Pythagorean mathematical harmonics.' (14, p. 3)

3. Using equivalent sets from the source material as a guideline, a new set for the number in question was "generated" taking into account the constraints. Given the variety of emphases of sets of an equivalent number of elements, this process of generation necessarily involved non-logical operations, especially since the intention was to maximize the incompatibility between the elements in any given set. The results are given in Annex 2

4. Two interesting and related difficulties emerged in comparing equivalent items from the source material.

  • Clearly some sets are formulated at a higher level of abstraction than others. The problem was, using the constraints as guidelines to generate elements of an equivalent set at an appropriate level of abstraction.
  • Clearly sets differ greatly in the nature of the elements, whether: stages, values, qualities, problems, methods, conditions, etc. Again the problem was to use the contraints to arrive at some neutral formulation of which the above might be considered aspects. In both cases the problem was to find appropriate words (whether general or neutral) to carry the incompatible qualities associated with each set.

5. For each set an underlying relationship or theme is common to each element. The incompatibility is embedded in the qualification on that theme.

The only similar exercise detected is a doctoral thesis in philosophy (20) which was composed directly onto a word processor (to facilitate experiments with alternative structures) using the poetic power of the German language to full effect

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