top study-index prior next ------------------------------------------------------------------------ BB MEMBRAN ANALOGY 1 ------------------------------------------------------------------------ In ABCX we have introduced the notion of synergetic models, dealing with the dialectic dichotomy SYNERGY and its terms CHAOS and ORDER. In the present chapter we shall illustrate the general principle of synergetic models with help of a simple physical analogy. (fig. BB1). Let us consider an elastic membran framed with a totaly rigid frame. We shall call 'OBSERVATION PLANE' the plane passing par the frame and delimited by its internal contour. The membran is sensitive to temperature, the frame totaly insensitive. At a given temperature the membran is flat. Its surface which we shall call the 'IMAGINATION SURFACE' is a plane coinciding with the observation plane. (fig. BB2). We warm the system up. The frame stays unchanged, but the membran's surface extends. It 'grows out' of the frame, cannot stay flat and develops hills and valleys, or basins. The imagination surface does not coincide more with the observation plane, but intersects with it along the OBSERVATION PATTERN composed of square FORMS. Square pattern is of course not the only one possible and has been chosen as illustration because of its simplicity. Another regular pattern could be for instance hexagonal. In general, the imagination surface and the observation plane may intersect along any pattern of convexe polygons. It is interesting to note that the basins interact among each other. If a hill disappears as result, for instance, of being pushed down by some external force, the whole situation will change: some of the basins close to the disturbance, or remote will change their size and form. Let us note that the interaction is of the type local to global: a local change of one basin may modify the whole situation. As for the imagination surface itself, it is no more a plane, it became a curved 2-d surface immerged in a 3-d IMAGINATION SPACE. Basins may be considered as volumes, imaginary objects or IMAGES in the imagination space delimited on one hand by the imagination surface and, on the other by the observation plane. Observation pattern may be now considered as projection of a SITUATION of images from the imagination space upon the observation plane. One may find surprising our choise of the term "situation" to denote the structure of images, which, geometrically seen, could be called a "configuration", or a "volume-pattern". We shall justify this choice in part C concerned with human mind as a modeling device and especially in CAB dealing with the faculty of imagination. BB MEMBRAN ANALOGY 2 Now, let us imagine two-dimensional beings living in the euclidian space coinciding with the observation plane. They would observe discrete, ordered polygons emerging as consequence of temperature increase. As long as their imagination does not transcede the 2-d euclidian space of their praxis, they will be unable to find for this phenomenon any reasonable interpretation. The phenomenon will appear to them as contingent, meaningless and, worse of all, as contradicting the basic principles of the physics. They will face an aparently unsolvable antynomy of CHAOS and ORDER. However, once freed from the 'common sense' restricting them to their 2-d praxis space, they may transcend it and conceive a model, which interprets simply the phenomenon without contradicting the physics (in our example the membran). Nevertheless, such a model, though simple for us, would require from them a great deal of creativity, imagination and intellectual courage. They would have to transcend the dimensionality of their praxis, conceive a 3-d imaginary space, immerge in it a 2-d imagination surface such that it would intersect with the 2-d observation plane along the observed pattern. Like some exceptionally creative slaves of the cave they will interprete the observed forms as projections of imaginary objects such as membran basins. Apparently contingent and inexplicable behaviour of the observed pattern, when interpreted as projection of necessary and necessarily interacting images will become itself necessary and meaningful. The originally contingent and meaningless phenomenon appears in the light of imagination as necessary and meaningful. NECESSITY and MEANING are effects of imagination. Imagination provides the SEMANTIC CONTEXT, or the SEMANTICS of observation. Summary. Dialectic reconciliation of apparent contradictions amomg the terms of the dichotomies SYNERGY (CHAOS / ORDER) and TOPOLOGY (CONTINUOUS / DISCRETE) may be illustrated with help of an imaginary model which interprets aparently contingent and inexplicable PATTERN of FORMS as projection of a SITUATION of IMAGES of higher dimensionality than the pattern itself. These interpretative situation represents the MEANING of the observed, apparently meaningless pattern.