REASON WORKSHOP WORKSHOPS ARCHIVE =============================================================================== MODEL OF MIND ------------- =============================================================================== SUMMARY OF THE CHAPTER. ----------------------- =============================================================================== Sensations, Images and Symbols appear in context of respective areas of Mind: SENSORIUM, IMAGERY and SYMBOLICS which are, consequently, their respective REFERENTIALS. NOTE: we introduce the neologism "REFERENTIAL", translation of the French Referentiel to replace the rather awkward "reference system", or "-frame". Indeed, referentials are seldom "systems" and never "frames", which wrongly suggest some "envelope" containing something undefined. As we shall see below in detail, our "Referential" points to context of Sensations, Images and Symbols. 2D contingent and chaotic sensations of Sensorium map into 3D Images or Objects of Imagery. Imagery is ordered by causality. In Perception (Sensorium mapping to Imagery) the causal Order is effective. In Action (Imagery mapping to Sensorium) the causal Order is final or teleological. Due to its Order Imagery is Meaningful. Dealing with objects of Imagery, we are under impression of dealing with Reality. Objects of Imagery map to network nodes in Symbolics. Order of Symbolics is logical and symbolic network structure is Necessary. Human faculty of Symbolizing consists in mapping objects of Imagery to Symbolics, thus expressing them with Statements and Symbols of our languages. Human faculty of Understanding consists in mapping Symbolics to Imagery, thus getting the Meaning of symbolic structures. We shall consider the Model as one of axioms of Relativistic Dialectic, which we justify in two ways corresponding to our definition of Axiom (see DOGMA AND AXIOM ): 1.Founding the Model in biological structures of Mind. Indeed our model resulting from purely morphogenetic and topological concepts corresponds within acceptable precision to structures of Mind determined by biological approach. We find this correspondence in Popper and Eccles "The Self and Its Brain" (Springer International) Page 327, Fig E5-7 where World 1 corresponds to our Sensorium World 2 - to Imagery World 3 - to Symbolics All subsequent references to World 1,2,3 confirm this correspondence. 2.Showing pragmatically, a posteriori, the adequacy of our model as support of human reason. We shall try to accomplish it in the following chapters. =============================================================================== BODY OF THE CHAPTER. -------------------- =============================================================================== ALLEGORY OF THE CAVE =============================================================================== At the very origins of our rationality, we notice, in the Ancient Greece, some models and theories whose general concepts remain foundations of our contemporary reason, as fresh today as they were at their origins. We find the Heraclit / Democrit dichotomy in continuous / discrete topology, in chaos / order, in integral / differential calculus, in Newton's or Einstein's Field Theories / Planck's Quanta. And Plato's Allegory of the Cave which after thousands of years of more or less idle speculations resurrects today as introductory version of a most advanced branch of science, the Morphogenetics. In his famous Allegory Plato depicts slaves born and chained in a cave so that they are perpetually facing the rear wall and turning their backs to the entrance. Objects of the outer world project their shadows on the rear wall. These shadows are the only aspects of the reality which the slaves may observe: vague, two- dimensional, flat forms entirely contingent and chaotic, arising, vanishing and changing without any apparent reason. Lacking any other communication with the reality, the slaves tend to confuse the observation with its source, to believe that the shadows are themselves the actual reality, a reality entirely contingent, chaotic, inexplicable and meaningless. However, as all humans, the slaves have the faculty of imagination, the gift of interpreting their observations. They can imagine external objects and interpret the shadows as their rudimentary aspects, as their projections. In other terms, they can build an imaginary model and use it to represent, to explain and to predict the reality. Nevertheless, only very few will have the courage to undertake this enterprise which indeed raises enormous difficulties. It is certainly simple to project 3D objects upon a plane. The relation is unique and exact: an object may project only one, exactly determined 2D aspect-shadow upon a specific projection plane. Unfortunately, MODELING requires the inverse operation: ascending from shadow- aspects towards its source-objects. Now this operation is neither unique nor exact. Indeed, a 2D projection admits infinity of 3D projectors. Lets imagine in the 3D space a sphere S and a thin coin C in a plane parallel to the projection plane (cave's wall), both of the same radius. Perceived aspects (projections) of S and C are identical and there is no reason to associate them with different 3D objects: it's impossible to create a model on the base of a single observation. Let's now suppose the coin turning. Consecutive observations of its aspects (projections on the projection plane or caves wall) will deliver circle, thick ellipse getting thinner and becoming a line, becoming in turn ellipse and circle. It doubtless takes a genius, but now it is not impossible to create a model. A genial slave may IMAGINE a 3D space transcending his given 2D, as well as a 3D object-coin turning in this space. =============================================================================== MEMBRAN ANALOGY. SENSORIUM and IMAGERY. =============================================================================== Plato's Allegory is amazingly similar to Membran Analogy, an introductory example of Morphogenetics, whether Thom's Theory of Catastrophes, or Haken's Synergetics. Let us consider an elastic membran framed with a totally rigid frame. We shall call 'OBSERVATION PLANE' or 'SENSORIUM' the plane passing par the frame and delimited by its internal contour. The membran is sensitive to temperature, the frame totally 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. 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 for instance of square FORMS. Square pattern is the simplest, but not the only possible one. Imagination surface may intersect with observation plane along any pattern of convex 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 whether close to the disturbance, or remote, will change their size and form, or vanish entirely, while others will appear. The interaction is of the type local to global: a local change of one basin may modify the whole pattern or Situation. As for the imagination surface itself, it is no more a plane, it became a curved 2D surface immerged in a 3D IMAGINATION SPACE or 'IMAGERY'. Basins may be considered as volumes, imaginary objects or IMAGES in the imagination space delimited on the one hand by the imagination surface and, on the other hand 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 choice of the term "Situation" to denote the structure of images, which could be called a "configuration", or a "volume-pattern". This choice is justified by the implications of "Situation" for human mind considered as modeling device and for the human faculty of imagination. Now, let us imagine two-dimensional beings living in the euclidian space coinciding with the observation plane. They would observe discrete, ordered polygons emerging in the continuous, i.e. chaotic observation plane as consequence of temperature increase. As long as their imagination does not transcend the 2D euclidian space of their praxis, they will be unable to find for this phenomenon any reasonable interpretation. They will see no way to understand this emerging of ORDER from CHAOS. However, once freed from the 'common sense' restricting them to their 2D praxis space, they may transcend it and conceive the membran model, which interprets simply the phenomenon. 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 3D imaginary space, immerge in it a 2D imagination surface such that it would intersect with the 2D observation plane along the observed pattern. Like some exceptionally creative slaves of the cave they will interpret the observed forms as projections of imaginary objects such as membran basins. Apparently contingent and meaningless behavior of the observed pattern, when interpreted as projection of meaningful and meaningfully ordered images will become itself ordered and meaningful. Apparently contingent and meaningless phenomenon appears in the light of imagination as ordered and meaningful. ORDER and MEANING are effects of imagination. We shall discuss in detail the concept of Order in future chapters. Let us mention here by anticipation that 1.Order of Imagery is causal, 2.in case of Perception (mapping of Sensorium to Imagery), causality is effective, 3.in case of Action (mapping of Imagery to Sensorium), causality is final. NOTE: Our Sensorium and Imagery seem to be restricted to the Visual, mapping respectively to the 2D retina and to the brain's faculty of composing 2D sensations to 3D images. However, all other types of sensations and images involve the same 2D/3D relation and topology. The entire human behavior is determined and controlled by a model whose principles are illustrated in a very general and simplified way by Plato's Allegory and Morphogenetic Membran Analogy. Our short discussion pointed out very superficially the complexity of such a model. Its most general idea is conceivable only to people with some basic intellectual training and experience. Its theoretical details, let alone its eventual realization, exceed the capabilities of most talented humans by orders of magnitude. Nevertheless, everybody uses it in every instance of his life and "simple" people use it often much more efficiently than sophisticated intellectuals. Fortunately, basic modeling problems, those determining our very survival have been solved for us by evolution: indeed, human brain is essentially a modeling device of enormous scope and efficiency. It performs modeling procedures concerning the daily routine often without involving the consciousness. We are under the impression of dealing with objects of REALITY, without being aware of actually dealing with IMAGES created in Imagery by the modeling activity performed by our brain. This level of genetically determined modeling may be called instinctive, or subconscious. Besides it, we may distinguish another level, involving conscious reasoning, which endeavors to improve some areas of instinctive modeling with respect to its conformity, scope, depth, or precision. We shall discuss it in the next section. =============================================================================== NETWORK ANALOGY, SYMBOLICS. =============================================================================== Sensations and Images appear in context of, or with respect to, respectively Sensorium and Imagery, which are, consequently, their respective REFERENTIALS. We are going to introduce now the third basic Referential, SYMBOLICS. Each of the basins of the example discussed above may be associated with an optimum (maximum, or minimum) point or ATTRACTOR. Projecting Attractors on the observation surface and interconnecting them with adequate integrals of basin volumes we obtain a network whose vertices and edges are respectively Attractor projections and their connections. It may be shown that for a multitude of physical phenomena (particularly for those involving, like our Membran, potential fields) it is possible to map a given Situation to an equivalent network. As examples of such phenomena let us mention the flow of viscous fluid through permeable and porous media, the flow of heat, the deformation of construction elements under given stress conditions, the electric flow in a medium with continuous distribution of resistance and capacity. All these phenomena are described by partial differential equations, which usually represent the mapping of a continuous Situation into a discrete network. In the case of electric flow the involved network is associated with the name of Kirchhoff. This last case is particularly interesting for us, as it encompasses electric stimuli in neural networks. A SITUATION of ATTRACTORS and BASINS may be mapped into a NETWORK of respectively VERTICES and EDGES. However, this mapping holds only for one given SCHEMA or particular distribution of vertices and edges. Within this schema the network is capable of simulating the dynamics of the Situation, i.e. the changes of potential at the attractors and the corresponding reactions of the basins (shrinking and expansion) respectively with help of similar changes of potential at the vertices. The mapping is reversible: a given Situation determines a specific unique network, a given network determines a specific unique Situation. To resume: an imaginary Situation may be uniquely mapped into a network whose vertices represent Image Attractors. We may say that vertices SYMBOLIZE images and that their structure, the network, provides a referential supporting symbolic forms of thinking. We shall call this referential SYMBOLICS. Let us mention by anticipation, as we did in the section on Imagery, that 1.order of Symbolics is logical, 2.Causality of Imagery maps into Necessity in Symbolics, Our model of Mind encompasses three basic Referentials: SENSORIUM, IMAGERY and SYMBOLICS. Human Reason encompasses two basic faculties: 1.Symbolizing, or mapping Imagery to Symbolics 2.Understanding, or mapping Symbolics to Imagery. We SYMBOLIZE by expressing Situations and Images with Statements (or Propositions) and Symbols of our languages. We UNDERSTAND Statements and Symbols by imagining them, by getting their meaning, by mapping them to Imagery. =============================================================================== MODEL AS AN AXIOM OF RELATIVISTIC DIALECTIC =============================================================================== We shall consider the Model as one of axioms of Relativistic Dialectic, which we justify in two ways corresponding to our definition of Axiom (see DOGMA AND AXIOM ): 1.Founding the Model in biological structures of Mind. Indeed our model resulting from purely morphogenetic and topological concepts corresponds within acceptable precision to structures of Mind determined by biological approach. We find this correspondence in Popper and Eccles "The Self and Its Brain" (Springer International) Page 327, Fig E5-7 where World 1 corresponds to our Sensorium World 2 - to Imagery World 3 - to Symbolics All subsequent references to World 1,2,3 confirm this correspondence. =============================================================================== 2.Showing pragmatically, a posteriori, the adequacy of our model as support of human reason. We shall try to accomplish it in the following chapters. =============================================================================== REASON WORKSHOP WORKSHOPS ARCHIVE