top study-index prior next ------------------------------------------------------------------------ B MODELING ------------------------------------------------------------------------ BA ALLEGORY OF THE CAVE 1 ------------------------------------------------------------------------ In the 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. Real 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 in their behaviour, arising, vanishing and changing without any aparent 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, 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 interprete 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 3_d objects upon a plane. The relation is unique and exact: an object may project only one, exactly determined 2_d 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 2-d projection admits infinity of 3-d projectors. (fig.BA1 (illustration of the cave: aspects a(O(1,1)), a(O(2,1)), a(O(1,2)), a(O(2,2)), a(O(1,3)), a(O(2,3)) of objects O1,O2 at times T1,T2, T3 and respective source-objects. O1: sphere, O2: coin. ) It is impossible to create a model on the base of a single observation. At T1 the aspects a(O1), and b(O1) are both identical circles and there is no reason to associate them respectively with a sphere, and a coin. However, we may: 1.Juxtapose and compare both observations. 2.Create the model, i.e. imagine sources O1, O2 on the one hand projecting at T1 the a(O(1,1)), a(O(2,1)) and, on the other hand changing so that at T2 they project a(O1(1,2)), a(O2(2,2)). 3.Test the conformity ot the model. It has been created on the base of several observations. Now it has to be able to predict new ones: given O(1,3) and O(2,3), the model has to be able to produce a(O(1,3)), a(O2,3)), agreing with actual observations at T3 and thus prove to be conform. Otherwise, it has to be adjusted. 3.adjust the model if the prediction fails. BA ALLEGORY OF THE CAVE 2 The entire human behaviour is determined and controlled by a model whose principles are illustrated in a very general and simplified way by Plato's Allegory. 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, excede the capabilities of most talented humans by orders of magnitude. Still 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 the 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 recognise and use common objects of our environment under the impression of dealing directly with the reality, without being aware of the actual modeling activities performed by our brain. This level of genetically determined modeling may be called instinctive, or subconscious. Besides it, we may distinguish other levels, involving conscious imagination and intelligence, which endeavour to improve some areas of the instinctive modeling with respect to its conformity, scope, depth, or precision. We shall illustrate the imaginary and intelligent components of human modeling with help of very simple analogies in BB and BC.