The modeling relation: how we perceive
D. C. Mikulecky
Professor of Physiology
Medical College of Virginia Commonwealth University
1.0 How do we perceive our world?
The world around us is something we take for granted. We rely upon on our senses to bring information about that world to us. The process results in something we call awareness. Science attempts to make the process as true to what is "out there" as possible. Hence, we developed the scientific method which involves methods for keeping our senses under control and, often, enhanceing them as well. The main process for this in the scientific method is measurement. Measurement is a complicated process and has been analyzed in great detail (Robert Rosen, Fundamentals of Measurement and Representation of Natural Systems, 1978).
2.0 How can we understand perception? The modeling relation.
The modeling relation is based on the universally accepted belief that the world has some sort of order associated with it; it is not a hodge-podge of seemingly random happenings. It depicts the process of assigning interpretations to events in the world in a diagrammatic form. The best treatment of the modeling relation appears in the book Anticipatory Systems (Rosen, 1985, pp 45-220). [see also the article by Dress]. Rosen introduces the modeling relation to focus thinking on the process we carry out when we "do science". In its most detailed form, it is a mathematical object, but it will be presented in a less formal way here. It should be noted that the mathematics involved is among the most sophisticated available to us. In its purest form, it is called "category theory". Category theory is a stratified or hierarchical structure without limit, which makes it suitable for modeling the process of modeling itself.
Figure 1. The modeling relation.
Figure 1 represents the modeling relation in a pictorial form. The figure shows two systems, a natural system and a formal system related by a set of arrows depicting processes and/or mappings. The assumption is that when we are "correctly" perceiving our world, we are carrying out a special set of processes that this diagram represents. The natural system represents something that we wish to understand. We believe that information about the natural system is brought to us by our senses. This is only partly a true picture of what goes on. Sensory information may be the origin of what it is that we are aware, but the awareness has other, less well characterized components.
2.1 The percept is what we have in our awareness.
The percept is often the result of immediate sensory input, but need not be. Very often, the entire modeling relation can be formulated in terms of memory or imagination furnished percepts. Once this is realized, a question should be brought to mind, namely, is the percept ever totally the manifestation of sensory data alone? The answer has to be "no".
In particular, arrow 1 depicts causality in the natural world. On the right is some creation of our mind or something our mind uses in order to try to deal with observations or experiences we have . The arrow 3 is called "implication" and represents some way in which we manipulate the formal system to try to mimic causal events observed or hypothesized in the natural system on the left. The arrow 2, is some way we have devised to encode the natural system or, more likely select aspects of it (having performed a measurement as described above), into the formal system. Finally, the arrow 4 is a way we have devised to decode the result of the implication event in the formal system to see if it represents the causal event's result in the natural system. Clearly, this is a delicate process and has many potential points of failure. When we are fortunate to have avoided these failures, we actually have succeeded in having the following relationship be true:
1 = 2 + 3 + 4.
When this is true, we say that the diagram commutes and that we have produced a model of our world.
Please note that the encoding and decoding mappings are independent of the formal and/or natural systems. In other words, there is no way to arrive at them from within the formal system or natural system. This makes modeling as much an art as it is a part of science. Unfortunately, this is probably one of the least well appreciated aspects of the manner in which science is actually practiced and, therefore, one which is often actively denied. It is this fact, among others, which makes the notion of objectivity as defined above have a very shaky foundation. How could such a notion become so widely accepted?
2.1.1 The Newtonian Paradigm and the modeling relation
Traditional science as described above is the result of many efforts, yet it has a core set of beliefs underlying it which Rosen refers to as The Newtonian Paradigm. There is no strict definition of what this is, but it is the entire attitude and approach that arises after Newton introduced his mechanics , especially, his mathematical approach. It certainly embodies the ideas of Descartes and the heliocentrists, for example. It also embodies all of the changes brought about by quantum mechanics. It is so much what modern science is that it could almost be used as a synonym. For these reasons, it has had a profound effect on our perception. It is so powerful a thought pattern that it has seemed to make the modeling relation superfluous. For The Newtonian Paradigm, all of nature encodes into this formal system and then can be decoded. All our models come from this one largest model of nature. In the modeling relation, the formal system lies over the natural system and the encoding and decoding are masked so that the formal system is the real world . The fact that this is not the case is far from obvious to most. The task then, is to understand why.
2.1.2 Putting it all together: the modeling relation is the key
Rosen calls the results of our sensory experiences as they manifest themselves in our awareness percepts. If all we did were to use measurement to objectively become aware of what our senses pick up, the situation would be simple. We would be like a piece of magnetic tape or computer memory filing away this information as it comes in. The key word in the definition of percept is awareness. There is more to that awareness than a mere entering into memory. The first thing we would have to do, even to merely file the information correctly is to discriminate and classify. In short, we form relations between percepts. What is fascinating about this is the fact that these relationships between percepts can be matched by relationships between objects used in the formal system. Here is the place where semiotics and other aspects of our thought process get mixed into the process in an irreducible way (Dress, 1999, a and b).
The confusion that arises from the failure to recognize this process at work is immense. Rosen's whole concept of the modeling relation is the explanation for why words like complexity and emergence have become so popular. The suppression of awareness of the process by the Newtonian Paradigm resulted in some real problems, surprises and errors. It was not until there was widespread recognition, consciously or unconsciously, that this paradigm was inadequate that these words became widely talked about. The world as modeled by the Newtonian Paradigm was but one possible picture of the world. Rosen named this world the world of simple systems or mechanisms.
There is another world, namely the one containing the natural systems we seek to understand, which can not be totally captured by the Newtonian model. This world, in fact, can not be captured by any number of formal systems except in the limit of all such systems. The name of this world is the world of the complex. Emergence then is the phenomenon of being surprised when the real world doesn't conform to the simple model, in other words, the discovery of its complexity. Since the entire real world is complex, discussions of degrees of complexity refer to the nature and number of formal systems being used to create models within the modeling relation. Unless this is realized, the amount of confusion generated trying to classify things by their complexity can be immense. There are many other definitions of complexity (Horgan, 1996 ) that exemplify this confusion.
Given the modeling relation and the detailed structural correspondence between our percepts and the formal systems into which we encode them, it is possible to make a dichotomous classification between various models of the real world. These models are either simple mechanisms or complex systems. It then becomes possible to formulate the "what is life" question in an entirely new way, one which leads immediately to an answer.
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