The modeling relation: how we perceive

D. C. Mikulecky

Professor of Physiology

Medical College of Virginia Commonwealth University

http://views.vcu.edu/~mikuleck/

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.