Introduction
Representation Theory
He is the very model of a modern major general! And that's a fact! ... Say what?
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A representation is a picture, or depiction -- a model -- of something. So a representation theory speaks to the key properties of what is modeled. For example, we have theories of geometry, or algebra, or geography, or philosophy. The value of the representation thus depends on how well it describes that something.
Simulation, specifically, is here a representation that has to account for the dynamics of an environments or personal virtual realities we create in experience, like at tennis courts, rock concerts, or schools. The settings are zones of consciousness.
How good are representations of the contexts? What tests might we use to tell? Perhaps the only way is to see how well we deal with our circumstances in the world, i.e., how well ideas work.
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To consider an example, in the process of tracking, intercepting, and hitting the tennis ball, you are faced with a number of specific tasks that require information on an ongoing basis. Like estimating distances, speeds, directions of motion, and accelerations, activating your muscles, directing your movements, and so on. You have to contend with a real ball that could be moving at high speed and with an opponent who is constantly in motion and who is likely using every stratagem to defeat you.
This is a familiar situation tennis players merely take for granted. But the familiarity masks a more penetrating problem, one that has occupied the mind of analysts for centuries. The problem, simply, is to get accurate knowledge of the world. For the tennis player this translates into getting an undistorted perception of his court activity, like characteristics of the trajectory. In short, this means knowing exactly what the ball is doing. He must distinguish between his subjective views and the objective tennis ball.
From science we understand that physical energy from (presumed) objects stimulates our senses and leads to experience of those objects. We say we form impressions of them. So in this sense the tennis player forms visual impressions of the events at the court. I.e., he forms images of them. And he only has those images to rely on to maneuver. The images determine his perceptual discriminations and his responses, and at the same time they are determined by what he does and by the objects he encounters in his maneuvers. In other words, he depends on what he can find by looking.
The athlete's job is to learn all he can about how the ball is moving: where it's located at any moment in time, what its speed happens to be, the direction it is taking, and how it is spinning. He needs to get to the truth of the situation. He wants to know how his opponent hits the ball and the way he himself should respond to it. But what he learns depends on his method of looking, by how he sees what he sees. And this is the issue of how we gain knowledge, the field of epistemology.
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For the most part in our everyday affairs we set aside and ignore the perspective nature of experience and "see" a world of real objects in space-time, and this is probably as good as it gets. We don’t question that the perceived objects are really "out there," occurring in some fashion objectively and pretty much as they seem (except not in perspective when not experienced). But this is to miss the subjectivity. If the objects as perceived in each other’s view were really that way in the objective world, they could be getting bigger and smaller at the same rime, a phenomenon we would think isn't possible in real space, or at least doesn’t make much sense. Yet the only way that it’s possible for us to see the world is precisely "in perspective."
The perspective of humans (presumed to be a characteristic common to all of us) is an interesting phenomenon and has its own special nature, a nature exploited in the fine arts and mathematical sciences. No matter where or in which direction we look, the world is in perspective. Indeed, if we rotate our gaze (in place), each new view in the rotational flow instantaneously yields a continuum perspective, with objects at a distance processed as much smaller than they would be if they were up close, as we say. In any direction, there’s that danged perspective again! This is as true on the tennis court as it is anywhere else. There is no obvious break in the visual continuity, no transition from perspective space to flat space and back again. Incredible!
In developing my tennis simulations to study the tennis problem (first for tracking and interception and later for hitting, and now for the integrated task), it was necessary to formulate objective and subjective aspects. I needed to distinguish between what was really out there and what the player perceived to be our there. So I first chose to prepare a mathematical description of the court, ball, and net as would be defined by physicists to represent the objective context.
Subjective/Objective Worlds
To create the distinction between the objective and subjective realms I used a linear, one-point geometrical perspective formulation, indicating the presence of a perceiver and subjective experience. (The formulation only approximates our normal perspective of the court, which has additional characteristics more difficult to portray, like viewing in perspective in every direction.) With this approach, the effect is to convert an objective, linear version of the context to a subjective picture as might be perceived by the athlete from a fixed location and a fixed direction.
This depiction of subjective and objective worlds delineates what to me is a common sense approach and constitutes an easy, even simplistic, answer to a question that's been a continuing matter of controversy historically and which to this day is considered by many to be unsolved. Essentially it is the mind-body question, which asks whether there are two real, fundamental world substances, mind and body, or only one, either mind or body (or what we now commonly refer to as "matter"), and whether or not they exist, and if so, how? This raises the question whether objects and experiencing minds are real or not and whether and how they can possibly interact, being completely different. If they can't interact, how can mind possibly know anything about matter? And how can matter influence mind? Whew!
A typical holder of the common sense view wonders what all the fuss is about. "Of course there are objects out there!" he would exclaim, and "Of course there are minds that experience them -- how can you possibly believe otherwise? You'd have to be crazy to play this game if your opponent was just a figment of your imagination!" Well, people have believed otherwise, and many still believe otherwise. The main protagonists have been the so-called physicalists (atomists, materialists) and the humanists (idealists, mentalists). The former gang thinks that everything in the universe is constructed of matter that bounces around strictly according to physical principles, and so-called self-directed human movements are nothing but reflex actions. The humanist, on the other hand, believes there are real minds, or spirit-like entities, that can emote, reason, and do all sorts of other purposeful things, as well as create our worlds, spontaneously.
For Plato, for instance, way back in the good old days of classical Greece, the realm of pure, higher to lower, ideas is what made up the real world. And everyday experience was mostly (if not all) illusion: mere shadows cast against the wall of our "cave" by the living fires. Among the lower ideas are the ordinary colors and sounds and all the other sensations of normal experience. (As I see it, without their ideas, the sensations would have no meaning.) Alternatively, equality, freedom, and the like, would be higher order ideas. What he would have said about tennis and tennis trajectories is anybody’s guess.
These days, some people say that the only reality we can know is the stuff that appears to us in the form of consciousness. This includes all that we see, hear, touch, smell, think, imagine, dream, etc. (This would be a lot like Plato, if we were to refer to the phenomena as ideas.) Others, holding a view considered to be naïve, believe that we perceive the real world directly, just as it is, with all its objects and sense attributes -- our perceptual mechanisms merely copy what is real. Still others believe that, real or unreal, what we perceive is all we ever know, and all we can possibly know.
At least two other policies stand out significantly historically as to how we might acquire knowledge of the objective world. One approach is by means of our mind, and the other is through our various sensors (rationalism vs. empiricism). But nobody has yet convinced the combatants that such a world actually exists. This isn’t to say they seriously believe that the objects aren't real. I don’t know of anyone who doesn’t in fact consider as true that there are real objects and real people "out there" in the world . Certainly it would take a very brazen and brave fellow to tell you, to your face, that you don’t exist. (For if you don’t exist, who in the world would the fellow be talking to?) No. It’s not a matter of belief that you or the other objects aren’t there, but rather a matter of proof.…As if you need convincing!
Rationalists in our midst would argue that minds really exist and have rational powers capable of seeing the truth about people and things such as a tennis court and the moving ball. In earlier times, the 17th century French philosopher, Rene Descartes, argued that proof of our existence lies in the fact that we think. He accepted the fact that the ordinary world was phenomenal (subjective) and that ultimate truth lay beyond it in the objective realm -- a world we can't really sense. (If we sensed it, it would be in the phenomenal world.) His famous declaration of proof is the statement: I think, therefore I am. He's talking high-powered intuition of course -- not what you or I might normally intuit. Yet, the fact remains, thinking itself is part of the phenomenal realm and by itself doesn’t prove the existence of a mind (outside of the phenomenal realm, where "things-in-themselves" resided, as Kant said) that is doing the thinking.
A century later, the British philosopher/empiricist, David Hume, who was a confirmed believer that our only route to knowledge is by means of our senses, argued that we can never prove either the existence of objects or the existence of minds. In fact, according to him, we can never get out of the phenomenal realm -- anything we might experience is subjective. Does that mean that the tennis court and the players aren’t real? Not likely! Indeed, if he had a tennis court I'm sure he would even have played. But according to Hume, our empirical evidence tells us nothing about the world outside of our perceptions; there is nothing that can be relied on as a source of ultimate truth.
This is troublesome to me, because there's no room in his scheme to refer to something "outside" the senses and to say our experience is only phenomenal. He might imagine something else, but even the imagining would be phenomenal. Yet the very admission of subjectivity presumes the existence of an objective world, else what would 'subjective' mean? It’s the distinction between an inside (subjective) and an outside (objective) that determines the meaning of the pairing, like one side or the other of my skin. Such a distinction, in my opinion, has to be palpable; there has to be a clear boundary between them, like the walls of a house. Where is the boundary here? Merely talking about a noumenal realm (as Kant referred to the supposed objective world) doesn't provide that boundary; we can't determine that in fact there is such a place to be distinguished. Yet there has to be some sense to the distinction, it is used so often.
Need for a Recognizable "Objective" World
Few if any of us would be prepared to admit that we (or the objects we see) aren't real. Indeed, everything we do presumes (but still doesn’t prove) the existence of the objective realm. So if we accept the notion that the phenomenal world is subjective, there must be a recognizable objective world for a proper distinction to be made. The question then is where is it?
Our models are naturally limited. I.e., our knowledge is limited, even in our specialties, our expertise. We depend on encounters with the world -- i.e., on facts -- to keep us in line. Models are guides, and facts are policemen. Knowledge likely reaches its highest levels in the theories generated by scientists or theory-making practitioners generally. But the conceptualizing (theorizing) doesn't end there. It goes on with each of us all the time, at any age, at one skill level or another. It's part of our perceptual, investigative nature.
We perceive (test) the objects and find they are real, or not. With every percept that we form we hypothesize, explicitly or implicitly, about the world around us. The objects we build are experiments. Every step we take is experimental: a test of what's real and what isn't, of what is present and what isn't, how fast an object is moving, and so on. That's why I say that perception is investigative. We construct our worlds, and the construction is an experiment. We do the best we can with what we've got to experience it.
Providing useful ideas is generally the job of science. But I prefer to think we should use any ideas that work, whether it comes from "science," or our personal judgments. So I’m quite willing to accept the notion that the tennis court and the ball motions are real, that we perceive them with some degree of accuracy, and that (using sharper concepts) we can get closer to the truth of the situations. This is an optimistic view, but it still doesn't make the job easy. Trajectory characteristics are still elusive. Neither our models nor our practical tests are unfailing. There's plenty of room for errors.
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