[From Bill Powers (960306.0930 MST)]
Hans Blom, 960306c --
I, too, look at a model in two ways: in the abstract, it is a
mapping of some space (in the mathematical sense) onto another one,
usually of a vastly decreased number of dimensions; in the
concrete, as a set of laws or equations or hypotheses that provide
a basis for predictions that test the implications of those
hypotheses.
You're thinking in terms of general philosophical one-upmanship; I'm
thinking in terms of what we put into a computer simulation that is
supposed to resemble what is inside an organism. What is inside an
organism's brain is not an abstraction, nor is it a set of laws or
equations or hypotheses (unless "the organism" means the highest levels
of your own symbol-manipulating processes). It is a neural computer with
inputs and outputs. I think that an introspective approach to model-
making has its uses, but sooner or later you have to stop contemplating
your navel and actually propose a workable model. In other words, at
some point you have to start talking like an engineer, and leave the
philosophy in the coffee-house where arguments can go on forever and are
merely a form of intellectual recreation.
Your Kalman Filter computer program is an engineering design for a
system that itself contains a simulation of some aspect of the
environment. Obviously, you know how to conduct a discussion at this
level. Of course from the standpoint of the system being thus
represented, this simulation is a _theory_ about the properties of the
environment; the system itself, the one you're modeling, has no direct
way to check that its simulation is truthful -- that goes, or ought to
go, without saying. But as engineers, we can compare our own physical
models of the environment with the properties of the internal
simulation, and represent the situation as if it involves an internal
simulation and a "real" external system, "real" meaning the environment
as we characterize it through our perceptions and our own agreed-upon
physics-models.
When you try to get too general about this problem, you start losing
useful distinctions. If every mapping is to be called a "model," then we
can't describe the functional difference between an internal simulation
of an environmental feedback function, a perceptual function that
converts a set of inputs into a representation of some apparent aspect
of the environment, or an output function that converts an error signal
into a set of reference signals for lower systems. We lose the structure
of the system we're trying to talk about, by using the same word for
everything. If we want to get anywhere, we have to agree on a level of
discourse and stick to it, and the level of discourse I'm interested in
is the one that preserves useful distinctions instead of merging them
into titillating philosophical generalities.
It would help a lot if you would simply read what I say and not assume
that you are privy to some deep philosophical insights that are denied
to me. I was careful in my post not to assert that there is a real
reality and that the system in question models it. I said, for example,
On the other hand, the "model" in your adaptive filter scheme _does_
contain representations (although not perceptual representations) of
hypothetical _parameters_ attributed to the world.
Note "hypothetical" and "attributed." You then informed me,
We will never know the parameters of the world, only the parameters
attributed to the world. There is always at least a transduction
(mapping) between the two, and we can only know and use the output
side of the transducer. But that may be enough.
I thought I had dealt adequately for the purposes with the point you
raised there, and was talking about the difference between two aspects
of an internal model: the fixed structure and slowly-varying parameters
of the model, and the variables at the input and output of the model.
All you're saying is the same thing I'm saying: we can't know the actual
nature of reality, and neither can the systems we model. However, it is
useful to assume that there _is_ a reality, and to speak, as engineers,
of the correspondences between the internal representations and the
"physical" reality (i.e., the reality as we represent it to ourselves
through our private models of physics, neurology, and so on). You do
exactly the same thing in your adaptive model: you compute a "real" x
using the formulas for the "actual" plant; you make an internal model
with the same structure as that of the plant, and compare its output x'
with a representation y of the "real" x. So just like me, you find it
convenient to assume that there is a real plant and that the internal
model approximates a representation of the "real" external organization.
While we are talking at this level of discourse, we simply put aside the
knowledge, which we both have, that this entire process of modeling is
taking place inside ourselves, and that neither of us can ever compare
these models directly with reality. If we get hung up on that idea, we
will give up on trying to build a working model and go back to the
coffee-house, where we can argue by assertion and never worry about
having anything we say disproven.
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Best,
Bill P.