[From Bill Powers (921220.1745)]
Wayne Hershberger (921219) --
I think I commented on that post. Anyway, here's what I have to
say now. Brace yourself: I have a lot to say.
You say:
I am saying that when taking something apart that works, one
wants to keep track of all the working parts and to not mistake
a limited set of parts for a complete set.
Here are some of the parts involved in perception as I model it.
^
···
Perceptual signal: how much of this perception
> is present.
---------------------------------------------------------------
========= Input function: operations applied to input
> Fi | signals (or variables) to calculate the
========= value of a function of the inputs.
----[SENSORY INTERFACE]-----------------------------------------
> > >
> > > Physical variables and their paths of
^ ^ ^ influence to the input function.
> > >
v1 v2..vn
Now, clearly the set of v's is a fixture of the model
environment. For a given set of v's, any number of input
functions Fi can be constructed (even in parallel) which
produce perceptual signals that depend differently on the
detailed behavior of the v's. Therefore the v's themselves should
not be considered as a part of the perceptual process.
The form of the function Fi determines how the perceptual signal
will change as the v's go through various detailed changes. The
value of the perceptual signal will represent an aspect of the
set of v's that will be invariant if the v's change in certain
proportions, and variant if they change in any other proportions.
Thus the magnitude of the perceptual signal represents the state
of the v's as seen through a particular form of input function.
While the v's remain constant, it is possible to alter the form
of Fi. Doing so will (in general) alter the value of the
function, which is to say that the perceptual signal will change
to a new value. If the v's then go through the same patterns of
change as before, the perceptual signal will no longer be
invariant for the same proportional changes as before, and it
will not vary in the same way as before when the v's go through
other patterns of change in other proportions. In short, the
perceiving system will experience a new entity in the environment
that obeys different laws even though the v's are changing in the
same ways.
I don't know the advanced concepts behind all this, but it's
clear that with n variables in the environment, we have an n-
dimensional space, each axis being defined by one v. If there
were two variables, an input function that computed weighted sums
of powers of the individual stimulations at the sensory interface
would create a two-dimensional family of curves which do not
cross. These parallel curves would trace out ways in which the
variables can change in v1-v2 space while producing a constant
value of perceptual signal. If the environment changes so that
the v's remain in the relationship defined by one of these
curves, the input function will produce a constant signal: the
system receiving the perceptual signal will experience a steady
environment.
If the environment changes so as to move the v's from one curve
to another parallel one, the perceptual signal will change
according to the separation of the curves. This kind of change,
orthogonal to the "curves of indifference," is reported as a
change in the perceptual signal.
The behavior of the v's is therefore perceived only along
trajectories orthogonal to the curves of indifference. All such
trajectories are equivalent in terms of the perceptual signal.
The curves of indifference are created entirely by the input
function; they are not a property of the v's, but of the
perceptual apparatus.
It is perfectly possible that there are natural laws relating the
v's. It might be true, for example, that (v1^2 + v2^2) =
constant. In that case, the v's would always vary in such a way
that the point v1,v2 lay on a circle on a plot of v1 against v2.
This circle would intersect the lines of indifference created by
the perceptual input function. As the v's varied, the point
representing them would move around the circumference of the
circle, and during one orbit the point would pass from one curve
of indifference to another and back again.
The perception, however, would not represent the fact that v1^2 +
v2^2 = constant. As the point moved uniformly around the circle,
the perceptual signal would vary in some sort of distorted sine
wave. The actual invariance represented by the natural law would
not appear in perception at all.
In fact the behavior of the perception is related lawfully to the
behavior of the point in v1-v2 space, but the law is due to the
form of the perceptual function, not to the form of the natural
law relating v1 to v2. The effect of the natural law constrains
the way the perception will change, but that constraint is not
evident in perception. All we see is the combination of the
natural law and the law represented by the form of the perceptual
function.
In adapting to a particular environment to get control of it, the
brain reorganizes. Perceptual reorganization alters the curves of indifference,
and thus alters the behavior of a given environment
that will be perceived. The brain's problem is to find
organizations of the input functions that will yield controllable
variables, and then controllable variables that have a bearing on
survival or well-being -- and it must do so without knowing
anything about the v's except what is represented in the form of
perceptual signals. All the criteria for selecting one perceptual
function over another must be internal, in the end.
In trying to learn how the brain's control systems become
organized, we have to try to figure out how it could settle on a
set of perceptual organizations that will yield an adequate set
of controllable perceptions. We already know that when multiple
systems perceive and control the same collection of v's at the
same time, there is a minimum-conflict arrangement in which the
various input functions provide orthogonal representations of the
external environment. This constrains only the whole set of
systems that operate simultaneously, so we can't deduce a priori
what the "axes" of each set of curves of indifference would be;
all we can say is that all the curves, ideally, would cross at
right angles where they intersect. Exact orthogonality isn't
necessary unless we exhaust the degrees of freedom of the
environment, which is highly unlikely to be a problem. But the
more orthogonal the axes of control, the smaller all the error
signals can be when all the reference signals are matched by
their respective perceptual signals.
Obviously the brain manages to arrive fairly quickly at a very
satisfactory set of control systems (although one can always ask,
"compared to what?"). So whatever the trick is, it must be fairly
simple. Perhaps it depends heavily on evolutionary preparation
for the rapid learning that occurs right after birth of a human
being. Figuring out what is required from than angle could be
complicated indeed.
At any rate, none of this answers the basic epistemological
question as to whether the final set of perceptions comes to fit
the environment in some special veridical way, or whether there
is a large component of arbitrariness in it. We have no way of
answering this question except to build a model of the brain that
shows how the self-organizing process interacts with a
hypothetical environment. Not having any way to look directly at
the v's in the environment, we will never be able to verify our
conclusions, whatever they are. The best we can hope to find,
eventually, is a story with the virtues of being both simple and
convincing. I don't think we are anywhere close to doing that.
I would like to know what you think of this argument. Do I need
to worry that you won't tell me?
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Best,
Bill P.