[Martin Taylor 960208 14:50]
Hans Blom, 960208b
_A_ perception has always been taken to be a scalar function of
time, and the mapping of n+1-space onto 2-space has often been
brought up in discussion of the hierarchy. The point you miss is
that there are assumed to be a large number, possibly >n, of such
mappings of n+1 space onto _different_ 2-spaces of perception.
Implying that the original n+1 space is recreated?
If the mappings (the PIFs of the elementary perfaction systems at one
level) are linear, then if they cover the basis space of the original n+1
space, they form an invertible transform. This means that the original n+1
space is not recreated, but redescribed without loss, and an inversion of
he transform can recreate it. A discrete Fourier transform is exactly such
a system. If there were a set of PIFs whose weighting functions followed sine
and cosine functions across the space, then there would be a scalar control
system for each frequency at each quadrature phase (controlling perceptions
that together constitute a complete Fourier Transform of the spatial input),
the result of which would be complete control of the spatial configuration.
Any set of linear PIFs that span the space has the same characteristic,
whether the PIFs are orthogonal or not. They form a transform R^n <-> R^n.
If the PIFs are not linear, the situation is more complicated, and it cannot
be guaranteed that the original space is recoverable, even if the set of PIFs
spans the data space.
ยทยทยท
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Hans Blom, 960208 to Bill Powers (960206.0600 MST)
You would at least have to point out how a control system
can be concerned not only with function -- maintaining variables near
reference levels -- but also with form -- size, weight, and less easy
to quantify things like maximum allowed complexity and such.
Isn't that one of the things that B:CP tries to develop? One of the
levels of the hierarchy, for instance, is called "configuration." We've
talked here about control of things like "self-image." Is that abstract
enough to serve as an example?
I doubt the notion of "competing control systems", at least in the
general sense, because a control system can only "test itself" (or be
tuned) when it is actually controlling. And only one control system
can do that at a time, of course, if they are not to greatly inter-
fere with each other.
I'm not sure what you object to, here. The words "of course" fly in
the face of the example of Bill's Arm Demo, or the 14 df version of arm
control. But maybe you are referring to an ability to learn from the
effects of one's own control. Even there, it's not at all clear that the
interference from non-orthogonal control systems would be any worse than
the interference from unpredicted (but to-be-modelled) disturbances. Surely
each learning control system would learn the correlation of its effects
with the effects due to the other, just as if those correlations were an
aspect of the environmental feedback path? I would have thought there to
be no more constraint on multiple control systems simultaneously learning
than on multiple control systems using the same set of effectors. The
further from orthogonality, the worse the interference, but unless the
effects of interference are nonlinear in a way that induces a bifurcation,
all that should be affected is the speed of learning, not the possibility
of learning.
In general, a control system has not just one purpose, but a great
many ones, most of which are, moreover, very difficult to pre-
specify.
That is not what I mean by purpose. One control system has only one
purpose, which exists physically as the magnitude of its reference
signal. I mean nothing else by purpose.
This is the too simplistic notion that I think gets us nowhere.
I don't see the contradiction that both Bill and Hans seem to see between
the first two quoted statements. In the hierarchy, the outputs of many
level N+1 perfaction units combine to form the reference signal for each
level N unit (multiple purposes). Within each level N unit, the reference
signal has but one scalar value (a single purpose). The higher levels want
it to do X so that they can achieve A, B, C. It _must_ do X, because that
is all it can do, its sole purpose in life. Obviously A, B, and C cannot
(in general) all be achieved simple by achieving X, but they can if Y and
Z, to whose reference signals they also contribute, are achieved at the
same time (cf. the Arm Demo).
Where's the contradiction?
Even
in the simplest one-dimensional control systems I recognize "goals"
or "purposes", often called constraints, that are required for the
control system to be a reliable control system.
These goals are in the mind of an outside observer or a designer, not in
the control system as it is acting, unless that control system is provided
with a perceptual function to evaluate them, and a reference value against
which to set the evaluation. If this situation prevails, you have one
control system performing the original design function and another control
system evaluating (and presumably acting to change the evaluation of) the
performance of the first. Otherwise, as in your example, all you have is
a saturable output function, not a purpose of any kind (though the designer
might have had a purpose when the design was made):
In my home heating
system, for instance, the volume of gas that can be burned per minute
is limited. This could be viewed as a hard-wired "purpose".
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A more efficient controller is no better than a less efficient one if there
is no limit on resources. Control systems won't evolve to greater efficiency
if there is no improvement in control by doing so. There will be improvement
if there is either a natural or a competitive difficulty in achieving the
control; such a difficulty could well be in obtaining an adequate energy
supply. But unless there is such a difficulty, why should a more efficient
control system have any advantage over an equally precise but less efficient
one? (I'll hint at an answer, though: (hsssh--don't tell anyone) Side-Effects
are thermodynamic heaters; control is thermodynamic cooling.)
Martin