MAps and vortices

[From Bill Powers (931221.1345 MST)]

Hans Blom (931221) --

Hans Blom? Yes, Hans Blom. I did it right.

That was a beautiful post on inner maps, Hans. You Dutch guys
kill me, the way you handle a language not your own.

There are some puzzling factors about inner maps. The bee
examples suggest that the inner map is a stationary thing, with
one movable point in it labelled "myself." This corresponds to my
experience, generally. But the map is limited in size; when we
move far enough in it, we have to recenter it before we drop off
the edge. At that point, some of the map drops out, and additions
to it come into view. This seems to indicate a HUGE storage
capacity for parts of the map we aren't presently using. Is this
really storage, or do we simply update the map and make the
current scene part of the map? And how do we recenter the map? Is
it stored in some gigantic two-dimensional (three dimensional!?!)
shift register? How do attributes get attached to points on the
map, like size, shape, color? Or is it that map coordinates
become part of the attributes of objects? Or are the essentials
of the map represented at some higher level, in more compact

I feel, as Rick says, clueless. This is an excruciatingly
important subject for PCT, yet all we have is little bits and
pieces of phenomena from which to try to guess at mechanisms.

There is a little bit of this problem even in trying to handle
visual control of pointing behavior. I model the systems as
lumped systems, but we know that the visual perceptual system
preserves spatial mapping of the retina all the way up to the
visual cortex (several places). A few years ago, in _Science_, I
saw an article on brain-mapping in which a visual target was
shown (measured) as a hump of activation in the visual map, and
when something was moved to that target position, another hump of
activation actually moved across the map to the target position.
Then I lost the reference and I can't find it now.

This, of course, suggests a completely different mechanism for
control of spatial perception from the one I use. Instead of
having a simple scalar signal the magnitude of which indicates
position, we have actual movement of activation regions from one
place to another in a geometrical map in the brain. Maybe this
gets translated, at a higher level, into position signals, but
there's the possibility that the map itself is used somehow to
derive error signals from differences in the _location_ of
objects in a literal map. Location? How can we get an error
signal out of relative locations of two centers of activation in
a spatial map? What could possibly detect and compare positions,
in a way that would generate a scalar error signal?

This makes the whole problem of understanding higher levels of
perception and control look extremely complex. That can't be; I
think there's some principle buried in there that would make this
method of perceptual control _simpler_ than the way I'm trying to
model it. After all, assuming a scalar signal representing
position in a visual field is assuming a LOT of hidden machinery.
It's just that we don't build things this way, so we have no
well-understood organizations to draw upon. Something simple and
obvious is staring us in the face here, but I don't see it.

This subject could absorb a lot of research effort, couldn't it?


Martin Taylor (931221.1100)--

Your capitalized line is excessive as written. I should like
to replace it with something like:

"derived by a means that has substantially less effect on the
external variable than does the control output."

Fine by me, but "substantially less" seems to mean some extremely
small numbers, in comparison with the energy range of ordinary
actions involved. Your example of touching something too small to
stand the touch just defines an extreme lower limit, and still
leaves a huge gap between sensory energy and output energy.

Over four billion years of evolution, control systems have
evolved to maximize their ability to control, which includes
minimizing the effect of sensing on the thing controlled.

I'm beginning to think that even the earliest true control
systems must have incorporated a catalyst of some sort, so that a
small input effect could produce a large output effect. While I
haven't been able to elucidate the idea yet, I think that
amplification is the key: anything that gives a "signal" an
effect on a macro variable. This creates the necessary
unidirectionality, so that sensing something has -- all right --
onlyt a minute effect on what is sensed. This is what makes it
possible for a control system to affect physical processes in an
arbitrary way, a way that is not dependent on the process itself.
That cuts the control system loose from the ordinary cause-effect
relationships that dominate the nonliving environment.

Didn't we talk about all this a couple of years ago?

Yes. Cliff Joslyin is about to publish a paper by me on the
subject of how life began, essentially like the ideas you talk
about in this post (any progress toward actual publication,
The test:

I suggested applying a mild jet of water oriented
circunferentially at some point near the drain rim. It should
be easy to compute the expected change in lateral momentum of
the water directly affected by the jet if there were no
feedback from effects around the drain rim.

This just moves the point of application of the disturbance to a
different place in the "loop."

The feedback in the vortex is not localized, but distributed.
Each packet of water is accelerated along a spiral by pressure
from above, and feeds forces back to slower-moving packets
spiraling just above and outside it, also absorbing angular
momentum from packets lower and inside it. The rotation is
sustained by transfer of angular momentum from the center

Is it lateral (angular) momentum that you are defining as the
controlled variable in the vortex? If so, I think we would find
very low loop gain. It is the conversion of downward force to
rotary motion that soaks up energy from the straight-through
path. The nonlinearity is probably square-law, because that is
how back pressure would rise (due to centrifugal force) with
angular velocity. This would make apparent loop gain the highest
for the largest disturbances ( disturbances increasing angular
momentum to the point where flow through the outlet stops). But
that would reduce the opposition to that from friction only, with
no energy supplied from the source. It seems to me that the
disturbance adding or subtracting torque to the circular flow
would have the same mechanical advantage as in the conversion
from downward force to circular flow -- or perhaps a much better

No point in guessing. It works the way it works.

One of the consequences of true feedback control is that the
operation of a control system is almost entirely insensitive
to variations in its own power supply.

This is true only if the power supply is strong enough.
... If you have enough power, it doesn't matter how much more
you have, but if you don't, every little bit extra gives you
the possibility of better control. Your amplifier can output

only as much as the power source gives it.

Yes, that's what I said. The vortex doesn't have this property. A
drop in the power supply is reflected immediately as a change in
the vortex.

I guess you still miss the point here. The shape of the vortex
is determined directly by the energy flow (among other things).
But the energy flow that does this determination is not the
_modulation_ energy that is always the signal in a control

And you missed my point. In living control systems, there is no
energy expended but the modulation energy. You seem to be
visualizing the output energy as a fluctuation in a continuous
energy flow through the muscles. But if there is no error signal,
the energy flow through the muscles is zero. There is no
background energy flow being increased and decreased by the error
signal around some mean value. The error signal is simply
translated into output forces, with a drain on the power supply
that depends on the amount of force. If the required force is
zero, the drain is zero: there is no energy flow to modulate.

When you speak of modulations on the main energy flow in the
vortex, you're simply partitioning the only energy flow there is
into conceptually different parts. This is like saying that you
don't have 5 marbles, you have 3 marbles and 2 marbles.

Let's work on that other example.
Best to all,

Bill P.