# MAps and vortices

**URL:** http://discourse.iapct.org/t/maps-and-vortices/6570
**Category:** CSG1993
**Created:** [December 21, 1993, 11:21pm UTC](http://discourse.iapct.org/t/maps-and-vortices/6570 "1993-12-21T23:21:52Z")
**Posts on this page:** 1
**Page:** 1

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### Author: ![William\_T\_Powers2](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/w/c67d28/32.png) [@William\_T\_Powers2](http://discourse.iapct.org/u/William_T_Powers2)
#### Post date: [December 21, 1993, 11:21pm UTC](http://discourse.iapct.org/t/maps-and-vortices/6570/1 "1993-12-21T23:21:52Z")

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[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  
form?

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,  
> Chris?).  
> --------------------------  
> 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  
> outward.
> 
> 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  
> one.
> 
> 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  
> > system.
> 
> 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.