# mappings -Reply **URL:** \ **Category:** CSG1996\ **Created:** [February 8, 1996, 3:02pm UTC](http://discourse.iapct.org/t/mappings-reply/14205 "1996-02-08T15:02:30Z")\ **Posts on this page:** 3\ **Page:** 1

**Author:** ![HANS\_BLOM2](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/h/f17d59/32.png) [@HANS\_BLOM2](http://discourse.iapct.org/u/HANS_BLOM2)\ **Post date:** [February 8, 1996, 3:02pm UTC](http://discourse.iapct.org/t/mappings-reply/14205/1 "1996-02-08T15:02:30Z")

[Hans Blom, 960208b] (Martin Taylor 960206 11:20) > > Well, that's enough, I think. Where a mathematician could ... > > also help is in pointing out that by going from an n+1-space to a > > 2-space something is irredeemably lost, which cannot be regained > > later where manipulation can take place only in 2-space; this is > > equivalent to stating that you cannot control your perceptions but > > at most a lower-dimensional projection of them. > After a lovely posting, you lose on the last sentence:-( You're correct. As so often, I again confuse reality with my impression of it. For a correction see my previous post. > \_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? > There's another point you miss, which is that you should not treat > "t" as unidimensional. If there is a function X(t), it has a > dimensionality that depends on its equivalent rectangular bandwidth. You're right, but that is a very different discussion that would only confuse things at this point, I think. Greetings, Hans ---

**Author:** ![\_Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/_/a9adbd/32.png) [@\_Martin\_Taylor](http://discourse.iapct.org/u/_Martin_Taylor)\ **Post date:** [February 8, 1996, 8:24pm UTC](http://discourse.iapct.org/t/mappings-reply/14205/3 "1996-02-08T20:24:58Z")

[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. > **···** > > ---------------- > > > 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". > > ------------ > 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