[Martin Taylor 991119 02:10]

[From Bill Powers (991118.0746 MDT)]

Anyway, you still don't understand my critique. The problem of

level-skipping is not what you describe: setting references for the angle

of the steering wheel and the location of the car in its lane at the same

time. The problem is setting a reference angle for the steering wheel

without considering that some other, higher, system, may _also already_ be

setting a reference angle for the steering wheel. That other higher system

will immediately adjust its output to restore the steering wheel to its

"proper" angle, or will adjust something else to compensate. In your verbal

description you said that the whole system would simply adjust itself to

solve the simultaneous equations just as the analog systems alone would do.

But that is incorrect, because the digital system can't be adjusted

continuously.>>>The higher analog levels would try to counteract the effects.

>

>Yes, this always happens in a many-to-many set of connections between

>levels.But if the systems are properly orthogonal it does _not_ happen. You can

control x+y completely independently of x-y, with no conflict at all.

Actually, I didn't talk about conflict, which I take to mean irreconcilable

settings of the reference signal values in different control units. I

talked--and I suppose you meant--mutual disturbance, and used "conflict"

loosely. On that assumption...

You seem to be saying two things: at the end of the quoted section you say

(1) If x, y, x+y, and x-y are all continuous analogue control systems, then

a change in the reference value for x+y will not disturb the perceptual

signal of x-y, no matter what the dynamics are of the environmental

feedback paths for the x and y control systems. So the x-y control unit

will therefore not alter its output to counter the non-existent

disturbance, and will not disturb the perceptual signal of the

x+y control unit. No matter what the external dynamics, each controls

without disturbing the other?

And in the previous paragraph you imply

(2) It is possible to set the reference values for x+y=7, x-y=2, and

find values for x and y that allow the values of x+y and x-y to match

their reference values, but it is NOT possible to set a reference range

(i.e. a categoric value "single digit") for "0<x+y<10", x-y=2, because

there are no values of x and y that allow this to be the case.

I find it passing strange to say it is not possible for the category

reference "true/false" to be matched by the perception derived from the

logical input function "0 < x+y < 10" at the same time as a reference

value of "2" for the perception x-y can be matched, simply because the

decision as to whether the category reference value is matched is binary

valued. But if the reference value for x+y is any exact number within

that range, you say there's no problem in getting both references

simultaneously matched.

That doesn't apply when one of the equations admits of only binary values

of its variables. The chances are extremely small that a solution will

exist.

Again, passing strange. The perceptual signal, the reference signal, and

the error signal _inside_ the category control unit are binary. The

inputs to the perceptual input function are not, and the output signal

need not be (ordinarily would not be, if the typical integrator output

function is used). How does the binary character of the internal

variables affect the simultaneous equations--quite apart from the

obvious fact that it is easier to satisfy multiple simultaneous

equations when some of them admit ranges of values rather than point

values as solutions?

Actually, as I pointed out earlier, the fact that some of the controlled

variables are categoric makes it easier to satisfy the equations together.

In fact, sometimes you can solve systems such as

0 < x+y < 10, 2 < x-y < 20, x*y = 8,

when you couldn't solve those three equations (except by a fluke) if they

were point equalities x+y=7, x-y=2, x*y=8.

>And I must apologize again, as,I hadn't seen that you had followed

>through my moment-by moment description of the changes of signal

>values when digital and analogue units combine to set refeences for

>lower-level analogue unitsI read it through but it was just a lot of arm-waving -- an analog pointing

system with an error of 30 degrees (as I remember the number) for example!

Why do you have a problem with the analogue system having an error of 30

degrees? How can this not happen when the arm has been to the right and

you now wnat it to be to the left, as in my example? Don't you believe

reference values can change?

What did you imagine that the output function would be doing?

What I said it would be doing. The output functions are perfectly

ordinary--I assumed integrators, I believe, except that I used a worst-

case situation for the category control unit and allowed its output

to be binary valued, in order to show that even this crudeness did not

create any real problem.

Martin, I'm just not going to get sucked into this.

That's been my feeling, too. I am aware that it is hard to get one's

mind around a configuration different from the one with which you have

spent so many decades, but it really isn't that complicated. I think

you are probably seeing the proposed structure in terms of a distortion

of the classical structure, whereas it is really quite easy to take it

on its own terms and see what it would do. Anyway, let's drop it for

now. I retain the opinion that none of the objections you have raised

are valid--maybe that's because I haven't understood the objections.

Anyway, in the way you have stated them they seem not to apply to the

organization I propose, or, as in the earlier part of this message,

as I interpret them, they are wrong.

You are right that words along the lines "You're wrong" "No, you're

wrong" get us nowhere. And I have a notion that maybe a variant of

Rick's 3-level demo which has a logical top level might be adequate

for looking at some of the issues. Or maybe not. But words aren't

going to change opinions--they seldom do.

At the moment I have 283 unread messages on CSGnet, and the number is

more likely to increase than to decrease. It would be interesting to

know, though, whether my impression from occasional sampling is correct--

that the "coercion" debate is covering exactly the same ground as last

year or the year before? Or has something new been said by anyone?

Martin