f and d variables; spontefaction is not EAB-control

[From Bill Powers (960202.0100 MST)]

Martin Taylor 960201 17:45 --

Y = y(f, d1, d2, d3...)

     this notation raises the question of why it isn't written Y =
     y(f1, f2, ..., d1, d2,...)

Because this is only a matter of arbitrary classification. The variable
Y is a function of a set of variables xi. Any one of the variables xi
could be used as a means of perfacting Y. A given perfaction loop must
sense the state of Y and compare it with an intended state Y0, but the
error could be amplified and applied to any (indeed, to _many_) x's,
each with the proper sign.

Consider driving a car. We treat a dragging brake as a disturbance
because it produces a lateral force on the car. The driver uses a
steering wheel because it provides a handy, reachable means of varying
the lateral force on the car. But in driving a small airplane on the
ground, one has a choice: the rudder pedals steer the nosewheel or
tailwheel, or if tilted forward with the toes, can be used to apply
differential braking to the main wheels. The differential drag from the
brakes is also used for steering. If there were two brake pedals in a
car, the car could be steered that way. In a larger airplane there is an
additional means of steering, through applying differential power to the
left and right engines. If there were a means of varying a crosswind or
of tilting the road, the driver could use those as still more alternate
or simultaneous means of spontefacting the path of the vehicle.

Normal (as opposed to laboratory) environments contain many variables on
which a spontefacted variable depends. Aside from practical
considerations, they are all potential means of affecting Y. Generally
we use the first means we come across that provides an adequate amount
of effect on Y without the need for excessive effort. Whatever x or
combination of x's we end up using, all the other x's add up to a net
disturbance. Which x's are means of spontefaction and which are
disturbances may change -- for example, when you arrive at a door with
your arms full of groceries.

     The distinction between f-variables and d-variables isn't in how
     they appear in the function y(f...d...), but in two pragmatic
     facts: (1) nothing the perfactor does will influence any d-
     variable, and (2) changes in any f- or d-variable are compensated
     only by changes in f-variables.

(1) is sometimes a consideration, but not often. (2) is my point. There
is no real distinction between "d-variables" and "f-variables" and the
classification can change.

···

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Bruce Abbott (960201.1820 EST) --

     Because the stimulus is not viewed as _causing_ a given response,
     but only as affecting its likelihood of emission, it would not
     generally be proper to say that the SD _determines_ the response;
     it is only an influence. However, the term "control" could also be
     used when the state of one variable _determines_ the state of
     another. This is the sense in which it is sometimes used by
     engineers, who might speak, for example, of a "motor controller"
     that "controls" the rotational speed of a motor, even though what
     is being referred to is an open-loop system in which the setting of
     the controller determines the amount of current flowing through the
     motor's windings.

Yes, even some engineers seem unaware of any important difference
between affecting or determining on the one hand, and spontefacting on
the other. We also speak of using the controls of a radio or a car or an
airplane, with the spontefacting system itself remaining in the
background and unconsciously being taken for granted. As I have said
more than once, you can watch the controls of the television set all day
and you will never see them do anything to alter the picture or the
sound. If the sound gets too weak, the volume "control" will just sit
there.

     I used the term "control" in both senses when describing the
     spontefaction system.

In that description, I think, you were not addressing the _degree_ or
_reliability_ of effect of one variable on another, which now seems to
be the dimension along which you distinguish influence from
determination. The critical consideration is not that one, but whether
there are other variables that can also affect the variable in question.

If you have y = f(x1,x2), either x1 or x2 might have a probabilistic
effect on y, but no matter how reliable the effect, x1 alone cannot
_determine_ the state of y, because there is an x2 which is also
affecting y. At most, x1 influences y.

If the function is stochastic, then only the mean value of the function
is determined, but it is still determined because no other variable
affects it. If the mean value is always zero, then the best you can say
is that the output is correlated with the input to some degree, with no
way of specifying causality.

The distinction in terms of degree applies to y = f(x), where there is
only one x that affects y. This equation states, implicitly, that there
are no other variables that can affect y. If there were other variables,
they would have to be listed among the arguments of the function, at
least as a representative aggregate variable. Without other variables
being mentioned, y = f(x) says that only x affects y. If the effect is
stochastic, there might be times when x does not affect y, but in the
absence of this effect, y will not vary because it does not depend on
any other variable.

Setting up system equations can result in subtle mistakes or omissions.
An example you have probably come across is in setting up a circuit to
accomplish a logical function. It's easy to make y depend on x by
writing "if x, then y" and wiring a contact to activate y. But sooner or
later you will realize that you have failed to implement the case "if
not x, then not y." It's easy to forget that y could be independently
activated. If you really mean "if x then y AND IF NOT X THEN NOT Y", you
have to make explicit arrangements for y to be NOT activated when x is
NOT true. This is obviously a problem when Y is the output of a set-
reset latch. Setting the latch will make Y true, but NOT setting the
latch will not then make Y not true.

In dealing with causal systems, each variable must be expressed as a
function of ALL variables on which it depends to any significant degree.
If a response depends on a stimulus, but may also occur without the
stimulus, then you have to list in the arguments all the _other_
variables that can lead to the same response. If those variables aren't
known, you're stymied; you can't complete the system equations. All you
can do is try to hold the environment constant in all the respects you
can think of; but not knowing what matters, you have no way of knowing
if you have succeeded.

In your examples of a closed loop, the distinction I pointed out was
that for the error signal and the input variable, there were _two_
arguments in the function, with "control" being assigned only to one of
them. So no matter what _degree_ of effect either variable had (normally
expressed as a coefficient of that variable in the function), neither
variable could properly be said to _determine_ the result. Except in
EAB.

     I noted that the disturbance would control (determine) the
     spontefacted variable in the absence of spontefaction.

For this to be true, you would have to specify that there is NO system
of any kind providing an output variable that also affects the variable
in the absence of spontefaction. You can remove spontefaction by
breaking the loop anywhere, but this does not necessarily remove the
output that is affecting the variable. You would specifically have to
break the loop between the output function and the variable. The
disturbance would then _determine_ the variable because it is the only
argument in the remaining function.

     In the presence of spontefaction the influence of (control by) the
     disturbance diminishes so that it is 1/(1 + G) proportion of the
     unspontefacted amount, where G is the loop gain of the system.

This is true, but I presume you're aware that the disturbance would not
spontefact the output regardless of the loop gain in the spontefacting
system (even if the gain is zero). That is, an arbitrary influence
applied to the output would not result in a change in the disturbance
tending to restore the output to its former state.

     But this got me to thinking about how "strong" and "weak" control
     would be defined.One sense of it is that Variable A has strong
     control over Variable B if Variable A represents the major source
     of variation in Variable B. But another sense appeals to how much
     A has to vary (in proportion to its normal range of variation) to
     produce a given amount of variation in B (in proportion to its
     normal range). This second definition is closer to the idea of
     "sensitivity." Both ideas seem to be tied up together in the idea
     of "strength" of control, in the EAB sense of the word. I wonder
     what a good metric for this would be.

I don't know why you're wasting time on that. Since control in your
usage can mean only influence or determination, and never means
spontefaction, all you need to work out is what you mean by strong or
weak influence or determination, which you already know. A strong
influence is represented by a large coefficient of the influencing
variable in the corresponding equation (or a high power of the
variable). The ratio of one influence to another is the ratio of the
coefficients (weights) for linear equations. If all the variables
capable of affecting the value of the function are listed, then the
value is completely determined by the states of all the variables,
regardless of the coefficients. If you simply list the coefficients, you
have taken care of both cases you're talking about -- the relative
amount of effect, and the "sensitivity" to any one variable.

     By the way, the disturbance would appear to exert excellent control
     over system output so long as the reference signal remained
     constant, while exerting very weak (perhaps even undetected)
     control over the sfv.

True, but the disturbance would still not vary so as to restore the
output to any particular value, when the output is arbitrarily altered
by changing one of the variables on which it depends. So the disturbance
would not spontefact the output. Your usage of "control" has no relation
to spontefaction.

YOUR USAGE OF "CONTROL" HAS NO RELATION TO SPONTEFACTION.

Come on, Bruce, I need an "ack" on this. I feel that I'm shouting down a
bottomless pit. What you're musing about is just determination or
influence. It has nothing to do with spontefaction, even though you
refer to it by the term "control." If you had realized this from the
start, you would never have thought I was joking.
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Best to all,

Bill P.

[Martin Taylor 960202 14:10]

Bill Powers (960202.0100 MST)

Very strange. You make all my arguments, and at the end deny my conclusion!

Martin Taylor 960201 17:45 --

Y = y(f, d1, d2, d3...)

    this notation raises the question of why it isn't written Y =
    y(f1, f2, ..., d1, d2,...)

Because this is only a matter of arbitrary classification. The variable
Y is a function of a set of variables xi. Any one of the variables xi
could be used as a means of perfacting Y. A given perfaction loop must
sense the state of Y and compare it with an intended state Y0, but the
error could be amplified and applied to any (indeed, to _many_) x's,
each with the proper sign.

The "f" variables are those that can be used _by the perfaction system_
since they are the only ones it can influence. That's the point you make
in the following discussion. If, by chance, changes in the "d" variables
happen to have countervailing effects on Y, that's good luck, but as far
as the perfaction system is concerned, nothing influenced Y and it need
do nothing. That's the distinction between "f" and "d" variables that
you seem largely to deny in:

    The distinction between f-variables and d-variables isn't in how
    they appear in the function y(f...d...), but in two pragmatic
    facts: (1) nothing the perfactor does will influence any d-
    variable, and (2) changes in any f- or d-variable are compensated
    only by changes in f-variables.

(1) is sometimes a consideration, but not often. (2) is my point. There
is no real distinction between "d-variables" and "f-variables" and the
classification can change.

In your discussion, (1) was the main point so far as I could see. For example:

In a larger airplane there is an
additional means of steering, through applying differential power to the
left and right engines. If there were a means of varying a crosswind or
of tilting the road, the driver could use those as still more alternate
or simultaneous means of spontefacting the path of the vehicle.

Normal (as opposed to laboratory) environments contain many variables on
which a spontefacted variable depends. Aside from practical
considerations, they are all potential means of affecting Y.

And are therefore all "f" variables. Other means of affecting Y (the
non-central direction tendency of a vehicle) are wind gusts, road bumps,
binding wheel bearings, impingements of mad bears, ... all "d" variables
that the driver cannot use to bring Y back to centre.

So why do you seem to disagree with me? Your points all lead to agreement.

Martin