[From Rick Marken (930317.1530)]

Here are some replies to a private post from Martin that he

said I could reply to on the net.

Rick,

You always post the equation as p(t) = o(t) + d(t), but in discussion

everyone, including you most of the time acknowledge that there is a

not-well-known function relating the output to the effects on the CEV.

If there weren't, wouldn't the cognitive outflow people be right?

This might be my fault; the letters p,o and d refer to variables,

not functions, and the t in parenthesis is an index, not an operand.

This equation just decribes physical reality in a compensatory

tracking task (if we think of p as the number representing the

CEV -- position of a line -- rather than the perception of that

line; as I said in another post, there is very good reason to

suspect that the perception of the CEV (in a tracking task) is

linearly proportional to the physical measure of the CEV).

The output function is really the function that transforms the

error signal into the output variable, o. So the output function, O,

is o(t) = O(e(t)) and O is likely to be highly non-linear. This is

indeed one reason why cognitive outflow models can't work -- but

another reason is that the intended result of the cognitive outflow

(the CEV) also depends on disturbances (actually, on their effects,

d(t)).

I said:

This is only a problem for those who think of control loops

sequentially. In the formula CEV(t) = d(t) + o(t) it is

always the current value of the output (occuring at time t) that

is combined with the current value of the disturbance. The fact

that o(t) might be the result of processes occuring earlier in time

is of absolutely no consequence. The physical fact of the matter

is that the current state of the CEV is determined, simultaneously,

by the current value of the disturbance and the current value of the

output.

Martin replies:

This cannot be a correct interpretation of the equation. The CEV does

not react instantaneously to output. The equation talks about signals

which add to form a perceptual signal, or else it talks about physical

effects that add to change the CEV and therefore the perceptual signal.

Either way, the three terms in the equation must be of the same form,

and that form is not the form of the output signal of the ECS.

The equation should read p(t) = P sub t (F(o) + D(d)) where P sub t is

function P evaluated at time t. F is some function of o, where o is the

history of all output, D is some function of d, where d is the history

of all disturbance. One can simplify this by saying simply that the

"disturbance" is D, rather than D(d), since perceptual control doesn't

care about the distinction. And if we reference p(t) to the CEV rather

than to the perceptual signal, we can eliminate the function P, just

evaluating F at time t. But we can't ignore F, as you and Bill have

both pointed out today. Allan is saying that F is uncertain. So do you.

He says past actions have side effects. That's not controversial in any

version of PCT that I know.

This confusion may all result from my notation. Think of p(t) as

the sequence of numbers (over time) that represent the position of

the cursor on a computer screen, o(t) are the numbers coming from

the joystick, d(t) are just smoothly varying random numbers. At any

time t, p(t) = o(t) + d(t); that is just the way the physical

situation is set up. I agree that o(t) at a particular time might

be the response to a perceptual input from time t-tau. But what

is currently on the screen, p(t) is always the simultaneous result

of the current disturbance number, d(t) and output number, o(t).

So time delays certainly do exist in control loops -- but they

are not pertinant to the question of whether or not there is

information about d(t) in p(t). The fact of the matter is that

p(t) is always a JOINT result of o(t) and d(t) (see Bill's earlier

post today on disturbances). This is a VERY important point to

understand. If we can't agree on this (that the perceptual input

to a control system is at all times the simultaneous, joint result

of both disturbance and output) then we are really thermo-

dynamically isolated from each other.

Best

Rick