[From Bill Powers (980406.0748 MST)]

There is a difference between PCT and many other explanatory schemes that

tends to be left out of discussions. PCT is an example of _system

analysis_, whereas few other psychological theories belong in that category.

In system analysis, a system is thought of in terms of variables that

interact via functions. In a true system analysis, every variable is

accounted for in terms of other variables, or as an independent variable.

Nothing "just happens".

The force exerted by a spring on its attachment depends on -- is a function

of -- the length of the spring, for example. The form of the function is

Hooke's Law, stating that force is proportional to the difference between

actual length and some resting length characteristic of the spring. In a

system of interconnected springs (for example, a bedspring), the length of

each spring would be determined by the sum of forces from other springs,

and the force generated by each spring would depend on the amount by which

it is stretched or compressed by forces from other springs. Some of the

springs would be attached either to fixed objects (the frame of the

bedspring) or to movable ones outside the network of springs (weights

pressing down on the network of springs); there we would find forces and

positions that are independent of what goes on inside the network of

springs, and those would be the independent variables.

The first rule of system analysis is that _every variable must be accounted

for_. Each variable must be some function of a set of other variables,

unless it is an independent variable determined by arbitrary processes

outside the system. The second rule is that each effect of one variable on

another must be mediated by a function: that is, a rule or equation which

allows the value of a variable (other than an independent variable) to be

stated in terms of the values of all the other variables that affect it.

And the third rule is that the parameters of functions must either be fixed

by the physical nature of the system, or be determined by system variables

that must in turn be accounted for.

To pick a recent example, one might propose that "attention" has some kind

of influence on the behavior of a system. What criteria must be met to

allow "attention" into a system analysis?

First, we must specify what sort of thing attention is. Is it a physical

quantity, a signal, or a function? If it is none of those, it is not

physical, and can't be part of a system model. If a variable, it must be

either an independent variable determined by something outside the system,

or a dependent variable determined by a function relating it to all the

other variables that affect it. If a function, the form of the function

must be specified, if possible, along with the variables that are related

through the function, as well as the parameters of the function that are

either physically fixed or dependent on system variables.

Now consider the following proposal: "attention is what determines loop

gain in a control system." By our usual definitions, loop gain is the

product of all steady-state proportionality factors encountered in one trip

around a control loop. This tells us immediately that if loop gain is to be

determined or influenced by attention, it is the steady-state gain factor

in one or more of the functions in the loop that is affected. In other

words, a parameter of one or more functions is being affected by attention.

The influencing agency, then, must be some other variable of which the

parameter is a function. This tells us that attention is a physical

variable, the state of which must be accounted for in terms of other

physical variables; if outside the behaving system, physical quantities,

and if inside it, (neural) signals.

If we don't mean that attention is caused by external physical variables

through a physical law, or that it is simply a neural signal for which we

still have to account, the only remaining choice is to say that "attention"

is just another word for "loop gain," turning the original proposition into

an identity and making it meaningless. All that has been proposed is that

loop gain determines or influences loop gain. The basic rules of system

analysis end up showing that we have proposed a dormitive principle:

something defined only in terms of its effects, and then used as an

explanation of the effects.

PCT is fundamentally a system analysis. Every variable is accounted for,

every relationship among variables is represented as a function. There are

no loose ends. Even in HPCT at the highest level, there are no loose ends.

The highest reference signals must be either outputs of higher functions

(ruled out by "highest"), fixed physical properties of the comparator

function at that level, dependent on physical variables outside the

hierarchy, or zero. Those are the only choices granted under system analysis.

Of course in doing a system analysis of a system with many unknown parts

and parameters, we must guess at many of the functions and variables. But

guess we must, because to end up with a complete analysis we have to make

sure that no variable or function is unaccounted for, even if we must

conjecture to do the accounting. Unless the accounting is complete, it is

impossible to make any predictions from a system model. System analysis

forces us to make our assumptions explicit, because unless we do we don't

have any analysis.

All models in the hard sciences abide by these rules of system analysis.

Essentially no models in the psychological sciences do, other than PCT.

Best,

Bill P.