[Martin Taylor 960201 17:45]
Bill Powers (960201.1415 MST)
There's an asymmetry in phenomenon X that doesn't show up in:
Let Y be some variable that is a determinate function of x1, x2, ... xn.
Y = f(x1 .. xn)
The basic indicator that phenomenon X (my next choice if "spontefaction"
is rejected) is taking place is that a change in one or more variables
x2 .. xn results in a change in x1 such that the value of Y is
maintained close to a specific value Y0. Of course you could interchange
the x variables; what matters is that one of them changes to cancel the
effects on Y of changes in any or all of the others.
As we normally think of perfaction
(aside...
>You can use any word you like to refer to this phenomenon
>that I am talking about, as long as we agree that this word will be used
>to denote that phenomenon and NOTHING ELSE.
)
there is one x-variable that is distinctly different from the others.
You call it x1, and then say that the x-variables can be interchanged.
But they can't. It is always the same one that varies if Y is perfacted
and any of the other x's are changed. The function should probably be
written so as to note this fact, distinguishing the one variable that
compensates for variations in the others:
Y = y(f, d1, d2, d3...)
But then this notation raises the question of why it isn't written
Y = y(f1, f2, ..., d1, d2,...)
which carries the implication that there are multiple environmental paths
for the output (as I understand it, the x-variables are supposed to be
observables, so that although there is only one value for the output of
the elementary perfaction unit, there are possibly many observables
influenced by or determined by that output value).
This second formulation represents one of the PPT maxims: "Many means to
the same end." When a d-variable changes, some pattern of change in the
f-variables restores Y to near its original value. But so also do the
other f-variables change when one of them alters its value (as it might,
if it also serves as an output from a different elemetary perfaction unit).
What stays (nearly) the same is Y.
Whether one wants to look at the different paths that the output takes
to influence the CEV depends on one's current interest. Sometimes it is
enough to consider only the single-valued output of the EPU. In that
case, the single "f" is what one would want in the expression. But that
can only be experimentally observed when the perfactor is limited to one
mechanism for influencing the CEV, as happens in a tracking experiment
with a single handle. In everyday life, the multiple f's are needed.
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.
The function is symmetric, but the pragmatics are not, at least not
in perfaction.
There's nothing new here. Just some musings on the implications of different
ways of writing a function.
Martin