[Martin Taylor 960206 12:00]
Bill Powers (960206.0600 MST) to Hans Blom
It is assumed in your model that the perceptual variable that
you call y is simply a direct representation of one environmental
variable x, plus a noise component. You do not consider that the
controlled perception y might be a function of multiple environmental
variables, or that there might be many different variables y which are
different functions of the same set of environmental variables. So your
model doesn't address the situation I am talking about, although it
could do so.
In your usual description of a perfaction loop--a diagram--you show one CEV
that is affected by one disturbance input and one influence from the
output function of the perfactor. You recognize verbally that there
are many _physical_ influences that contribute, but nevertheless the
CEV has to be scalar, because the perceptual variable derived from the
function that defines the CEV is scalar. The diagram and the verbalism,
and your mathematization as Y = y(x1,....xn) can all be reconciled in
a way that cleanly brings Hans's "one environmental variable" into the fold:
Let D(t) = d(x2(t), .... xn(t))
then Y(t) = y(x1(t), x2(t),...,xn(t)) can be written Y(t) = y(x1(t), D(t)),
with one scalar environmental influence and one scalar influence from
the perfactor output. In my earlier posting (separating the x's into
f-variables and d-variables, the same can be done with the f-variables,
writing F(t) = f(f1(t), ...., fn(t)). We then get Y(t) = y(F(t), D(t)),
which is the old original form p = o+d for the sensory input, with time made
explicit and a general function replacing the summation.
I think you are making a distinction without a difference, since d(x2,...xn)
can be any function at all that has a scalar value. There may be good
reasons for distinguishing between your and Hans's approaches to control,
but to argue that he ignores the multiple influences on the CEV is not
one of them. So far as the perfaction loop is concerned, they all boil
down to one scalar influence. Nothing whatever in the loop has any access
to how this scalar influence can be decomposed into different physical
influences. All that matters is the total number of degrees of freedom
concerned, and that depends on the time evolution of the scalar-valued
waveforms.
Martin