Tao of PCT, Piaget

[From Rick Marken (931027.0830)]

Tom Bourbon (931026.1251) --

The names we have used to identify "kinds" of experience reveal the
workings of logical categorization, something removed from the direct
experiences. Those are forever unnamed. The Tao that can be named is not
Tao. The categories of "lower-level" perceptions that can be named are not
categorical lower-level perceptions.



Chuck Tucker sent me two books by Piaget, who was about as close as one
could get to PCT without being there. Piaget didn't make it, I think,
becuase he was basically a mathematician/logician rather than a modeller.
Here is a quote from Piaget's introduction to _Experiments in

"The two most general characteristics of a state of equilibrium (physical,
biological as well as cognitive) are stability and that which makes
stability possible, which is to say compensation of perturbations."

It's not hard to see the concept of control lurking in this description
of equilibrium. "Stability" seems to refer to the fact that when there
is control, a controlled variable is kept (stabilized) in a reference
state. This view is reinforced by the fact that stability is achieved
by "compensation of perturbations" which is easy to read as "actions
that compensate for disturbances to the controlled variable". Unfortunately,
Piaget never tries to build a model of an "equilibrating" (controlling)
system so he is never clear about the fact that 1) what is stabilized
is a perceptual variable 2) the value at which the variable is
stabilized is determined by the setting of another variable (the
reference signal) inside the system and 3) compensating actions act
on the controlled variable -- not on the disturbances themselves --
so that these actions do not necessarily reveal much about the nature
of any particular disturbance to the controlled variable.

Piaget's failure to understand the nature of equilibration (control)
did not prevent him from doing some ingenious tests that give hints
about the kinds of variables people can control at different developmental
stages. The first test described in _Experiments in contradiction_
is a real cutey. Kids are presented with a set of seven disks, A-G,
of imperceptibly increasing size: B>A, C>B, ete. The difference
between adjacent sizes is only about 2mm in diameter -- imperceptible.
But the difference between A and G IS perceptible. So there is a logical
contradiction if the kid agrees (from pairwise inspection) that A=B=C...
and also agrees that A<G. Young kids see no problem (logical
contradiction) while older kids do notice it but have trouble recesolving
the problem. The oldest kids get the "solution" (that there are actually
imperceptible increases in the size of disks A to G)-- or, at least,
these kids understand the solution when told.

Piaget seems to be very interested in kids' ability to "imagine" solutions
to problems. My impression (from a PCT perspective) is that Piaget is
learning that kids cannot produce certain types of imaginations at certain
ages becuase they have not developed the ability to have those types
of perceptions yet. I bet the young kids have a problem solving the
disk "contradiction" becuase they cannot IMAGINE an imperceptibly
increasing SEQUENCE of sizes going from A to G; these kids cannot
perceive and control sequences yet. The older kids can "solve" this
problem because they CAN imagine the sequence; these kids can perceive
and control sequences.

Piaget's technique has many components that resemble components of "the
test": 1) it is done one subject at a time (a big plus) 2) there is a
"disturbance" (demonstration that G>A in this case) which implies a
controlled variable (the hypothesized controlled variable is never
stated, however, making it hard to see the goal of Piaget's testing,
from a PCT perspective, anyway) 3) the subject is given a chance to
"compensate" for the disturbance -- usually only in imagination,

My quick take on Piaget: his theorizing is useless but his
clever tests and observations can provide a lot of hints about
the types of variables that people can control at different ages.
Piaget's tests are easy to replicate and can be recast relatively
easily in the form of tests for controlled variables.