Powers (1988), Powers (1979), Sequence level

[CCHERPAS]

[From Chris Cherpas (971010.1654 PT)]

Bill Powers (971008.0725 MDT)--

By all means play with the equations, and use actual numbers. I guarantee
that you's come out of it with a vastly increased understanding.

Thanks for the exercises concerning amplification and slowing.
They helped, especially in seeing monotonic vs oscillating patterns.
Of course, a vast increase in understanding does not necessarily mean
the absolute level of understand is that great!

I got another perspective, indirectly, after just reading Powers (1979)
"A Cybernetic Model for Research in Human Development," also in
_Living Control Systems_.

Bill Powers (1979, pp183-184)--

"There are many ad hoc solutions to this problem, involving variable
control of speed and nonlinearities with just the right properties,
but they are all complex in comparison to the one I propose. I assume
that in most human control behaviors, error sensitivity is very high,
so high that under normal conditions there is essentially 0 error
at all times. To take care of the deleterious effects of too much
error, I simply assume that reference signals normally vary
continuously, not in an on-off manner."

This article, especially at the end, when a particular order is
considered for developing a new control system, is really getting
me thinking about a PCT approach to structure certain computer-based
tutorial sequences...

Bill Powers (1979, pp183-184)--

(1) perception: the variable to be controlled must exist as a neural
   analogue;
(2) recording: the possible states of that variable must be experienced
   and remembered;
(3) selection: one previous state of the variable must be selected as
   a reference signal;
(4) comparison: the error between the actual and intended states of the
   variable must be judged;
(5) action: the error must be converted into those changes of existing
   lower-level reference signals that will correct the error;
(6) practice: this entire series must be iterated over and over to
   refine each element of the control system so that it functions
   under all conditions without instability.

We currently do a lot of (6), without being all that specific about
what goes into (1)-(5). Sometimes a developmental sequence builds
up to the point where you pretty much have to face a kind of crisis
that only acquiring a higher order control system can resolve (something
Hugh Petrie wrote about), but that isn't the "normal" mode of
education, pretty much by definition. Also, to modularize the
material, it's handy to have different "modes" (testing, tutorial,
practice, review, etc.). Obviously, the test for a controlled variable
is a useful procedure for thinking about the way a "testing mode" works.

Bill Powers (971008.0725 MDT)--

A reference signal can skip levels only if there is no control system
active at an intermediate level. The reason is obvious: if the reference
signal results in a perceptual signal changing at a lower level, the
intermediate level system will see an unwanted change in its own
perception, and will change its output to the lower level to correct the
change. In doing so it will cancel or partly cancel the effect of the
higher level's output, leading to conflict.

Nice. You sure talk good for an engineer. Regarding the
educational enterprise again, there's been a lot of work specifying
standards ("educational objectives") for grades K-12 by
state/fed governments over the last decade and it seems to keep
increasing. A big problem is that it's really hard to see how
these statements are supposed to be translated into curricula.
The connections are loose, or exemplar-based at best. By analyzing
a pretty big sample of these, I've found some of the "best" exhibit a
kind of how/why structure, even if the specification of the "target"
controlled quantity is vague. Specifying something about adjacent
levels helps. Your resolving my confusion about reference signals
skipping levels adds another constraint to this jello-like world.

Meanwhile, another problem has reared its ugly head as I study the ways
of the PCT: Powers (1979) had only 10 levels which reminded me that I
have trouble seeing the sequence level as it is in the 11-level structure.
Mostly, sequences seem really specific to me. "What are they doing way up
there above categories?" When a sequence is under good control,
it seems unitary _like_ an event that has events in it.

If I do recognize a general series ("ah, it's one of _those_ kinds of
sequences"), then I think this could be a variant of categories.
If I lose control of a specific sequence ("now what comes after abcdefg...?"),
I seem to "start" down at the relation level (nextness, the precedence
relation) to fix it. As that fails, I might start reasoning at the program
level, maybe "using" categories such as beginning, middle, end, etc.,
but trying running starts and testing specific possibilities which seem to be
perceived at the same "kind of level" (whatever that could mean)
as events. I can reconstruct a lost sequence, so to speak, but it doesn't sound
right until it has a wonderful lower-than-relation feel to it. So,
even after locating the missing part, I run through faster and faster
until it's all down there where it belongs.

Maybe the words "event" and "sequence" need to be combined to name that
level better -- sevent? evquence? While at the category level, there
are those more general series -- Cateries? Sategories?

Maybe there's an analogy to configurations here. A configuration has
a certain unity to it, like an event, but it can sub-configurations, and
same so for sub-events. Finally, a configuration is not just the
right _collection_ of edges/etc. (e.g., it's not OK to have the mouth
on the forehead to be your friend's face); and a sequency event, isn't
just the right collection of transitions/etc. -- order matters. And
when order matters, don't you perceive sequence?

Best regards,
cc

[Bill_Powers1]

[From Bill Powers (971014/0400 MDT)]

Chris Cherpas (971010.1654 PT)--

Meanwhile, another problem has reared its ugly head as I study the ways
of the PCT: Powers (1979) had only 10 levels which reminded me that I
have trouble seeing the sequence level as it is in the 11-level structure.
Mostly, sequences seem really specific to me. "What are they doing way up
there above categories?" When a sequence is under good control,
it seems unitary _like_ an event that has events in it.

...

Maybe the words "event" and "sequence" need to be combined to name that
level better -- sevent? evquence? While at the category level, there
are those more general series -- Cateries? Sategories?

This takes us back to the time when the event level included what I now
call sequence. The problem here is that there are "canonical" perceptions I
think of as typifying a level, but when we try to assign words to the level
other associations spring up and it all gets confusing again.

What I think of as an event is something that seems to happen all at the
same time, even though close inspection shows that it really consists of a
lot of details happening in a temporal pattern and in parallel. A spoken
one-syllable word is an example: "plank." Obviously it's not possible to
say "plank" at a single instant, yet we hear (and feel) it as if it's a
point-event. The same is true of a visual event like the bounce of a
golf-ball on a concrete sidewalk. When, exactly, does the bounce occur? You
can't say it's the instant of contact, because if you remove everything
before and after that instant there's no bounce any more -- just a snapshot
of a ball slightly flattened on the underside. The bounce really includes
the approach and the rebound as well as the contact.

On the other hand, a sequence involves the ability to distinguish the
elements, as in punching in a phone number: 2-7-2-2-7-3-1. These numbers do
_not_ seem to occur all at the same time: if they did, we wouldn't be able
to distinguish the sequence. When we say "the ball bounces" we hear three
events in a particular order: the, ball, bounces. If we heard the same
events in a different order -- bounces, the, ball -- we would recognize (a)
the same word-events, and (b) the difference in their temporal ordering. If
we detect an error in ordering of the events, we can alter which event
comes first, second, and third until the sequence is perceived as correct.
In doing so we don't change the events; all we change is their order. This
suggests to me that the perception of events is different from the
perception of ordering or sequence. And since we can't change the
event-ness by altering the sequence, it would seem that sequence is a
higher level of perception than event.

Another thing to notice about the elements of a sequence is that they're
discrete occurrances or entities. Suppose you have two relationships: ball
next to cup, ball in cup. At the relationship level there are continuously
variable spatial relationships; the ball can be any distance to one side of
the cup; it can be above the cup and partly in it, more completely in it,
or all the way in it. It can be on the way into the cup or on the way out
of it. It can bounce into the cup and out again. At this level there are no
discrete boundaries between one state of a relationship and another state.
But when we _describe_ a sequence of relationships we speak in categories:
first the ball is _next to_ the cup, then it is _in_ the cup (or the other
way around). Before we can talk about a sequence, we have to reduce all the
variations of beside-ness or in-nesss to something we can symbolize with a
single label. The sequence is then constructed from those labels, not from
the continuouly-variable relationships. When we say the ball is next to the
cup, the term "next to" actually refers to a continuum of relationships,
but the continuum disappears as soon as we go from the world of analog
perceptions to the world of discrete symbols. Then we can see the sequence
as ball next to cup, ball in cup ("put the ball in the cup" is possible
only if the ball is not already in the cup).

Maybe there's an analogy to configurations here. A configuration has
a certain unity to it, like an event, but it can [contain?]

sub->configurations, and

same so for sub-events. Finally, a configuration is not just the
right _collection_ of edges/etc. (e.g., it's not OK to have the mouth
on the forehead to be your friend's face); and a sequency event, isn't
just the right collection of transitions/etc. -- order matters. And
when order matters, don't you perceive sequence?

I suspect that these sub-configurations and sub-events are a product of
higher-level interpretations. If you ever perceive more than one
configuration at a time (chair _and_ legs), I suspect that you're
perceiving them in parallel, using different configuration-perceivers, just
as you would be doing if you perceived chair _and_ cushion or chair _and_
cat (sitting in the chair). The basic perceptual model in PCT is a
"massively parallel" model, in which each distinguishable kind of
perception is generated by a physically distinct perceptual input function.
In contrast, the other kind of perceptual model says that there is a
_single_ perceptual input function that produces different outputs
indicating which entity is present at the input (the perceptron is
organized that way). In the latter kind of model, the output signal has to
be coded so you can tell which kind of input it's supposed to represent, or
you have to have some sort of priority scheme so that the output that is
finally produced (if there are many potential output paths) suppresses all
the others, leading to a single unambiguous output that serves to identify
"the" input.

Real perception seems to have some features of both kinds of model. There
are classical examples, such as "THE CAT" in which the H in both words is
actually the same configuration, an H with the sides slanted in at the top,
or an A with the top somewhat open. On the other hand, there are
counterexamples such as the way we can pick out a single A in a field of
repeated H's, so rapidly that it's impossible to think of applying a single
"recognizer" to each configuration in turn, getting either an "A" signal or
an "H" signal from it.

I think that a parallel model can resolve some of these conflicting pieces
of evidence. The open-A or slanted-H configuration, in the PCT model, would
produce signals from _both_ input functions, the one that detects CAT and
the other that detects THE. There would be no perceptual input function
organized to perceive TAE or CHT, so the only two signals actually
appearing would be those standing for "THE" and "CAT." When we see
something like CxT, where the x stands for a blot, we can perceive CAT,
CUT, or COT, and at a low level (where logic does not insist that there can
be only one word at a time) we might perceive, to some degree, all three.
It's only at the higher levels that we would say "Lie down on the CxT"
requires us to select the meaning that goes with COT rather than the other
two. Even then, with a little imagination, we can supply a higher-level
scenario to justify either of the other two choices.

The hardest part of understanding lower levels of perception is keeping the
higher levels out of the picture -- particularly categories. When you see
an apple, it's damned hard not to think "apple." When you look at your
hand, it's very natural to think "hand" and "fingers" and "fingernails" and
(in my case) "spots." We're compulsive about naming and categorizing
things. Instead of seeing the particular example of an apple that is before
our eyes, we think of the category it exemplifies, "apples," and fail to
see the actual example with all its individual and unique characteristics.
This blinds our consciousness to the differences; it is just as much an
example of prejudice as would be seeing a person with a brown skin and
thickish lips and thinking only "nigger."

Best,

Bill P.