WORDS & CONFUSION

[Tom_BOURBON3]

Tom Bourbon [931214.1217]

More on words, confusion and confused again.

[Martin Taylor 931210 12:10]
(Tom Bourbon 931209.1320)

I had posted in reply to Bob Clark.

Martin:

Thanks, Tom. Now I have a much better appreciation of what it is that
raises antennae when you hear the word "dynamics." I dissociate what I
have been talking about from the kind of thing you present. It's not
the same objective or even domain of thought, despite perhaps using
methods with the same mathematical background. As Bill P says, having
a common mathematical background doesn't give things equal validity.

I guess I have to be more careful about what I presuppose in respect of
how people will interpret stuff. You have explained some reactions I
have up to now considered quite bizarre.

After that exchange, Rick and Martin began an exchange under the heading,
"confused again," which seems to oscillate around the idea that calculus can
be applied to the description and analysis of control systems, which
comprise a subset of dynamic systems.

···

On my side, I am still trying to learn how Martin, and others, conceive of the relationships among PCT, information theory and the study of nonlinear dynamical systems. In a reply to Rick, Martin [Martin Taylor 931210 14:45] said:

"Before
joining CSG-L, I and some others here had been developing our own dynamical
approach to cognition, but it wasn't at all like what Tom quoted. We
were dealing with interacting physical systems, using as a text a set
of introductory books in what is called The Visual Mathematics Library.
They are called, misleadingly, "Dynamics: The Geometry of Behavior" by
Abraham and Shaw, Aerial Press 1984. I say misleadingly because the
behaviour in question has nothing to do with biological behaviour. It
is the behaviour of equations, and relates to all physical systems."

And he continued:

"The "dynamicists" I
referred to in my postings were people like Abraham and Shaw, probably
Prigogine and Nicolis, and people like that. Not people who look at the
various approaches to a human goal as defining an attractor dynamic (which
they do, in a loose sort of way) and treating that fact as an explanation
(which it isn't)."

I have not gotten hold of a copy of Abraham and Shaw, but I have seen, a
couple of years ago, Nicolis and Prigogine (_Exploring complexity_, 1989).
The dynamical psychologists I quoted also cite the people (A&S, N&P) cited
by Martin. The psychological dynamicists obviously see their work as an
extension or facet of mainstream dynamical analysis. I grow more confused!

In my search for more clues about possible connections among information
theory, dynamical analysis and PCT, I came across the following brief
article, from which I will quote a few passages. Martin, can you try to help
me see how the author's ideas might differ from yours, or resemble yours?

JAS Kelso (1992) "Theoretical concepts and strategies for understanding
perceptual-motor skill: From information capacity in closed systems to
self-organization in open, non-equilibrium systems," J. Exptl. Psy: General,
121, 260-261.

This was published as part of the APA centennial celebration last year. It
is Kelso's invited "brief impression" of a "classic" paper published nearly
40 years ago:

PM Fitts (1954) The information capacity of the human motor system in
controlling the amplitide of movement. Journal of Experimental Psychology,
47, 381-391.

Fitts's article is often cited as containing the first recognition of the
idea that movement time is "affected by" both the distance and the required
precision of the movement. The article is often said to be the first, or
one of the first, to bring information theory, a la Shannon, into psychology.
In the article, Fitts stated what has come to be known as Fitts's Law:

Movement Time = a + (b * [log base 2] of 2D/W),

where D = distance from starting position to center of target and W = width
of target.

In contrasting Fitts's article with recent work, Kelso writes about
recent conceptions of people as systems more complex than those studied
by Fitts. Recently, psychologists have "identified synergies and
coordinative structures" as solutions to the problem of coordination in
complex biological systems. To quote Kelso:

============================================
"This does not necessarily mean informational complexity as found in the
Shannonian view, which stems from the statistical mechanics of closed
systems. Rather, the existence of synergies in open, nonequilibrium systems
implies a smaller set of informationally simple but functionally meaningful
chunks. Their representational structure may be said to correspond to
attractive collective states of a dissipative dynamical system. Semantic
information appears to be created in dynamical systems by a cooperativity
among participating elements."
. . .

"How might Fitts (1954) see the field now, nearly 40 years after his seminal
paper? On the information-theoretic side he would see several important
developments. Among these are efforts to extend information theory into
nonequilibrium systems by Haken (1988) in Stuttgart (TB: see the note below)
and explicit attempts along similar lines to incorporate semantic
information into computational theory and computer design by Shimizu's
group in Tokyo."

============
Kelso's Note: "Haken (1988) developed the maximum entropy principle of
Jaynes. The latter has a nice ring to it for psychologists: 'If any
macrophenomenon is found to be reproducible, then it follows that all
microscopic details that were not under the experimenter's control must
be irrelevant for understanding and predicting it'" (Jaynes, 1985, p. 256).

H Haken (1988) _Information and self-organization_, Berlin:
Springer-Verlag.

ET Jaynes (1985) Macroscopic prediction. In H Haken (Ed) _Complex systems:
operational approaches in neurobiology, physics and computers_ (pp.
254-269). Berlin: Springer-Verlag.

Back to Kelso's text:

"Some years ago . . . I suggested that the reason for the *lawfulness*, or
regularity, evident in Fitts's Law was because the surface relation between
movement time and amplitude emerges from harmonic basis functions (e.g.,
mass-spring dynamics) tailored by boundary conditions (e.g., spatial
accuracy requirements). Guiard (in press) has recently produced quite
compelling evidence along this line. In particular, he observed deviations
from linearity (simple harmonic motion) in a cyclical aiming task as the
tolerance or accuracy requirements were systematically increased. The
relation identified by Fitts is lawlike, one assumes, because of the
ubiquity of periodic motion (regular and irregular) in nature and the
corresponding role of the (nonlinear) oscillator as an archetype of
time-varying behavior. It is important to note that whether such a
dynamical system exhibits postural states or discrete, rhythmical (or even
chaotic) behavior depends solely on its parameters. In this view, Fitts's
Law itself arises as a consequence of applying parameters to an underlying
dynamical law created by the nervous system for a specific goal-directed
action."

These brief quotes from a short commentary by Kelso provide some glimpses
of how closely the psychological dynamicists believe their work meshes
with that of information theorists and nonlinear systems dynamicists. For
example, twice Kelso cited the work of Hermann Haken. Haken has published
extensively on information theory and dynamical systems analysis, and on how
those areas are related. Kelso, Mandell and Schlesinger (1988) did a
Festschrift in his honor at the Center for Complex Systems, at Florida
Atlantic University. The papers are published as, _Dynamical patterns in
complex systems_, which is not readily available here.

All I have to show for my exploration is a clearer idea of the historical
links between information theory and nonlinear dynamical systems analysis,
and a greater sense of confusion over how either of those fields might apply
to PCT, other than at the level of abstract *descriptions* of the
superficial *appearances* produced by control systems as dynamic systems.
My faiure to see more to it than that does not mean there is nothing more,
only that I haven't been able to find it.

Martin, or anyone else, can you give me some help?

Until later,

Tom

[_Martin_Taylor]

[Martin Taylor 931214 16:00]
(Tom Bourbon 931214.1217)

On my side, I am still trying to learn how Martin, and others, conceive of
the relationships among PCT, information theory and the study of nonlinear
dynamical systems.

I hope my reply to Rick this afternoon has cleared up the PCT<->dynamics
link. I had not anticipated the information-theory tarbaby to creep so
close, since it had not seemed anywhere nearby in the preceding discussion.
But here it is again. Indeed, information theory is appropriately applied
in dynamical analysis, attractors being manifestations of the destruction
of information about prior states. Control systems are more appropriate
to locally divergent systems, in that they, too, reduce the information
available about prior states, whereas the divergences actually increase
it. But this kind of thing doesn't seem to have much to do with what
Kelse is talking about.

I'll look up the Kelso paper you reference. I, too, am confused by the
sections you quote, and I simply don't make sense of phrases such as:

"the existence of synergies in open, nonequilibrium systems
implies a smaller set of informationally simple but functionally meaningful
chunks."

Or much of the rest of what you quote. And I suspect I will have to find
the Haken references, too. My understanding of information theory is much
more down-to-earth, and it is based on what is in the Prologue paper
you picked up in Durango.

The second part of your Kelso quote, about the mass-spring dynamics,
seems irrelevant to information and control, as cited. And the section

"This does not necessarily mean informational complexity as found in the
Shannonian view, which stems from the statistical mechanics of closed
systems. Rather, the existence of synergies in open, nonequilibrium systems
implies a smaller set of informationally simple but functionally meaningful
chunks. Their representational structure may be said to correspond to
attractive collective states of a dissipative dynamical system. Semantic
information appears to be created in dynamical systems by a cooperativity
among participating elements."

is quite opposed to my view. I accept the Shannon approach, but based
on the subjective probability distribution (all that is available to
real physical systems). The Shannon approach does not mean physically
closed systems at all. The last quoted sentence implies that Kelso is
thinking of something entirely different, and it sounds a bit mystical
to me.

The psychological dynamicists obviously see their work as an
extension or facet of mainstream dynamical analysis. I grow more confused!

I have a suspicion that the confusion might be lessened if you think of
what they are doing as looking for what Dag calls a description, rather
than a model. But I'll look up Kelso. I'd hate to be put back into a
bag from which I thought I had escaped, at least not until I know where
the bag's opening is.

Martin

[Tom_BOURBON3]

From Tom Bourbon [931215.1047]

[Martin Taylor 931214 16:00]
(Tom Bourbon 931214.1217)

Me:

On my side, I am still trying to learn how Martin, and others, conceive of
the relationships among PCT, information theory and the study of nonlinear
dynamical systems.

Martin:

I hope my reply to Rick this afternoon has cleared up the PCT<->dynamics
link.

It helped me form a better idea of what you think about the link, but left
me with some lingering uncertainties.

I had not anticipated the information-theory tarbaby to creep so
close, since it had not seemed anywhere nearby in the preceding discussion.
But here it is again.

I'm sorry you think of this as a tarbaby. If "it" (the question of whether
information theory implies PCT and, if so, in which ways) is a tarbaby to
you, remember that in the Uncle Remus stories the tarbaby most often ended
up sticking to its maker, rather than the intended victim. I am merely
trying to understand the possible relationships among information theory
(IT), dynamical analyses (DA), and PCT. It is clear that some people,
including a few on this net, think there are important relationships. I
recall that you introduced the IT-PCT linkage to the net "long ago," if
I can use that phrase in reference to csg-l. To me, the short piece by
Kelso seemed to provide clues about how someone else thinks about the IT-DA
connection and I was curious about your thoughts on the article.

I appreciate your thoughtful reply to my questions, and I was pleased to
learn that you see some of the same problems as I, in the Kelso article.
Still, in some places where you see clear differences between Kelso's ideas
and yours, I cannot find the distinction. After reading your post, I now
suspect that one of the biggest impediments to my seeing the same
distinctions as you arises from the similarity of your writing style to the
ones often used by IT-DA psychologists. I will use the following brief
example, quoted from your post, to illustrate my point:

Martin:

Indeed, information theory is appropriately applied
in dynamical analysis, attractors being manifestations of the destruction
of information about prior states.

My first reaction is that this sentence looks very much like what I see in
the IT-DA literature. At the most obvious level, you are saying that indeed
the two "approaches" do apply to the same systems. My problem is at another
level. I see you attaching concrete meanings and roles to what I believe
are metaphorical terms, just the sort of thing I see in IT-DA psychology.
You seem to be saying:

There are Prior States (PSs). There is Information "about" PSs (IPSs).
Something (X) "destroys" IPSs. (Destruction, the noun, refers to the
transitive verb, destroy, which implies that an agent acts to destroy an
object of the action.) When X destroys IPSs, there are "manifestations" of
the destruction. The manifestations are "attractors."

Martin, I am not reying to be difficult or cute. I *do* admit to being a
very simple-minded person when it comes to material like this. I know your
sentence was "short hand" for many other ideas; however, when I encounter a
sentence like the one I quoted, I *must* try to identify objects and
predicates -- the agents, actions and objects of actions. In the present
case I am left wondering what does the destroying; what is destroyed; if
IPSs is destroyed do the PSs themselves survive, or are they also destroyed;
is the act or process of destruction "manifest," or is it the *result* of
the destruction that is manifest; exactly what is "a manifestation," why
should it should be renamed "an attractor," and what is gained in the
renaming; is that all that most people have in mind when they speak about
attractors.

Somewhere in there is something that seems to be of great significance to
you. I am trying to understand exactly what it might be. The fact that
I am thoroughly lost, right at the start, makes it impossible for me to
appreciate the distinctions you try to draw elsewhere in your post.

Me:

The psychological dynamicists obviously see their work as an
extension or facet of mainstream dynamical analysis. I grow more confused!

Martin:

I have a suspicion that the confusion might be lessened if you think of
what they are doing as looking for what Dag calls a description, rather
than a model. But I'll look up Kelso. I'd hate to be put back into a
bag from which I thought I had escaped, at least not until I know where
the bag's opening is.

It is one thing for me to think in those terms about what they do, but that
would not be a proper construal in the numerous instances where they write
about these ideas as models and mechanisms.

I'm not trying to put you into, or back into, a bag, Martin. PCT has run
hard up against information theory and dynamical systems analysis, many
times. Your posts have helped me realize there are some major differences
of opinion among those who write favorably about IT, and DA, and IT-DA
linkages. But that realization does not answer all of my questions about
whether or to what degree IT and DA are important in PCT. I seem to be
stuck on the metaphorical appearances of it all.

Thanks, for your willingness (albeit sometimes grudging willingness) to pick
up the tarbaby. If we reach a resting place in this discussion, I'll share
some of the very effective lemon-based solvent we often use to remove the
inevitable tar left on our feet after a walk on the Texas beach.

Until later,

Tom

[_Martin_Taylor]

[Martin Taylor 931215 19:30]
(Tom Bourbon 931215.1047)

I'm not trying to put you into, or back into, a bag, Martin. PCT has run
hard up against information theory and dynamical systems analysis, many
times. Your posts have helped me realize there are some major differences
of opinion among those who write favorably about IT, and DA, and IT-DA
linkages. But that realization does not answer all of my questions about
whether or to what degree IT and DA are important in PCT. I seem to be
stuck on the metaphorical appearances of it all.

Thanks, for your willingness (albeit sometimes grudging willingness) to pick
up the tarbaby. If we reach a resting place in this discussion, I'll share
some of the very effective lemon-based solvent we often use to remove the
inevitable tar left on our feet after a walk on the Texas beach.

I have written to Tom privately on this posting, offering (somewhat
reluctantly) a private dialogue on the issue. I am not prepared to
go into a public discussion on information theory and PCT, given the
quality and tenor of the last go-round on the issue, and the evidence
provided by the current "physics" discussion that a new attempt would
have no different result. I have neither sufficient frustration tolerance
nor a sufficiently low workload (at my "day job"). Maybe later, maybe not.

Martin

[Tom_BOURBON3]

From Tom Bourbon [931216.1544]

[Martin Taylor 931215 19:30]
(Tom Bourbon 931215.1047)

Tom, then:

I'm not trying to put you into, or back into, a bag, Martin. PCT has run
hard up against information theory and dynamical systems analysis, many
times. Your posts have helped me realize there are some major differences
of opinion among those who write favorably about IT, and DA, and IT-DA
linkages. But that realization does not answer all of my questions about
whether or to what degree IT and DA are important in PCT. I seem to be
stuck on the metaphorical appearances of it all.

Thanks, for your willingness (albeit sometimes grudging willingness) to pick
up the tarbaby. If we reach a resting place in this discussion, I'll share
some of the very effective lemon-based solvent we often use to remove the
inevitable tar left on our feet after a walk on the Texas beach.

Martin:

I have written to Tom privately on this posting, offering (somewhat
reluctantly) a private dialogue on the issue. I am not prepared to
go into a public discussion on information theory and PCT, given the
quality and tenor of the last go-round on the issue, and the evidence
provided by the current "physics" discussion that a new attempt would
have no different result. I have neither sufficient frustration tolerance
nor a sufficiently low workload (at my "day job"). Maybe later, maybe not.

There is no need for a private dialogue, Martin, but thank you for the
reluctant offer. It is not my intention to encroach on your limited time.
The paragraphs from me, that you quoted above, were part of a post in which
I described my attempts to understand the distinctions you draw between your
ideas and those of people like Kelso and Turvey. My recent efforts along
that line were prompted by the recent round of discussion here on csg-l,
in which dynamical systems analysis (DSA) emerged once again, along with a
mix of implications and assertions that DSA could do much to inform PCT.
(I do not attribute all of those implications and assertions to you.)

The discussion seemed to be falling back into some of the familiar ruts. In
an attempt to add a different perspective, I quoted material by Kelso
and Turvey and some of their associates, in which they speak of human
performance and analyze it, or talk about it, "in the language of DSA."
(They often use the phrase I show here in quotes.) One article in
particular described Kelso's ideas about how information theory (IT) and
DSA pertain to human performance (see Tom Bourbon [931214.1217]). Like
Kelso, although perhaps for different reasons, you sometimes express a
belief that IT and DSA do, or should, play important roles in PCT. One of
your self-assigned projects of long-standing is to determine if you can
prepare either a demonstration or a proof that PCT *necessarily* follows
from IT.

In your reply [Martin Taylor 931214 16:00] to the post in which I quoted
Kelso on IT-DSA, you declared that his ideas and yours were quite different.
In my reply to you (Tom Bourbon [931215.1047]), I cited a brief example of
why I was unable to see all of the distinctions you were trying to draw.
In particular, I could not follow this comment of yours about IT and DSA:

Martin:

Indeed, information theory is appropriately applied
in dynamical analysis, attractors being manifestations of the destruction
of information about prior states.

My non-understanding extended to the subsequent sentence (quoted below),
which I did not include in my reply. In this sentence, I believe you were
indicating that, like attractors, control systems also destroy, or at least
reduce, information about prior states. You said:

Control systems are more appropriate
to locally divergent systems, in that they, too, reduce the information
available about prior states, whereas the divergences actually increase
it.

Once more, I confess my inability to follow your reasoning, which is in part
due to my problem with disentangling the several agents, actions and objects
of actions, that are declared or implied in your passage. I am disappointed
that you have elected to withdraw from the discussion of these topics on the
net. Surely I am not the only subscriber who would like to understand your
thoughts on the links you see among and between IT, DSA and PCT. I am
especially disappointed that you are ending the public discussion with the
thought that to pursue it would be futile, given:

the
quality and tenor of the last go-round on the issue, and the evidence
provided by the current "physics" discussion that a new attempt would
have no different result.

Concerning the discussion of "physics," you have concluded [Martin Taylor
931215 17:20] that:

I don't have the
tolerance Mary ascribes (with good reason) to Bill, giving kindergarten
lessons day after day. After this, forget it. As you and I have all
said, it really doesn't matter for the dynamical analysis of control
systems whether you understand the thermodynamic ramifications.

When your tolerance is renewed, or when you complete your proof that PCT
necessarily follows from IT, I am certain you will find some of us
kindergarteners still willing to listen.

Until later,

Tom