Posted by
lrudolph on
URL: http://friam.383.s1.nabble.com/Assistance-sought-The-meaning-of-constraints-tp6165767p6166137.html
Dear Nick,
I am also reviewing a book--actually, two booklets
and a book chapter--in the sense that I am working
mightily to incorporate into a book I am editing
and partly writing (on mathematical models for use
in psychology) a discussion of their virtues
and vices. In my case, the matter being reviewed is
not by a psychologist but by a historian, Henry Adams.
Adams spent much of his life trying (and conspicuously
failing) to do what *I* would call making a mathematical
model of history, though he only occasionally spoke of
mathematics and mathematicians and much more often
of physics and physicists (19th century in all cases).
Sometimes (as in the booklets "A Letter to American
Teachers of History" and "The Rule of Phase as Applied
to History") he tried to adapt thermodynamics to his
purposes; at other times (as in _The Education of
Henry Adams_, particularly the chapter "The Dynamo
and the Virgin") he talked in terms of "dynamics"
more generally.
His failure to get anywhere at all (as I see it)
started with his (predictable?) failure to make any
sense *at all* of "forces" in his context.
I would (not only, but largely, therefore) caution
you, Nick, against importing any notion of "force"
into your explication of your psychologist's "distinction
between constraints and causes"; "forces" are not needed
to explicate "constraints" (or "causes") as far as I'm
concerned, and they carry an awful lot of misleading
and potentially destructive "excess meaning" (to use
your term).
So, then, what are constraints in my lexicon (that of
a mathematical modeler who is enlightened to the extent
that physics is *not* taken as the unique, or prefered,
domain for models and model-prototypes)? _The constraints
on a particular system are whatever specifies it among
all systems of the same general type._ Of course, all
the nouns and adjectives in that last sentence are open
to contentious negotiation: what's a "system"? what's
the "type" of a system, what do "particular" and
"general" and "same" mean? what (even) does "all"
mean? I hope we don't have to go all the way there.
Here is an example (drawn from theoretical robotics, not
from psychology or history). A "robot hand" can be
mathematically modeled (to a first, but useful,
approximation) as a system of line segments (the
bones of the fingers and thumbs) located in ordinary
3D space. To model a hand at all, those line segments
need to meet up in certain ways (e.g., the segments
that represent the bones of a single phalange have to
form a "chain" in which successive segments have one
endpoint--a joint--in common). To model a humanoid hand,
the line segments have to be appropriately limited in
number (e.g., if "-oid" is taken fairly strictly, not
too many to a chain, and not too many chains altogether),
and their "degrees of freedom" have to be specified
as well (e.g., the inter-segment joints are R joints,
with one degree of angular freedom; maybe there's a
"thumb" with an S joint, having two degrees of angular
freedom, at one of its two loose ends; the lengths of
the line segments should be specified, at least by
giving a range of possible lengths).
Everything in the last paragraph after "3D space"
could be read as giving (some of) those "constraints"
on a (general) "linkage system" that make it a
"robot hand linkage system", if one's focus of interest
were so wide that it included both general linkage
systems and robot hand linkage systems. On the other
hand, if one's focus narrows only to "robot hand
linkage systems", then you might not want to call
*those* descriptors "constraints"; rather, within
the universe-of-discourse that covers only "robot
hand linkage systems", the constraints would be
(in part) *specific* lengths for joints, *specific*
range restrictions on the angular degrees of freedom,
and (if you want to make life hard for yourself)
further specifications, for instance, the requirement
that segments cannot pass through each other during
any motion of the system.
There are no forces in sight. One way to "explain"
their absence is to say that what has been described,
so far,is a "kinematics" model of the robot hand; and
that, if you want to actually be an engineer and make
(or plan to make) a physical robot hand, you will have
to put in some physics--meaning (here) forces (as well
as materials specifications [which could, reductively,
be phrased exclusively in terms of forces: but with
a huge expansion in verbiage and diminution in human
understandability])--and then do "dynamics". Some of
the dynamics you do will explain, retrospectively,
why you can successfully ignore the "forces" in the
kinematics model: they are "doing no work".
In the psychological case, where you-all already are
(if I've been following) in a quandary as to what,
if anything, plays the role in a satisfactory
description of "causes" of feelings that is
analogous to "force" in a satisfactory description
of "causes" of motions of billiard balls (etc.),
I think that to push the analogy with physics (which
is set up by using the word "force") so far as to assume
that everything in sight can be reduced to "forces"
(some of which then turn out, after sufficient clever
analysis, to be "doing no work") is unjustified, probably
unjustifiable, and in any case only to be done as a last
resort.
I guess the short version of my screed is, "What's a
'constraint' depends on what you're trying to talk
usefully about." This may have something to do with
"context"; I know nothing about Juarrero and whether
what she means by "context" has anything to do with
what I might mean by it, here.
Lee
> Dear anybody,
>
>
>
> I am reviewing a book by a psychologist in which the author makes a
> distinction between constraints and causes. Now perhaps I am over thinking
> this, but this distinction seems to parallel one made by Feynman in his
> famous physics text, where he defines a constraint as a force that does no
> work. If I have it right, the idea goes like this: If you place a bowling
> ball on a table the ball neither receives work from gravity nor does the
> table do any work holding the ball up because the ball does not move, and
> work is just the movement of mass. Indeed, even if you were to slide the
> table out and, with great effort, were to hold the ball in the same position
> for an hour, you wouldn't be doing any work, either. Similarly, in a ball
> rolling down an inclined plane, the plane itself does no work because even
> tho it affects the motion of the ball, its effect is always perpendicular to
> the motion of the ball and there fore affects its motion neither one way or
> the either .. i.e., does no work!
>
>
>
> Now I would leave it at that except that Alicia Juarrero in her book also
> makes a huge distinction between forces and constraints, one which I think
> our own Steve Guerin applauds. It is the constraints that make it possible
> for far-from-equilibrium systems to self organize and do work. Perhaps I
> can make this work with Feynman's definition if I think about the dam beside
> a water wheel, and the water wheel itself, as applying constraints to the
> water (they do no work themselves) which make it possible for the falling
> water to do work. Am I still on track, here?
>
>
>
> Now Juarrero goes on to make a distinction between between context sensitive
> and context-free. I have read these passages dozens of times and I just
> don't understand this distinction. Can anybody out there explain it to me
> as to a Very Small Child.
>
>
>
> Thanks,
>
>
>
> Nick
>
>
>
>
>
>
>
> Nicholas S. Thompson
>
> Emeritus Professor of Psychology and Biology
>
> Clark University
>
>
http://home.earthlink.net/~nickthompson/naturaldesigns/>
>
http://www.cusf.org <
http://www.cusf.org/>
>
>
>
>
>
>
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