Arm model; falling moths; HCT language model

[From Bill Powers (920320.1100)]

Wayne Hershberger (920319) --

Here's the diagram I use for a pair of muscles (somewhat improved). I lay
them out in a straight line although they really lie along opposite sides
of a bone and work across opposite sides of a joint, like a pulley.

                            alpha signals
                         > >
                         > >
                    --------- ---------
Anchor--////////---| ---------Load-------- |---/////////--Anchor
                    --------- ---------
        Elastic Contractile Contractile Elastic

I consider the differential signal, a2 - a1, to be the composite driving
signal. When a2 increases and a1 decreases, the movable central parts of
the contractile elements both move to the right. The springs do not change
length. Thus the load moves to the right. There is no applied force after
the move.

With a2 > a1 the configuration looks like this:

MUSCLE MODEL a1 - delta a2 + delta
                         > >
                         > >
                    --------- ---------
Anchor--////////---| ---------Load-------- |---/////////--Anchor
                    --------- ---------
        Elastic Contractile Contractile Elastic

A force applied to the load (the "load point") to the right relaxes the
right spring and stretches the left one, creating a restoring force to the
left toward the undisturbed position of the load. This leftward force is
the muscle force opposing the force applied to the load. I assume that the
force does not alter the configuration of the contractile part; only the
signals determine how far in the plungers are.

The control systems using this pair of muscles are shown this way; the
spring is zero-centered:

                     Reference Gamma
                         > length gain Reference
                --<- comparator <----------Kg------- |
               > ^ <-----Kd---- length error |
          error> > damping | sensor |
           sig | | d(length)/dt| ---------- |
               > > > > > >
       output | force gain |<-|Mechanical|<-----
         gain Ko Kt |Comparator|
               > > Force sig | |
               > ------- ----------
               > > ^
               V Spring |tendon |
            ------ Ks |sensor |
    load ------ |--///////---O-----Anchor |
            ------ |
     ><------------------------------->| |
                    > >
                     ----------muscle length--->-----

The effective spring constant with high loop gain, is Ks/KoKt - Kg/Kt. It
can thus be zero, if Kg = Ks/Ko. The apparent mass is Kt*Mo, where Mo is
the actual mass (or moment of inertia). I misspoke myself when I said the
apparent mass was reduced. Typical values used in the model are

Kg = 50 NSU/radian
Kt = 50 NSU/newton
Ks = 50 newton/radian
Ko = 1 newton/NSU
Kd = 0 to 10 NSU per radian/sec

"NSU" means "nervous system unit." "Lengths" in the above diagram are
converted to radians of movement about the joint.

To answer your question, the values of the gamma inputs for each control
system are set to 0 units in azimuth, 0 in elevation, and 512 in elbow
flexion (the units are such that 4096 angle units = 360 degrees).

When gravity is turned on, with the alpha reference inputs set to zero (a
mode of the model available for testing), the arm slowly sags as if sinking
through heavy molasses. The actual positional loop gain is quite low. I
don't think that the stretch reflex loop is actually a position control
system; its evolutionary purpose seems to be to alter the apparent arm
dynamics, mass, and spring constants to make control by larger loops
(possibly involving the joint angle receptors) very stable and independent
of limb segment interactions. I don't really understand why it works as
well as it does. The bare mass-spring properties of muscle and arm are
drastically altered by the control system parameters when set for the best

It will be interesting to see what happens when I put in the sixth-power
muscle spring nonlinearity, the force-velocity dependence of the muscle,
and the changing mechanical advantages as the joint angle changes. Version
3. I should also put in the different response of the muscle to onset and
offset of signals, and the branches of the biceps and triceps that span
both shoulder and elbow joints. All this really requires modeling the
opposing muscles separately. Maybe Joe Lubin and his students, plus Greg
Williams, would like to carry this on to version 3. I want to take a
vacation from this arm model now and get some other things done (after
writing a paper with Greg for publication).


Avery Andrews (920319) --

So my judgement so far would be that if it what is going on is >avoidance

of being eaten via quick departure from the vicinity of the >bat and the
accompanying sonar signal, its control, otherwise it ain't.

My judgment would be just the opposite, because I don't think a moth can
perceive "being eaten" or "departing from the vicinity." The moth has to
get by on perceiving and controlling some fuzzy blobs of light, some
smells, and some sounds of variable intensity and possibly direction
relative to its body. It can't possibly make use of the information that
controlling these perceptions will help it survive, or even that it's being
threatened by a "bat" and all that this implies to a human being. It would
need a brain the size of yours to control for such things.

The moth doesn't behave as it does because that behavior is material to
survival. Cause and effect run the other way. The moth survives because it
controls for the variables it can perceive, with respect to the reference
levels it uses. Controlling a certain sound relative to a low or zero
reference level is apparently enough to permit its survival (usually, or
sometimes) when in the vicinity of bats; however, it has no idea what that
sound means, or that the consequence of this behavior is "survival." It's
just a bad sound, to be avoided. Neither does it have any idea that it's
falling through space when it closes its wings. That's a human perception.
It just makes its wings feel a certain way and that suffices to control the
level of the sound, to a sufficient degree. The moth can't know anything
about the details of why this works. Nor does it need to, to manage its
little world as well as a moth can. We could explain to the moth why
controlling for just those variables in just that way is a very good idea
for the moth, but the moth wouldn't understand.

I imagine that we would look much the same to a vast cool intelligence from
an advanced civilization elsewhere. We control what we perceive, and we
survive, but we don't really know why this works.
Bruce Nevin (920320) --

Language in general is a way of representing nonverbal perceptions for
our inspection and study, and possibly for our manipulation. I don't
care whether these sentences expressing background knowledge are
"basically" or "in origin" nonverbal or in language. By the >correlation

of nonverbal perceptions with word-perceptions, nonverbal >perceptions
become available for control as part of language, and >things in language
like assertions, injunctions, maxims, attributions, >prohibitions, and
instructions become available for setting nonverbal >reference perceptions.

Frame this and hang it on the wall. I think this statement consolidates a
large amount of progress toward a coherent HCT theory of language. If you
keep talking like this, you can expand as many reductions as you like and
I'll remain meekly silent. You're starting to define the problem. The
better you can define it at this level of discourse, the quicker all those
messy details will fall into place.

Here's a thought to chew on. Part of the problem most people have in
communicating and/or thinking is their very failure to see that the
meanings communicated by the words they produce and hear are incomplete and
ambiguous. If they tried to expand all communications, either your way or
my way, they would discover how bad is the information they're receiving
and emitting. "I'm glad you agree with me," they would say, "but what,
exactly, are you agreeing with?"
Best to all

Bill P.