# Social control; Mass-spring model

[From Bill Powers (930416.1330 MDT)]

Ken Hacker (930415) --

Not to break into your discussion with Mary, or answer for her,
but one of your remarks caught my attention:

... social interaction, by definition, involves involves a
working out of control similarities and differences, but also
the creation of co-dependent or co-operating set of references
that may or may not be those held by either of the individuals.

I'm curious about the nature of a "reference" (i.e., a goal,
intention, desire, etc) that may _or may not_ be held by either
of the individuals in a social interaction. How can a goal not
held by either party to an interaction have any effect?

ยทยทยท

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Avery Andrews (930416.1048) --

Sounds like a good starting outline. Point a) is particularly
important to develop. An organization made of multiple control
systems _is_ a coordinative structure, and in fact provides the
missing explanation as to what makes one work. Here are some
thoughts that might be incorporated in the paper.

All that "equations of constraint" can do is lay out the
conditions that must hold in order for a system to prove stable
against variations, or for a coordination to be established. They
do not spell out how those conditions can be met or maintained.
You can say that a variable will be controlled against
disturbances if for every disturbance there is an equal and
opposite effect on the variable from another source. That is an
equation of constraint defining control. But that equation gives
no hint as to how the opposing force can be made to appear in
just the amount and direction required.

difference between the mass-spring model and a control model is
nonexistent in terms of the equation of constraint -- the second-
order differential equation. But the differential equation does
not _explain_ how that particular relationship among mass, force,
acceleration, velocity, and position is brought about. For that,
some sort of model is needed.

The mass-spring model of limb position control is one
possibility. The claim is that an applied force causes a
deviation inversely proportional to the spring constant of the
muscle, the resistive force increasing with the deviation while
the driving signal activating the muscle remains constant. The
restoration of the arm to the original position after removal of
the disturbing force is brought about by entirely by the spring
tension independently of the signal that sets the resting
position of the limb. Therefore with a constant driving signal,
the muscle will automatically resist disturbances and restore its
proper position after a disturbance.

The control model offers a different explanation for the same
phenomenon. When a disturbance occurs, sensors report the
beginnings of a deviation, and feedback effects alter the driving
signal entering the muscle. This changes the resting length of
the muscle in the direction opposite to the applied force. The
difference between the new resting length and the actual position
generates a stretch in the elastic part of the muscle, creating a
force opposed to the disturbance but without any corresponding
change in position of the arm.

In either case, the restoring force is due to a difference
between the actual position of the arm and the resting position
set by the neural signal; the force is caused by the stretch of
the spring component of the muscle. In the passive case, however,
generating that force requires that the arm position change
enough to create the restoring force. In the control case, the
stretch of the spring component is generated by a change in the
driving signal, which alters the resting length of the muscle and
creates the required spring stretch without requiring that the
arm move at all (a control system with an integrating output can
restore the arm precisely to its original position even while the
force disturbance continues).

There is no dispute about the proper model of the muscle. A
muscle generates force by virtue of a difference between its
momentary resting length and its actual length. Neither is there
any dispute about what determines the resting length: it is set
by a neural signal that enters the muscle and determines the
average shortening of the contractile component.

The dispute between the control model and the mass-spring model
concerns whether the muscle force is produced primarily by a
change in the actual length, or (through feedback processes) by a
change in the resting length. This boils down to a testable
proposition: when a load is applied to an arm, does the neural
signal entering the muscles change, or does it remain constant?
Does the muscle contract, or does it simply stretch? If the
contraction changes to a marked degree, then the negative
feedback control model is correct. If it remains constant while
the muscle stretches, the mass-spring model is correct.

In fact there is no doubt that the feedback explanation is
correct. Several generations of studies of the reflex systems
show that a limb is far stiffer against disturbances with the
stretch feedback path intact than with it interrupted. For
example, see fig 6.5, p. 150, in McMahon, T. A., _Muscles,
reflexes, and locomotion_, Princeton, NJ, Princeton University
Press, 1984. In this diagram, the decrease in stiffness for
moderate forces, when the feedback is interrupted, is about a
factor of five. So about 80 per cent of the resistive force is
due to feedback, and only 20 per cent to muscle stretch.

The feedback stiffening of a limb against disturbance is greatly
increased when higher-level feedback paths are intact -- for
example, with the visual feedback link intact, the limb will not
deflect under a steady disturbance much more than can be detected
by eye, a matter of a fraction of a millimeter, even though the
applied force be several kilograms (the weight of a substantial
book placed in the hand). Under the assumptions of the mass-
spring model, the implied stiffness of the muscles would have to
be tens or hundreds of times the actual stiffness in order to
account for the ratio of deflection to force.

We can therefore claim that the mass-spring model, while
plausible on the surface, is refuted.
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Best,

Bill P.