[From Bill Powers (2001.11.01.2300 MST)]
Rick Marken (2001.11.01.0730)]
OK. I guess I'll wait for Bill to explain it.
The three main spinal reflexes are (1) the tendon reflex, (2) the phasic
stretch reflex, and (3) the static stretch reflex.
In reverse order:
The static stretch reflex is a control system that tries to make muscle
length match a length specified by a reference signal known as the Gamma
efferent signal. The phasic stretch reflex can be seen as another control
system that tries to keep the rate of change of muscle length at zero.
Alternatively, it can be seen as adding a first-derivative component to the
static muscle length error. The tendon reflex is a control system that
tries to keep sensed muscle force (detected as strain in a tendon) matching
a reference force.
The length control system's comparator is the muscle spindle; it
mechanically measures the difference between the contraction of small
muscles in the spindle (caused by the Gamma efferent signals) and the
contraction of the main muscle. The error signal goes into the spinal motor
neuron, contributing to the net muscle force reference signal. The phasic
or rate-of-change stretch signal also goes to the spinal motor neuron. Also
entering the spinal motor neuron is the Alpha efferent signal which allows
higher centers to contribute to the net force reference level. Finally,
also entering the spinal motor neuron (with a minus sign) is the signal
from Golgi tendon receptors, which is the perceptual signal representing
muscle force. So all three systems operate via the spinal motor neuron.
Naturally we're speaking of aggregate systems here, one muscle being
activated by large numbers of spinal motor neurons.
Because both the length-error and force signals enter the spinal motor
neuron, the effect is much as if all the comparisons took place in the
motor neuron -- you can switch connections around and get an exactly
equivalent (mathematically) Virtual Comparator. If the limb is fixed
spatially so it can't move, the length and force control systems combine to
act like a single force control system. If the limb is free to move, the
systems combine to produce a single position control system. Both reference
signals, Gamma and Alpha, contribute to the net effect in either case.
It gets even more interesting. The muscle, as has now been shown by many
workers, has an exponential force-length relationship. When you oppose two
such muscles, the effective spring constant can be varied by tensing them
to varying degrees in opposition to each other. This gives higher systems
the ability to alter the spring constant and the damping in the overall
limb position control system. And I think there is some evidence that the
Gamma efferent system is the output of autonomic or cerebellar systems,
with the Alpha efferents being mainly associated with voluntary movements.
All this is accomplished by a very simple-looking arrangement. The diagram
of the systems in an early chapter of BC:P (not handy right now) is still,
evidently, valid.
This same arrangement, very nearly, is seen in the cockroach's motor
control systems, showing that the basic control systems evolved far before
human beings did. The cockroach has not changed observably in the past 600
million years, as near as we can tell from the fossil record. Of course we
can't see how much its control systems might have improved over that length
of time.
I'm sure that Kenny sees a guiding hand in all of this. But that, Rick, is
a losing battle, because the only way to win it is to abdicate the basic
principles of science and claim that you know the absolute truth. Some
people may be willing to do that, but I'm not.
Best,
Bill P.
P.S. I _will_ download your book materials, after I get my new desktop
computer up and running -- the old one went bad again and it wasn't worth
the expense to have it repaired another time.
Meanwhile some 900 E-mails have accumulated unread. I have