[From Bill Powers (940503.0740 MDT)]
Avery Andrews (940503.1508)--
RE: Tai Chi
You make very slow and deliberate movements, with the long term
goal of getting good coordination of upper and lower body
movements. I think that this might be a matter of developing
good level 2 perceptions (sensations). The low speeds of
movement and often rather awkward-feeling positions provide
what ought to be ideal conditions for reorganization to produce
new postural sensations and control-systems for them.
I can see some suggestions of level 3 (configuration) and level 4
(transition) in your descriptions. I think of level 2 as consisting
of sensations like effort, the kind of sensation you get when you
pull or push on a heavy object, or when you "make a muscle" by
tensing opposing muscles. A configuration, on the other hand, would
be a set of limb and body poses controlled by varying muscle
efforts, with a fixed reference-configuration corresponding to a
particular static pose or arrangement of body parts. A fixed
reference level for transition, then, would be a fixed rate of
change of configuration, with the magnitude of the reference signal
corresponding to the speed of change.
This seems to be supported by your description:
Another principle is that you never go ballistic-any movement
should be able to be halted or reversed at any time (`walking
like a cat', as opposed to 'walking like a dog'). So control
of motions seems to be firmly based on a prior control of
postions,
Yes, positions as I think of level 3: fixed configurations. The
principles relating the hierarchical levels require that
1. For the higher perception to be controlled the lower must be
variable, and
2. Lower perceptions, if changed in the right combinations, can be
changed without changing the higher perception (this implies, of
course, that there are unused degrees of freedom at the lower
level).
If you hold an arm out in a particular configuration, such as with
the elbow bent, you can vary the effort sensations without changing
the configuration, by running the muscles in parallel up and down
their tension curves (raising and lowering the opposing tensions
simultaneously). But to alter the configuration, you must alter the
relative contraction of opposing muscles: that is, the muscle
sensations are a little different in the new pose from the
sensations in the old one.
If you change the reference signal for configuration, the actual
configuration will track the change. As you say, stopping the change
in reference signal stops the change in configuration; reversing the
change in reference signal reverses the change in configuration.
With configuration control, the configuration is set by the current
value of the reference signal, and remains constant as long as the
reference signal is constant.
For the slow movements of Tai Chi, I would guess that the rate of
change of configuration (transition) is being sensed and controlled.
A constant transition reference signal requires a constant rate of
change of configuration to exist, to produce a constant perception
of velocity. The velocity is set by the magnitude of the transition
reference signal. For slow movements, the reference signal is set to
a constant low value; for faster movements, to a higher constant
value. The output function of a transition system is probably a set
of integrators, so that a small error signal causes a small rate of
change of output, and so on. That changing output becomes the
changing configuration reference signal. Reducing the transition
reference signal to zero leaves the reference signal for
configurations constant (the output integrators hold their output
values when the error drops to zero).
It seems possible that the reason for the slow movements is to
extend the dynamic range of transition control as near to zero as
possible.
This has nothing to do with the rate feedback at the spinal level,
which is present mainly for damping and stabilization, and is not
separately sensed.
Since configurations involve joint angles, they are relative to the
body rather than a fixed external coordinate system. This means that
configurations relative to the environment can change without
changing transitions: the whole body can move while maintaining many
configurations unchanging. What can change while what else remains
constant depends on the available degrees of freedom.
From the little I have seen of Tai Chi, there are also at least
"event" perceptions under control. That is, there seem to be
stereotyped movements which involve smoothly varying velocities and
positions through a set pattern of changes.
And finally, the event reference signals might be the outputs of
relationship control systems. While the positions, transitions, and
events are controlled for each limb, the limbs appear to be
controlled in a way that establishes particular controlled
relationships among them. One arm slowly extends while the other
slowly retracts, for example, maintaining a particular relationship,
such as symmetry, between them.
You have a nice portable laboratory and instructors who are very
experienced with its use. How do your experiences with Tai Chi jibe
with my guesses about the levels of control?
···
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Best,
Bill P.