Too many df's

{Joel Judd 950113}

Avery says:

The actual problem is that these "excess" df's are actually resources
which you can apply in various ways in different situations and the
problem is figuring out how to use them effectively.

The same "problem" could describe points of articulation for speech as
any person with a speech impediment, speech therapist, or ventriloquist
could demonstrate.

Joel

···

TO: CSG-L INTERNET Any user on the Internet, not at DESE Proj. Box

FROM: JUDDJ DESEINST Joel Judd - DESE - Division of Instruction

DATE: January 13, 1995
SUBJECT: Too many df's

(Bruce Nevin Fri 930113 10:17:51 EST)

{Joel Judd 950113}

The actual problem is that these "excess" df's are actually resources
which you can apply in various ways in different situations and the
problem is figuring out how to use them effectively.

The same "problem" could describe points of articulation for speech as
any person with a speech impediment, speech therapist, or ventriloquist
could demonstrate.

Funny, how elusive the obvious can be. Thinking about this, it seems to
me that the controlled perceptions in speech are probably acoustic, and
that what we observe as "points of articulation for speech" probably
amount to little more than familiar means for controlling those
perceptions. The bit of rudimentary testing I was able to do a couple of
years ago seemed to support this.

I don't understand how habits and skills work. They appear to be
familiar pathways through the field of available degrees of freedom,
rather than control of the manner of controlling a higher-level
perception (this path through the field of dfs, rather than the other
possible paths). I don't know enough to think clearly about it--my
speculations are too wobbly for words. Probably something obvious.

      Bruce

[Martin Taylor 950113 16:15]

Avery Andrews, Joel Judd, Bruce Nevin

If you have a bunch of control loops that share common pathways (or even
if they don't--the trivial case), there is a maximum number of independently
controllable degrees of freedom. The classic "conflict" comes about because
there are two independent perceptual signals, but at one point in the two
loops, the pathways share one single degree of freedom, the common CEV.

You have been talking about a set of control systems in which the "bottleneck"
(the point of minimum number of degrees of freedom) is the set of perceptual
signals to be controlled. If the output degrees of freedom (say, muscles)
are fewer than the number of perceptual signals, then you can manage the
control only by time multiplexing--shifting the commitment of some part of
the bottleneck from one control loop to another at a rate fast enough
that control can be maintained over a set of sufficiently slowly changing
perceptions.

But then, the actual degrees of freedom involved DO include considerations
of the bandwidths of various parts of the channels, and what you are doing
is trading off available temporal degrees of freedom for the lacking
spatial degrees of freedom. Roughly speaking, the temporal degrees of
freedom for a signal can be considered as having a rate of 2/bandwidth;
that's the number of "statistically independent" samples in the signal.
So, if you have one output signal that can be varied with a bandwidth of
10 Hz, you can (in principle--it never works in practice) use it to control
two perceptions for which the disturbance varies with a bandwidth of 5Hz.
But you can't use it to control accurately two signals for which the
bandwidth of the disturbances total more than 10 Hz.

Bottom line--there's no problem with parts of the control loop where a bunch
of control systems share a larger number of degrees of freedom than the
number of degrees of freedom to be controlled, but there is a problem
when the output or the environmental feedback path (or the sensor systems)
have fewer degrees of freedom, totalled over time, than the number of
degrees of freedom for which control is attempted.

Martin

PS. If I don't answer some message, it may be because our mail system
garbled it. One of Bill Powers' messages was garbled, but I got the sense
of it (I think). My response was trashed before I could send it, so I'm
rewriting it off-line. There may well have been other messages with
missing parts, as I suspect happened to Bruce Nevin's message of yesterday
about tweaking speech synthesis.