Newsgroups: bit.listserv.csg-l
Date:         Tue, 25 Aug 1992 14:22:13 EDT
From:         mmt@BEN.DCIEM.DND.CA
Subject: Re: D of F; monkeys

[Martin Taylor 920825 14:00]
(Bill Powers 920825.0800)

We still have a conceptual problem about what is meant by "degrees of freedom."

>Suppose  the 10 variables (which we agree are controlled at the
>sensation level) are 10 notes on a piano, controlled by striking the
>keys with 10 fingers. There are certainly 10 degrees of freedom for
>controlling the loudness of these notes. Plotting a point in 10-
>dimensional loudness space specifies a loudness for all of the 10
>notes. So this should use up all the degrees of freedom available.

at any instant. Yes.

>Now we can add one more dimension: repetition rate of each note. And
>another: rate of increase of repetition rate. And another: rate of
>increase of loudness as the repetition proceeds. (This does not add 10
>more dimensions for each, as I said in my last post -- only one for
>each).

You can't have a perception of repetition rate without having at least one
repetition.  For that, you have to have a duration over which the tone is on
and a duration over which it is off, or an epoch at which a rapid rise gives
way to a fall.  You must be able to determine whether the the tone amplitude
at time t+delta(t) is different from that at time t.  If the range of possibly
discriminable amplitudes at the second sample is the same as at the first sample
regardless of what that value was at the first sample, then the second sample
provides another degree of freedom.  To get a repetition rate requires at least
three independent samples, and probably many more (it would be three only at
the fastest repetition rate that could be perceived as repetition rather than
as a low tone).  So to achieve the one degree-of-freedom description that is
repetition rate, one needs several degrees of freedom for the amplitude of the
tone, which is to say several independent samples of the tone.  The same set
of independent samples could be used to determine the rate of change of
repetition rate, except that you need a minumum of 5 or 6.  Each independent
sample provides another degree of freedom.

So, if there are 10 notes, each with a possibly independent repetition rate,
the number of degrees of freedom you need for amplitude evaluation is at a
minimum 30, and probably many more, although each repetition rate number takes
only one of those df, leaving quite a few for other parameters of the note
amplitude envelope.

One probably does not perceive describable structures (trying to choose a
neutral word) for most amplitude patterns.  That, in my view, is a consequence
of our inability to control as many df as we can sense, either instantaneously,
or even more so, over time.
============

>>" ... motor neurons in the monkey cortex encode not the force being
>>applied by the muscles, but the force needed to counter the (visual)
>>disturbance added to the location of a target on which a cursor was
>>maintained in the presence of a constant bias force that was already
>>being compensated. "
>
>Motor neurons don't encode forces needed to do something else. They
>just produce forces by using muscles. This quote is an example of the
>tunnel vision that pervades medical-style research: label everything
>by its effects, and attribute the cause arbitrarily in the middle of
>the loop. To explain to Georgeopolis why the above statement is
>nonsense would require re-educating him from High School onward. Of
>course he's looking at part of a control system. But how could we ever
>explain that?

Sorry, it was my wording, not a quote from the original article.  I am agnostic
as to what the cortical neurons signal. They described them as being thought
to encode force, and I guess I just took the words.

Why I introduced the article before and now again was because it seemed to
me very clear evidence of the existence of a distributed control system
demonstrated in actual neural output. The neurons respond with a signal
that has nothing to do with the forces applied, but that relates directly
to the error signal induced by the disturbance (the authors say that the
neurons encode something they call "dynamic force" as opposed to the static
bias force, but this sounds like a bit of waffle to me).  The data seemed
to me as direct a demonstration of the neural mechanism of control, as opposed
to the perceptual fact of control, as one could wish.  PCT studies normally
demonstrate control by looking at the CEV that is presumed to provide the
percept.  Here we have not only that, but an apparent window into the
control hierarchy itself.  I don't see why that should bother you.

Martin
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