Degrees of Freedom

[from Gary Cziko 920318]

Martin Taylor 920318 16:30 says:

To change the subject: is no-one interested in my argument that the degrees
of freedom problem leads to modular reorganization

I just got a phone call from Bill Cunningham in Fort Monroe, VA, who said
he is very much interested in this topic but due to computer reorganization
is unable to respond to CSGnet, although he does receive mail.

He wanted me to let people know it may be a few weeks before he can
communicate with CSGnet and hopes that this topic stays alive.--Gary


Gary A. Cziko Telephone: (217) 333-4382
Educational Psychology FAX: (217) 244-40538
University of Illinois Internet:
1310 S. Sixth Street Radio: N9MJZ
210 Education Building
Champaign, Illinois 61820-6990

[Martin Taylor 940609 19:00]

Bill Powers (940609.0910 MDT)

I know you won't see this until the end of June, but I post it now in case
I forget later:

I believe that your estimates of "potentially controllable degrees
of freedom at the sensory input" are too high by a factor of 10^4 or
10^5, and your estimates of degrees of freedom at the output are too
low by a factor of 10.

There are two assertions here, and I must ask on what basis you make each.

The second one first: are you saying that we have nearer 1000 independently
movable joints, or that the average speed at which we can move a joint is
nearer 10 Hz than 1 Hz? Personally, I seem to be able to oscillate a finger
at something like 4Hz, but my leg at something more like 1 Hz. I cannot
independently bend the top joint of any finger, though I counted it as
an independent joint in my count of Order 10^2 joints (within a factor of
2 or 3, I said, but I actually counted about 125, being very generous), and
I find it very difficult to desynchronize fast bends of hip and knee (fast
being about 1 Hz).

Could you, on your return, explain where your figure of 1000 output
degrees of freedom per second comes from?

Your first assertion is simply that the redundancies in the world and in
our perceptual apparatus require that we use only 1 part in 10^10 of the
information provided by our sensory apparatus. We know for sure that our
eyes transmit to the optic nerve only 1 part in 10^2 of the light pattern
impinging on the retina, and I accounted for that. We do not know from
studies in machine vision how to reduce the information content of static
scenes by as much as a factor of 10^3, but I assumed that evolution had
allowed us to take better advantage of the statistics of sensation than
we yet know how to do with our computers. I allowed a factor of 10^5 or
10^6, taking into account what you claim I did not understand, your

argument that many control systems for which the controlled variable
seldom departs from its reference level (such as as "no touch on the
neck") can be left fully operational and connected to the motor
outputs without any effect on the "output bottleneck."

All of that was included in my very extreme guess as to how much statistical
data reduction could be done in reducing the number of controllable
degrees of freedom. Yet you say that you think the potentially
controllable degrees of freedom are still OVERestimated by a factor of
10^4 or 10^5. The mind boggles! I could have accepted a criticism
that I had underestimated by a factor of 10 or 100, because I think
I strained credibility in how much statistical reduction is possible
from the coherence and stability of the environment. I think the ball
is in your court to show where a further reduction of four or five
orders of magnitude could come from.

I believe that giving certain perceptions special powers, such as
"alerting properties," is a vestige of S-R thinking.

I really don't mind what you call it, and I'm not claiming that the argument
leads to giving certain perceptions special powers forever. It is quite
conceivable that the nature of what forms an alerting stimulus changes
according to momentary changes in higher reference signals. There's
nothing to say that the nature of all alerts is built in. And if alerts
occur at higher levels, I would bet dollars to doughnuts that they are
being changed all the time.

I'm quite happy with changing which perceptions are actively controlled
as a consequence of changing high-level references. That's no problem
and obviously necessary, and does not involve alerting. However, you
seem to be concluding that changing which perceptions are controlled as
a consequence of unpredicted disturbances is not part of PCT. I don't
know why.

We always have enough
outputs to control the inputs that matter to us and that are
potentially controllable.

Always??? Usually, yes, or our species would not be represented on Earth.

The job of the alerting system, whatever mechanism it might use, is to
allow us to determine which inputs should matter to us at any moment,
out of all the many that we could be controlling. Call it a "draft
prioritizing system" rather than an "alerting system" if you want to
use words that would allow you to dismiss it as excessively cognitive
and computational, the way you dismissed "Hamming distance" and

If we don't have enough outputs in a given situation,
we create new outputs or multiplex those we already have,

Create new outputs??? New fingers? Telepathically controlled robots?
Whatever do you mean? Multiplexing has been taken care of in the
initial analysis, so that doesn't help.

One thing that might possible reduce misconceptions: I do not claim
that reorganization has produced ECUs with PIFs that cover the whole
space of potentially controllable perceptions. "Potentially controllable"
degrees of freedom depends on the degrees of freedom of the sensory
input. "Actually controllable at some time" is the number of different
PIFs. This could be higher of lower than the number of controllable
degrees of freedom (not df/sec, which depends on the bandwidths of those
PIFs). If the PIFs cover the dimensionality of the sensory input but
are not orthogonal, then there are more of them than there are potentially
controllable perceptual degrees of freedom. If they fail to cover the
dimensionality of the sensory input, then there might be fewer perceptions
actually controllable than there are sensory df. But no matter what,
there cannot be more simultaneously controlled df for perception than
there are output df.

When I get back, I hope we can resume this discussion on a basis of
explaining phenomena, with emphasis on verifying that there is a
phenomenon to be explained in the first place.

Might be possible. Since you will see this after you get back, I'll
put the salutation in the past tense:

Hope you had a great trip, and set off a PCT explosion in Europe.