# Degrees of Freedom

**URL:** <http://discourse.iapct.org/t/degrees-of-freedom/3397>\
**Category:** CSG1992\
**Created:** [March 18, 1992, 10:01pm UTC](http://discourse.iapct.org/t/degrees-of-freedom/3397 "1992-03-18T22:01:37Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![\_Gary\_A\_Cziko](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/_/3ab097/32.png) [@\_Gary\_A\_Cziko](http://discourse.iapct.org/u/_Gary_A_Cziko)\
**Post date:** [March 18, 1992, 10:01pm UTC](http://discourse.iapct.org/t/degrees-of-freedom/3397/1 "1992-03-18T22:01:37Z")

</div>

[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: g-cziko@uiuc.edu  
> 1310 S. Sixth Street Radio: N9MJZ  
> 210 Education Building  
> Champaign, Illinois 61820-6990  
> USA  
> ------------------------------------------------------------------

---

<div class="post-metadata">

**Author:** ![\_Martin\_Taylor](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/_/a9adbd/32.png) [@\_Martin\_Taylor](http://discourse.iapct.org/u/_Martin_Taylor)\
**Post date:** [June 9, 1994, 11:43pm UTC](http://discourse.iapct.org/t/degrees-of-freedom/3397/2 "1994-06-09T23:43:37Z")

</div>

[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  
"uncertainty."

> 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.

Martin