# Correlations and information

**URL:** <http://discourse.iapct.org/t/correlations-and-information/3179>\
**Category:** CSG1993\
**Created:** [April 3, 1993, 3:58am UTC](http://discourse.iapct.org/t/correlations-and-information/3179 "1993-04-03T03:58:07Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Human\_Factors\_Lab](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/h/b3f665/32.png) [@Human\_Factors\_Lab](http://discourse.iapct.org/u/Human_Factors_Lab)\
**Post date:** [April 3, 1993, 3:58am UTC](http://discourse.iapct.org/t/correlations-and-information/3179/1 "1993-04-03T03:58:07Z")

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[From Rick Marken (930402.1800)]

Allan Randall (930402.1130 EST) --

> Are you then saying that this almost perfect information about the  
> first derivative is not "significant" information?

It is not really information at all. This perfect correlation is  
a result of having a perfect integrator in the output and a  
linear contribution of o to p (with a coefficient of 1). Anything  
else would have produced a much lower correlation between the  
first derivative of the disturbance and perception. So if you  
are thinking that the perception carries information about the  
disturbance (tells you what the disturbance is) then you would  
sometimes be guessing WRONG about the form of the disturbance based  
integrating the perecptual signal.

Let's say that you now claim that the integral of the perceptual  
signal, int(p) , equals the disturbance (as shown in Bill's demo).  
Now I give you 100 segments of p obtained in different tracking  
tasks. Fifty of these segments have been obtained in tasks where the  
cursor (p) was determined by the following equation -- p = o + d.  
Fifty were obtained in tasks where p = ko + d, where k was differnt  
in each case. Now you run all 100 segments through your disturbance  
detector , int(p). You would consider all 100 resulting estimates of  
d to correctly represent the d actually presented on each trial. In  
fact, you are only right about half of them (and you don't know  
which half). It is in this sense that the int(p) detector -- which  
correlates perfectly with the disturbance in Bill's example --  
actually provides NO information about the disturbance. It's because  
you have no way of knowing (except by looking at the disturbance itself)  
when int(p) is and when it is not an accurate representation of d.

> You and Rick continually insist on measuring information with things  
> like correlation and variance statistics. This is not accurate.

I think this is a misunderstanding; but I am willing to admit that I  
have not been clear about this -- until now, I hope (see my comments  
above).

Martin Taylor (930402 11:10) --

> Up until today (or rather two days from now), you have said that the  
> disturbance and the output correlate 0.99xxx in many many postings. Now,  
> to retain your position that there is no information about the disturbance  
> in the perceptual signal, you have suddenly shifted to the position that  
> the correlation between disturbance and output is 0.00.

The first part of this seems a bit strong (there is no information  
about the disturbance in perception regarless WHAT position I might have  
changed) and the second part is just wrong -- I never said that the  
correlation between disturbance and output is 0.00. In fact, the  
correlation can range from close to 1 to close to 0. What I realized was  
that the relationship between distrubance and output in IRRELVANT to the  
question of whether or not there is information about the disturbance  
in perception. What is relevant is how well a receiver can determine  
D given P. Hopefully, you are working on the perceptual signals I sent  
to determine how well this can be done. Think of it as a signal detection  
experiment. I'll give you signals (p strings) and you tell me which  
D you think they represent.

> You can't have it both ways. Either the disturbance and the output are  
> correlated, as experiment and model both show, or they are not,

Not so simple, I'm afraid. This correlation depends on many things;  
the gain of the output and the feedback function from output to input  
being two of them. By varying these parameters the correlation between  
o and d can be made to range from near 1.0 to near 0.0; through it all,  
there is no information about the distrubance in the perceptual signal.

> P = O + D was a given because that is what has always been  
> claimed as a basic property of the loop.

Well, it's now time to go beyond p = o + d. In order to really  
bring the point home we're just going to have to admit that  
p = g(o) + f(d). And that's functional notation; I'll tell you  
right now that it's the g function that is the killer for the  
idea that there is ANY information in p about d. I've tried to  
be linear about this -- but now it's no more mister straight guy.

> It [information about the disturbace] IS used, most explicitly and  
> adequately.

We shall see.

If it's any comfort to you, I will succumb to data. I was perfectly  
willing to accept Bill Powers' first derivative data; and I was all  
set to admit that there IS information about the first derivative of  
the disturbance in p. But then I realized that this was information  
in the same way that Martin's old perceptual transient provided  
information about the disturbance; it only provides information on the  
information that you know a lot about what the information is being  
sent about.

I won't consider the information you claim exists in p to be worthy  
of the name "information" if you can't use the p strings (messages)  
to reliably tell me which d strings "sent" them.

Best

Rick

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**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:** [April 3, 1993, 8:29pm UTC](http://discourse.iapct.org/t/correlations-and-information/3179/2 "1993-04-03T20:29:58Z")

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[Martin Taylor 930403 15:15]  
(Rick Marken 930402.1800)

Rick,

Remember that the claim was ONLY that the information in the perceptual  
signal is enough to permit the OUTPUT signal to be reproduced. The  
original claim that the output signal was a mirror of the disturbance  
was yours. Our claim is only that to the extent that the perceptual  
signal is controlled, it has passed information about the disturbance  
that has come to be manifest in the output signal.

Now that you have renounced the claim that there is information about  
the disturbance in the output signal, you have to think hard about what  
is meant by "control," but your original logical inconsistency has been  
removed (we had a little pool about how you would get around the problem,  
but none of us bet that you would renounce the idea of control to be able  
to retain the claim that there's no information about the disturbance  
in the perceptual signal. That was really a breathtaker for us).

Neither the output signal nor the perceptual signal can deal with  
disturbances that change too fast. I'll let Allan, probably on Monday,  
check out your perception sequences, but a first visual glance suggests  
that at least one of them involves fast-changing disturbances. But we  
shall see. If the perception is well controlled, then the result will  
be like the disturbance. Come to think of it, the perceptual signals  
you have provided are clearly not well controlled, since you assert  
that the reference is zero throughout, and the perceptual signals are  
drifitng away from zero in one case.

You very clearly do not understand the concept of information. One can  
have an informational relationship between two signals even if their  
correlation is zero, but a non-zero correlation is an absolute demonstration  
of an informational relation.

> Not so simple, I'm afraid. This correlation depends on many things;  
> the gain of the output and the feedback function from output to input  
> being two of them. By varying these parameters the correlation between  
> o and d can be made to range from near 1.0 to near 0.0; through it all,  
> there is no information about the distrubance in the perceptual signal.

If the output function can be generated from the perceptual signal, as  
we have shown, this paragraph is equivalent to saying that red can  
be green or blue, but throughout it all, 3 is greater than 7. It is  
a total renunciation of logic (or of mathematical definition).

When the perception is not well controlled, the relation between  
the perceptual signal and the disturbance is harder to determine. When  
there is no control, it is easier again, because the perceptual signal  
IS the disturbance. Between these extremes, the perceptual signal  
contains a mixture of part of the disturbance and part of its derivative.

> Well, it's now time to go beyond p = o + d. In order to really  
> bring the point home we're just going to have to admit that  
> p = g(o) + f(d). And that's functional notation; I'll tell you  
> right now that it's the g function that is the killer for the  
> idea that there is ANY information in p about d. I've tried to  
> be linear about this -- but now it's no more mister straight guy.

Wonderful. Now we can start talking seriously about information.  
That function g(o) isn't even a function, is it? Remember "variable  
means to a constant end; variable ends by constant means"? This  
is the starting point for the next phase of the information discussion.  
Great to get here at last!

Martin