[From Rick Marken (950217.1100)]

Me to Martin:

You intellect is truly too dizzying for me.

Martin Taylor (950217 10:4) --

Sorry, but I thought that Laplace Transforms were a standard way of

analyzing control systems, not "arcane mathematical gymnastics." The rest

was quite straightforward, with very little of the mathematics that bother

you.

It wasn't the mathematics that bothered me. It was verbalizations like this:

The "incontrovertible demonstration" was precisely the use of data to show

that they [variations in d] can [be inferred], PROVIDED that the output and

feedback functions are known. The information needed to specify those

functions is fixed, AND IS INHERENT IN THE ACTUAL STRUCTURE OF THE CONTROL

LOOP, whereas the information from the disturbance approaches infinity over

infinite time.

Why would the information needed to specify those functions matter to

the operation of the control system itself? How does information

"inhere" in the struture of a control loop? How can I know that it inheres

in this way? How do I know that information from the disturbance approaches

infinity over time? How do I test any of these claims--other than by asking

you, of course;-)?

I like simple, clear tests of theories so it's easy for me to tell what's

going on. It seemed to me that we got to a point in the "information" debate

where there was an opportunity for a simple test of information theory; we

agreed that I would send you a perceptual signal obtained from a control

model and you would send back the corresponding disturbance variable

(assuming there was just one) that was being resisted by the control system.

If you were able to do this with several perceptual signals, it would prove

to me that there IS information in the perceptual signal that can be used to

generate the outputs that are compensating for the effects of the

disturbance. If not, it would show that control systems don't "use"

information in perception to generate outputs; control systems CONTROL

perceptions.

This simple test was never done because you kept saying that information

theory required more and more details about the control system (output

function) and its environment (feedback function) in order to reconstruct the

disturbance. Eventually, it became clear (to me) that information theory was

just another name for control theory; what you needed was exactly what a

control theorist would need in order to determine the disturbance given the

perceptual signal. Moreover, you said that the simple test I thought we

had agreed to was really just a reflection of my dismal understanding of

your explanation of information theory. So there was no test.

Eventually it also became clear that information theory does not fail tests.

The most dramatic demonstration of this occurred when you predicted

(and claimed that the predicitno was based on information theory) a high

correlation between the derivatives of perceptual and disturbance variables.

About one hour after the prediction Bill Powers posted a circular cloud that

represented the actual BEST relationship (at optimal lag) between the

derivatives. This apparently posed no problem at all for information theory

since you quickly came back to say that Bill's result was EXACTLY what

you expected -- information theory confirmed again.

It is difficult for me to get excited about testing a theory (like

information theory) when I know (as I know now) that, whatever the result of

the test, it will be consistent with the predictions of the theory. So it

probably hopeless to suggest this but maybe we can make this discussion of

information substantive if you would suggest one simple test that would put

information theory on the line? Does information theory make some

quantitative prediction about the behavior of a subject in a simple tracking

task-- a prediction that can be tested against data? Can you describe an

experiment I can do to test a QUANTITATIVE predciction of information theory?

Perhaps a prediction regarding the effects of disturbance bandwidth on some

parameter of tracking performance?

Since you say that almost everything I say about information and information

theory is wrong, I think it would be best if you told me exactly how to do

the experiment, how to derive the prediction, how to measure the

variables, etc. I'll just collect the data and see if it matches the derived

prediction. If you do this, please remember to keep it as SIMPLE as possible -

- not only for my sake but also for the sake of people who are watching and

who are reading through this quickly. Try to come up with something that

provide a CLEAR, SIMPLE test of information theory.

Perhaps information theory DOES have something worthwhile to contribute to

our understanding of purposive behavior. I just haven't seen it yet.

I have no personal investment in the failure of information theory. I did

study information theory in graduate school and what I learned was that

it is a way of measuring the channel capacity of organisms viewed as input-

output devices. So the information theory I know seems completely

incompatible with the PCT model of purposive behavior. But maybe it's not.

All I'm asking is that you show me evidence of something information theory

accounts for in actual purposeful behavior -- the kind we see in our simple

little control tasks . I don't want more descriptions of what information

theory can do; I want to SEE what information theory actually does -- in a

real control task.

Best

Rick