[From Rick Marken (930331.0800)]
Martin Taylor (930330 11:20) --
Let's consider a thought experiment to test this.
EXCELLENT THOUGHT EXPERIMENT! Now let's do it as a simulation,
shall we?
If I understand the
claim, oft repeated, Rick means that no function that takes as input
(a) the perceptual signal and (b) any other signal that is agreed to have no
information about the disturbance can reconstruct the disturbance, but
that nevertheless the disturbance is mirrored in the output.
I'll buy it.
I'll leave the logical problem with the "mirroring" unaddressed, and
assume that Rick accepts as correct what he says, that the output
mirrors the disturbance.
What's the "logical" problem with the "mirroring"? You can look at
the data from our tracking experiments and see that o = -d to within
a few pixals throughout an experimental run. When both o and d are
measured in screen units, the time traces of these two variables will
be symmetrical about a line corresponding to the fixed screen position
of the target. I call this characteristic of the graph "mirroring".
In my thought experiment, I will take the ECS, and add a simple function
that takes as its input the reference signal to the ECS (which I think we
can agree has no information about the disturbance) and the perceptual
signal, which Rick CAPITALIZES as having no information abou the disturbance.
Excellent! For simplicity, let's make the reference signal a constant
when we simulate your model. But a variable r will work too -- just
trying to keep it simple.
Let us see whether a function can be constructed that takes these two
inputs and produces a signal that matches the disturbance. If so, I
would consider it conclusive evidence that information about the disturbance
is to be found in the perceptual signal.
OK!
------------> Signal X (which should match the disturbance)
>
mystery function M(r, p)
^ ^
> >
> > V (reference signal R(t) into ECS)
> > >
> <-------|
> V
>---------->comparator------- error = P-R
> >
perceptual output
signal P(t) function O(error)
^ |
> V
> output signal
> (accepted as mirroring the disturbance)-------------------------------------------------------------------
If Signal X matches the disturbance, the perceptual signal must be the
route from which the mystery function M(r, p) gets the information about
the disturbance. Right?
Right!! I completely agree with your proposal as diagrammed above.
I think a good first candidate for M(r,p) would be the function
O(r,p), right? Ah, I see you think so too:
Now let the function M be indentical to O(R-P). Signal X will then be the
negative of the output signal, which is the disturbance.
It is at this point that experience will triumph over the "obvious"
conclusions of your thought experiment. I think it's time to fire up
the simulator; really!
The only question
here is whether O(error) is a function or a magical mystery tourgoodie.
Your magical mystery tour will really begin when you run the simulation!
I
prefer to think we are dealing with physical systems, and that O is a
function.
Therefore, information about the disturbance is in the perceptual signal,
and moreover, it is there in extractable form.
QED.
And a right excellent proof i'tis. Now try the simulation.
Best
Rick "There is no information about the disturbance in controlled
perception" Marken