The Heart of Darkness

[From Rick Marken (960323.1845)]

I just re-read your post, Martin [Martin Taylor (960323 16:30)]
and I realized that I fell victim to one of the classic blunders.
The most famous is "never get involved in a land war in Asia" but
only slightly less well known is this: "Never get involved with
Martin Taylor when information theory is on the line". (With
apologies to "Princess Bride" author William Goldman).

I realized I was being dragged into the quagmire when I re-read
the last paragraph of your post:

Indisputably there is control under all conditions, but that was never an
issue.

Actually, I thought that this was _the_ issue. E.coli shows that you can
control when the results of your actions are completely unpredictable.
The fact that the undisturbed movement of the dot after a press is
a straight line (and thus, "predictable") is irrelevant, as I showed
in the experiment where there was _no_ movement after a press; the
dot just moved to a randomn location on the screen. So you can control
a variable even though your influence on that variable is completely
unpredictable.

The issue was whether the quality of control varied with the
predictability of the e-coli course after an unpredictable course change
generated by the controller person. You said it didn't in your experiment,
but in mine it does. We need to find out why the difference.

And now I am slogging knee deep into the quagmire. If I struggle to
get out I will only get in deeper. But here I go -- burble, burble.

When I said that behavior with and without the disturbance was equivalent
I was talking _qualitatively_; I meant that with or without the disturbance
there is control. In fact, as you note, performance with the disturbance
was not as good as it was when no disturbance was present. We found, however,
that the subjects were able to compensate for about 90% of the influence
of the disturbance we used in the E. coli study. So we found what you
found; poorer performance with a disturbance present; but I choose to
emphasize the remarkable fact that, disturbance or no disturbance, there
is control even when the results of action are unpredictable.

Best

Rick

[Martin Taylor 960324 13:00]

Rick Marken (960323.1845)

I just re-read your post, Martin [Martin Taylor (960323 16:30)]
and I realized that I fell victim to one of the classic blunders.
The most famous is "never get involved in a land war in Asia" but
only slightly less well known is this: "Never get involved with
Martin Taylor when information theory is on the line".

I hadn't realized information theory was involved until you said so.
Sorry to have hit a hot button:-)

When I said that behavior with and without the disturbance was equivalent
I was talking _qualitatively_; I meant that with or without the disturbance
there is control. In fact, as you note, performance with the disturbance
was not as good as it was when no disturbance was present. We found, however,
that the subjects were able to compensate for about 90% of the influence
of the disturbance we used in the E. coli study. So we found what you
found; poorer performance with a disturbance present; but I choose to
emphasize the remarkable fact that, disturbance or no disturbance, there
is control even when the results of action are unpredictable.

That's a relief. I was concerned that I might be doing something wrong
in my stack (which I have cleaned up a little since I sent it to you, so
you'll probably get an updated version in due course).

Where I have a problem, and why I jumped in with what I thought would have
been an innocuous comment the other day, is in your statement that "the
results of action are unpredictable." As I see it, that's not true. Only
the direction of movement following a "tumble" (hit on the space-bar,
mouseclick, ...) is unpredictable. The result of the action "do nothing"
is ordinarily totally predictable. If the e-coli is going where you want
it to go, your action output is zero, but you are still controlling, aren't
you? If you couldn't predict where it would be going next instant, on
what ground would you choose to press or not to press the space-bar/mouse?

In your sense, the "results of action" are always unpredictable in the
real world outside the laboratory. When you turn a door-knob, you don't
know that the latch will actually move and the door-handle not fall off
(example from experience--in the bathroom:-). But in my sense, the results
of action are predictable in that some consequences are more probable
than others. In the case of e-coli, you know within a few tens of msec
whether you are going to want to press the bar soon again. If it jiggled
all over the place in an unpredictable path, you couldn't know that.

In Rick Marken (960323.1720) you say:

One language problem: "quicker" is not the same as "higher amplitude."

Yes. But the result is the same; control is poorer (as you found in
your HyperCard experiment) with a higher frequency disturbance. But,
as with amplitude, this has nothing to do with predictability. Control
is poorer with a higher frequency disturbace even when the disturbance
is predictable (a sine wave, for example).

Analytically, the results are quite different. A change in frequency can
lead to loss of control in a linear system, but a change of amplitude
cannot. That's why integrating output is a good thing; it reduces
high-frequency gain and reduces or eliminates to possibility of
oscillation or resonant output growth. A high amplitude disturbance
only increases error because the proportion of the disturbance countered
is a constant at any given frequency, once any transients have dies away.

ยทยทยท

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Back to square one: none of the above involves information theory, though
the arguments might be quantified using it, I suppose. All I'm doing is
pointing out the surface facts of the situation, noting that control is
possible when the e-coli path is predictable _after_ the bar press, but
would not be if the future path could not be predicted from current
observation. In the Hypercard stack, the disturbances that affect prediction
of the path are relatively gentle, but they do make it more difficult,
as you agree you also found.

So I think we really have no disagreement here, except for your finding
quagmires where there are only little spots of dampness.

However, I think the interchange also points up a fact that you often
invoke: in control systems, the obvious is often not the truth.

Martin