The Irrelevance of Predictability

[From Rick Marken (960324.1500)]

Martin Taylor (960324 13:00) --

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.

You can look at it that way, but the demo I keep mentioning (and
describe in more detail below) shows that the "predictability" of
movement after the press is irrelevant; if the dot just stays put in
a new position after a press (so there is no continuation of movement
to predict) you can still control the position of the dot.

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?

On the usual ground: the _error signal_, which represents the difference
between reference (goal) and actual position of the dot: if the dot is
not at the reference position (error) then press, otherwise (no error)
don't press.

In your sense, the "results of action" are always unpredictable in the
real world outside the laboratory.

Indeed, this is exactly true; the results of our actions would be
completely unpredictable if it were not for the fact that we _are_
control systems. Controlling can be thought of as the way we make the
results of our actions precisely predictable; when we are in control,
we are forcing the results of our actions into "predictable" (reference)
states.

When you turn a door-knob, you don't know that the latch will
actually move and the door-handle not fall off

Right. The result you wanted was an open latch; instead you got a
handle on the floor (and a latch that was still closed, I presume);
so it looks like you lost control of the perception of "latchedness"
of the door. But I bet you will regain control of that variable soon.
That particular loss of control was the result of a large disturbance
(the broken handle); ordinarily the handle doesn't break but the amount
of force required to open the latch is unpredictable; since you can
control "lachedness", you adjust your actions (force exerted on the
handle) as necessary to produce the intended result (an open latch).
The result of controlling "latchedness" is usually quite predictable;
if you want the latch open it ends up open;if you want it closed, it
ends up closed. There is no prediction of the force needed to produce
the intended result; just closed loop control.

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.

But these "surface facts" are not facts at all; that's why I keep
replying. It is simply not true that control would not be possible
"if the future path could not be predicted from current observation".
The "predictability" of the path of dot movement after a press has
nothing to so with the possibility of control in this task.

Try setting up this version of the E. coli demo: after a mouse click
the dot moves randomly to one of 10 positions (marked with circles)
on the screen. Select one of those 10 circles as the reference (target)
position. Now see if you can control the dot (get it to the target
circle) by clicking the mouse.

Easy, isn't it? Especially if the dot happens to be on the target circle
on the first trial. In this demo, the position of the dot after a
press is completely unpredictable (although the dot stays put after
a press so maybe you will say it's still predictable; you can predict
that it will stay where it ends up; but then you have to explain how
that kind of predictability makes it possible to decide on the appropiate
action to take; after all, the dot stays where it is after a mouse
click whether it lands on a target or a non-target circle).

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

I'm afraid that we have a real disagreement; you say that control is
only possible if the results of action are predictable to some extent;
I say that control is possible whether or not the results of action are
predictable.

I submit that the best way to solve this disagreement is for you to
start agreeing with me;-)

Best

Rick

[Martin Taylor 960325 11:05]

Rick Marken (960324.1500)

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

I'm afraid that we have a real disagreement; you say that control is
only possible if the results of action are predictable to some extent;
I say that control is possible whether or not the results of action are
predictable.

Oh, dear. What I thought was a little spot of dampness turns out to be
a quagmire after all. The real world does intrude on our perceptions,
doesn't it:-)

I think that the issue can be resolved easily, but I'm quite prepared to
be wrong. I'm working on the basis that we are controlling all the time,
and you are not. Is that it?

You say that we are not controlling when our output is zero. That's why
you are able to introduce the following example:

Try setting up this version of the E. coli demo: after a mouse click
the dot moves randomly to one of 10 positions (marked with circles)
on the screen. Select one of those 10 circles as the reference (target)
position. Now see if you can control the dot (get it to the target
circle) by clicking the mouse.

Easy, isn't it? Especially if the dot happens to be on the target circle
on the first trial. In this demo, the position of the dot after a
press is completely unpredictable (although the dot stays put after
a press so maybe you will say it's still predictable; you can predict
that it will stay where it ends up; but then you have to explain how
that kind of predictability makes it possible to decide on the appropiate
action to take; after all, the dot stays where it is after a mouse
click whether it lands on a target or a non-target circle).

Of course I say that it is predictable. You defined the situation so that
it is. So long as my action is null, the dot stays where it went
(unpredictably) when my action was non-null. How that kind of predictability
makes it possible to decide on the action is the same as in any other
control situation. I expect that my null action will result in the dot
not moving, and that my overt action will result in it moving somewhere
other than where it is (or possibly staying put). If I rely on my prediction,
I can keep the dot on target as long as I want. I can keep observing, but
I don't get the dot to stay on target any better than I do by relying on
my prediction--that is, I can if your statement of the setup is trustworthy
in fact.

For the results of action to be unpredictable, that must apply to ALL of
our control action, not just occasional moments. You have to show that
control is possible even when the result of null action is unpredictable.
In your example, there are moments of unpredictability interspersed in
long stretches of high predictability of the effect of output.

There's another apparent problem, perhaps of language. You seem to say that
if any aspect of a prediction is inexact, then the thing is "unpredictable."
I take predictability to be a matter of degree, from complete (as with the
dot that stays on the circle unless I make an overt action), to nil (a
physically impossible situation, but one that can be approximated if
your dot moved to a new target circle on every frame of the screen refresh).

I ask you whether you could control the dot at all if the dot moved
to a new circle at every screen refresh, regardless of your action?

I submit that the best way to solve this disagreement is for you to
start agreeing with me;-)

I accept that you are like a little circle, and my dot would stay in it
if I made no action after arriving in it. But would this little circle have
been the right one to have chosen as a target?

Isn't it fun to swim in mud?

Martin

[Martin Taylor 960325 13:30]

Bruce Abbott (960325.1040 EST)

Bruce's posting highlights a different view on the predictability issue.

What is critical is
that the participant have information about the current state of e-coli's
movement relative to target (i.e., change in error) and be able to act on
that information before the information becomes outdated. The disturbance
must fall within the participant's response bandwidth.

A minor quibble: it's not "response" bandwidth, but "control" bandwidth.
And "bandwidth" is another word for "unpredictability", a word I have been
trying to avoid, as it comes perilously close to the notion of "information
theory." Bruce is right, nevertheless.

In Rick's example, he postulates a dot that moves to some randomly selected
little circle if one clicks the mouse, and that stays where it is forever
when you don't click the mouse. I argued that the subject's "null" action
output results in entirely predictable behaviour on the part of the dot,
and that some of this predictability is required if control is to be
possible. "Control" involves observation, and the perfect predictability
of the result of the null action means that observation is not necessary
at all. In that sense, the subject _need not_ control the dot, but _may_
do so. It would be impossible to tell from observing the subject's actions
whether the dot was being controlled or not, since in either case the
subject would be producing no output.

Now let us change the postulated experiment, to say that after a time T
of being stationary, the dot jumps to a different circle. Now the subject
cannot keep the dot in the target circle without actually observing and
controlling. The long-term predictability does not matter. But what does
matter is that the time T before the next dot move must be long enough
that the subject can determine whether the dot is in the target circle,
_and that it will still be there in the time it takes to decide to click
or not click the mouse_. The important predictability is over the period
of the loop delay, in other words. One can control if the effect of one's
action (even a null action) is predictable better than by pure chance.

The other side of the coin is in the need to observe, if the intention is
that the real-world correlate of the perception should maintain a state
that gives the perception its reference value. If one is assured that the
dot will not move, one can maintain a perception of it as being in the
right place (perhaps an imagination-based perception), without ever
observing it after the first time it is seen in the desired place. If you
know that it moves only at noon on April 1 each year, you can limit
your actual observance to just after that time, and generate non-null
actions (mouse clicks) until the dot is restored to its desired place.
If it is known to move once per second, you may be able to get it onto
the desired place sometimes, by clicking fast, but if it needs 3 or 4
clicks on average before it arrives there, it will spend _very_ little
time at the desired place, since you can't control such perceptions at
a bandwidth much over 3 or 4 Hz, if that. And if it moves 5 times per
second regardless of what you do, you will never have it on the desired
circle more often than it would be if you just left it alone.

So there are actually two separate issues: whether predictability is
sufficient to permit control, and whether it is great enough that you
don't have to control as much (in the case of the dot, that means you
don't have to observe as often, but in the case of continuous variables
it could mean you don't have to observe as closely if you have an integrating
output).

I'm pretty sure that any disagreements are due to different ways of looking
at the same elephant, but I'm not completely sure that this is the case.
Rick might be looking at a cuddly tiger instead.

Martin