Vancouver's experiment

[from Jeff Vancouver 961125.09:55 EST]

Well I tried to program the spiral experiment using Visual Basic. I was
completely unsuccessful. I stopped when I could not figure out how to
record the X and Y coordinates of the mouse. Instead I compromised with
a less than adequate solution, but it approaches what I seek.

Below are the data from several different type of runs. I edited the
"visible" word to label the condition. Recall that in the blanked
condition one still has kinesthetic and vision feedback of the mouse, as
well as feedback from the screen when the blacked out cursor passes over
the edges of the target. I had initially suggested blanking the entire
screen, but doing it during runs not as a run. So, I closed my eyes to
simulate blanking the screen (I still get the kinesthetic feedback, but
that is it. I tried three variations on this theme. First, I alternated
eyes open, shut, open for 10s (called Alt 10s). Time was measured using a
paced "one and two and . . . " counting to myself. Then I tried eyes open
and shut alternating every 2s (called Alt 2s). Finally, I tried eyes open
for 3s and closed for 1s (called 3,1,3). I discuss the results below.

jeff
  6.31 visible
  6.21 visible
  6.01 visible
117.72 Alt 10s
  6.44 visible
115.10 Alt 10s
28.38 Alt 2s
36.67 Alt 2s
32.29 Alt 2s
29.16 Alt 2s
11.66 3,1,3
10.41 3,1,3
11.87 3,1,3
11.38 3,1,3
32.79 3,1,3 Mouse got stuck
12.19 3,1,3

On the second to last run the mouse ball got stuck on some dirt on about
the last 4s of the run so it did not move.

It is perhaps interesting to note that I did substantially better in the
Alt 2s then the Alt 10s even though my eyes were closed half the time in
Alt 2s and only a third in Alt 10s, the ability to correct more often once
my eyes were opened accounts for the better performance (given that when I
opened my eyes I was always making a substantial correction -- esp. in
the Alt 10s condition).

Otherwise, the data clearly show the advantage of closed-loop control.

I think that the data (mine and others) clearly demonstrate that we use
closed-loop control. If there are any open-loop only advocates out
there, I invite a different interpretation.

Now that this point has been made, I would like to get on to the point I
was trying to make. Unfortunately, I am at the mercy of the Pascal
programmers.

The point I was trying to make is that control with the mouse, screen, or
whatever blanked (i.e., model-based control), is better than random,
static (no movement), or linear trajectory performance. Thus, as a
comparison, the average RMS from those models needs to be added to the
output.

I am not looking for an "excuse" here, I am looking for a reconciliation.
I think that reconciliation is in the nature of the transfer function _we
all think_ is created to track the spiral. That given sufficient time to
create such a function, it can create a controllable perception of the
movement of the target even without the target being visible. This
function will not be as good as it would with on-line data, but it will be
better than if no function were there (as indicated by comparing to
random, no movement, or linear/trajectory movement). Any takers?

Later

Jeff

···

_________________________________________________________________________
                           Jeffrey B. Vancouver
Assistant Professor Phone: (212)998-7816
Department of Psychology Fax: (212)995-4018
New York University e-mail: jeffv@psych.nyu.edu
6 Washington Pl., Rm 578
New York, NY 10003

[From Bill Powers (961125.0930 MST)]

Jeff Vancouver 961125.09:55 EST --

Below are the data from several different type of runs.

Very nice, Jeff. I appreciate simple direct solutions to problems. Blank the
screen? Close the eyes!

jeff

6.31 visible
6.21 visible
6.01 visible
117.72 Alt 10s
6.44 visible
115.10 Alt 10s
28.38 Alt 2s
36.67 Alt 2s
32.29 Alt 2s
29.16 Alt 2s
11.66 3,1,3
10.41 3,1,3
11.87 3,1,3
11.38 3,1,3
32.79 3,1,3 Mouse got stuck
12.19 3,1,3

On the second to last run the mouse ball got stuck on some dirt on about
the last 4s of the run so it did not move.

That last notation shows why closed-loop control will always work better
than model-based control when it's available. There's no way to predict when
the mouse is going to get stuck. If your eyes had been open when that
happened, there still would have been more error, but it would have been a
much smaller increase and it wouldn't have lasted four seconds..

It is perhaps interesting to note that I did substantially better in the
Alt 2s then the Alt 10s even though my eyes were closed half the time in
Alt 2s and only a third in Alt 10s, ...

Um, Jeff ... equal time open and closed is closed half the time, isn't it?
Regardless of the cycle time?

the ability to correct more often once
my eyes were opened accounts for the better performance (given that when I
opened my eyes I was always making a substantial correction -- esp. in
the Alt 10s condition).

Also, your sampling with different lengths of eyes-closed time gives us an
idea of how rapidly the mental model departs from the reality without
concurrent feedback. The longer the eyes-closed time, from 1 second to 10
seconds, the greater the error. The error is about doubled after 1 second.
This says that the internal world-model, if there is one, isn't a very
accurate model. You might try repeating this experiment about 50 times and
seeing if your eyes-closed performance improves substantially. I haven't
improved much over about 100 trials.

The point I was trying to make is that control with the mouse, screen, or
whatever blanked (i.e., model-based control), is better than random,
static (no movement), or linear trajectory performance. Thus, as a
comparison, the average RMS from those models needs to be added to the
output.

I think you're saying that we need a baseline against which to compare the
performance. I agree; that would be a fairer comparison. However, it still
doesn't answer the basic question of how control is carried out with the
eyes closed (if "control" is the word).

Hans Blom asked about this before, and now you're also raising the question
of how the person could continue to produce a spiral (of sorts) without
present-time visual feedback AND without a world-model. Here's a rough idea,
which I haven't really developed into a full-blown working model but which I
am sure would work with a little tinkering. This, at least, is a little
better than the vague solution I mentioned to Hans.

To make life easier I'll assume that there's a level of kinesthetic control
at which position can be controlled in angle and radius relative to some
center, as kinesthetically sensed. Any other coordinate system could be
assumed, but this one is easiest. I'll just show the kinesthetic angle
control system.

            from integrating output function
                    in visual system

                           >
                        velocity ref
                           >
                           >
             ------->----[Comp] --->----- (velocity error)
            > >
            > >
    angular velocity [Integrator]
            > >
         [d/dt] |
            > angle ref signal |
            > -------<------
            > >
            > --->-----[Comp] ---->------ (angle error)
            > >
            > >
           angle [Integrator]
            ^ |
            > >
               [Lower level systems]

Note that to move the mouse at a constant angular rate, all you need is a
_constant_ velocity reference signal. The integrator in the upper system
would turn a constant (small) error signal into a _constantly changing_
angle reference signal. The derivative (d/dt) in the input function cancels
the lag in the integrating output function, so the overall response is
proportional, as far as stability is concerned. The lower system makes the
perceived angle follow the changing reference signal. Passing this constant
rate of change through the first derivative in the upper system yields a
perceptual signal of angular velocity proportional to the rate of change of
angle.

Suppose now that there is a visual system that is detecting position error,
and converting it, through an integrator, into the reference angular
velocity for this kinesthetic control system. If the visual system
experiences a blackout, the proper response is to clamp its error signal to
zero (the model-based control system also needs a special response to loss
of input). The assumed integrator in the output of the visual system
receives a zero error-signal input, so its output remains fixed. This means
that the angular velocity reference signal for the kinesthetic system also
becomes constant, and the kinesthetic system continues to move the mouse (as
kinethetically detected) at a constant angular velocity. When the visual
input returns, the angular velocity reference signal will be increased or
decreased as necessary to correct the visual error.

The same sort of thing would happen in the kinesthetic radius control system
at the same level.

If the visual integrator is leaky, we will see a decay in the reference
signal and a change in the angular velocity, which will result in an
increasing actual error as long as the visual input is blanked. How big the
error will be depends on how fast the integrator leaks.

This rough sketch shows how a system that contains no explicit internal
world-model can do some of the things that a model-based control system can
do -- particularly maintain an ongoing output, including curvatures, for
some time after loss of input information. A different approach to
adaptation would be required, of course.

There are other designs that would also work, and might work better than
this one. But the point is that it't not hard to get ONE of the main effects
of model-based control without having any actual world-model in the system.

Best,

Bill P.