[From Bruce Abbott (950213.0925 EST)]
Bill Powers (950212.1640 MST)
Rick Marken (950212.1710)
Your instrumentation of the inverted-T experiment is great. However, the
model needs to have the illusion built into it, too, if it's to fit the
data. That is, the model needs an adjustable "anisotropy" factor in the
perceptual function which reports vertical size differently from
horizontal size. By adjusting the anisotropy factor, you should be able
to get rid of that "terrible RMS error" in the predictions.
Yes, that's why I was asking for suggestions for ways to model the
situation. As you can tell from my labeling of the horizontal and vertical
lines of the T, I was thinking of the horizontal line as an external
reference which the participant tries to match in order to zero out the
error; I like your proposal better as it makes explicit the fact that both
line lengths are perceptions. However, it seems to me that functionally the
two models are isomorphic. I'll work up an analysis incorporating your
version(s) and see how they do. In pursuit tracking, do you normally treat
the moving spot as part of the perceptual input rather than as reference? I
ask because the inverted-t demo seems to me to fall into the same class.
An interesting question is how to derive the "anisotropy" for a given run
from the data. It would show up as a constant error from reference in
either the subtractive or ratio model. This error could be fed back into
the perceptual function as the anisotropy factor during a second fit of the
model to data.
Could you send the Turbo code? I'd like to try it out.
I'm planning to post the code on CSG-L after I've had the time to clean up
the program a bit and add some comments here and there.
By the way, previous research indicates that the illusion is reduced but
not eliminated by tipping the t on its side. Thus it cannot be fully
explained by some kind of perceptual anisotropy induced by the non-circular
shape of the visual field or, for that matter, the non-square shape of the
monitor, as Susan Schweers (no date/time stamp) suggests.
Regards,
Bruce
[Martin Taylor 950213 14:50]
Bruce Abbott (950213.0925 EST) and Susan Schweers (no date stamp)
On the vertical-horizontal illusion:
By the way, previous research indicates that the illusion is reduced but
not eliminated by tipping the t on its side. Thus it cannot be fully
explained by some kind of perceptual anisotropy induced by the non-circular
shape of the visual field or, for that matter, the non-square shape of the
monitor, as Susan Schweers (no date/time stamp) suggests.
Back in 1961, a summer student and I studied the vertical horizontal
illusion in a situation where we were very careful to have no visible
anchoring points. Nothing could be seen in the visual field except for
the end-points of the lines whose length was to be compared, and these
points were presented in a carefully defined location on the retina.
What we found was that the illusion seems not to be a vertical-horizontal
illusion, but a radial-tangential illusion, in which the centre-point is
"6.5 degrees from the fixation point, along the 244.2 degree meridian
through it (measuring clockwise with vertical as 0 degrees)."
Ref: D.G.Pearce and M.M.Taylor, Visual length as a function of orientation
at four retinal positions. Perceptual and Motor Skills, 1962, 14, 431-438.
At this remove in time, I can't say what the individual subjects did. But
the radial-tangential illusion with such a centre will generate the
foveal horizontal-vertical illusion.
Incidentally, the hardest part of the experiment is to get people to
maintain fixation on an invisible spot. If you have a small dim blue
light at the right intensity, it can be clearly seen in the dark if you
look even slightly away from it, but vanishes if you look straight at it.
After some practice, subjects can avoid seeing it for quite a few seconds
at a time. It might be interesting to do a pursuit tracking study in
which the target is made invisible provided that the cursor is within
a narrow tolerance band of it, but reappears when the error is larger
than that small tolerance limit. Such a study could be used to determine
the effective bandwidth of disturbances having a range of actual computed
design bandwidths.
Martin
[From Bruce Abbott (950215.1730 EST)]
Martin Taylor 950213 14:50
What we found was that the illusion seems not to be a vertical-horizontal
illusion, but a radial-tangential illusion, in which the centre-point is
"6.5 degrees from the fixation point, along the 244.2 degree meridian
through it (measuring clockwise with vertical as 0 degrees)."
Martin, I suspected that you, a perception researcher, would have some
information about the inverted-t illusion to contribute. I'll take a look
at that paper you referenced. My undergraduate research methods class of
several years ago undertook a brief study of this phenomenon using stimuli
drawn on sheets of white cardboard with an adjustable vertical strip. One
of the stimuli consisted of the usual inverted t; another simply showed
three large dots marking what were supposed to be the end-points of the
horizontal line and the (adjustable) top of the vertical line. We found
that in both cases our participants on average adjusted the vertical segment
so that the three end-points formed an equilateral triangle. This
explanation of what the participants were "really" doing in this task
predicts that the vertical line will be 0.87(horizontal).
The inverted-t program came about because I was curious as to how this
illusion would affect a participant's ability to keep the length of the
vertical line equal to the constantly-varying length of the horizontal line,
and wondered how this effect would be best represented within the basic PCT
model. As such I view it more as a vehicle for learning how to model such
effects than as a research project on the illusion itself. Even if there
were no perceptual distortion of line length, there is still the problem of
comparing the lengths of two lines oriented at right angles; I find it
difficult to do this while tracking the changes in the length of the
horizontal line. Control is likely to be relatively poor under such
circumstances, compared to ordinary pursuit tracking.
An alternative would be to apply the disturbance to the vertical line
(controlled by the mouse) while holding the horizontal line fixed, thus
changing the task to compensatory tracking. Participants would be given a
series of different fixed horizontal line lengths during the study. This
procedure would provide a close analog to the traditional "method of
adjustment," and it would be interesting to see whether the results would be
comparable.
Regards,
Bruce