# Ambiguous figures

Re: Ambiguous figures
[From Rick Marken (2004.05.07.1350)]

Martin Taylor (2004.05.07.14:03)–

No. Each box represents 9 continuous minutes of viewing, but for the

statistics that are displayed, the time is reset to zero at each

switch of the percept. To be concrete, let’s imagine a small segment

of those 9 minutes, during which the following events occurred (B =

switch into Bubble, D = switch into Dent, numbers = seconds between

events).

B 2.0 D 1.3 B 5.2 D 0.5 B 3.1 D 2.6 B …

The diagram would start at {0, 1} {time, probability that no switch

has yet occurred). For the “switch out of bubbles” curve, at time

2.0 it would drop to {2.0, 2/3} since on 2/3 of the occasions when

Bubbles were being seen, no switch to dent had occurred.

You lost me. Where did the 2/3 probability come from? All I see is that a trial starts out with a person saying that they see bubbles (B). Then 2 seconds later the person says that they see dents (D). How does this translate to a 2/3 probability of switching out of the perception of “bubbles” after 2.0 seconds?

At time 3.1

it would drop to {3.1, 1/3}, and at 5.2 it would drop to {5.2, 0}.

Where does time 3.1 come from? Doesn’t the first switch back to bubbles (B) occur after 3.3 seconds? And, again, how is the 1/3 probability calculated?

Maybe I missed it but could you explain what the participants were actually doing in this experiment? Were the subjects asked to fixate on a single point in the display? It seems like eye movements, leading to new views of the image, would have a lot to do with when (and whether) there was a perceptual shift. When I want to go from seeing the “wife” to seeing the “witch” in the well known “wife/witch” figure (reproduced in my “Looking at behavior through control theory glasses” paper) it seems to me that I scan over the image a bit to foveate new features of the image.

Best regards

Rick

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Cell: 310 729 1400

Re: Ambiguous figures
[Martin Taylor 2004.05.07 22.13]

[From Rick Marken
(2004.05.07.1350)]

Martin Taylor (2004.05.07.14:03)–

No. Each box represents 9 continuous
minutes of viewing, but for the

statistics that are displayed, the time is reset to zero at
each

switch of the percept. To be concrete, let’s imagine a small
segment

of those 9 minutes, during which the following events occurred (B
=

switch into Bubble, D = switch into Dent, numbers = seconds
between

events).

B 2.0 D 1.3 B 5.2 D 0.5 B 3.1 D 2.6 B …

The diagram would start at {0, 1} {time, probability that no
switch

has yet occurred). For the “switch out of bubbles”
curve, at time

2.0 it would drop to {2.0, 2/3} since on 2/3 of the occasions
when

Bubbles were being seen, no switch to dent had occurred.

You lost me. Where did the 2/3 probability come from? All I see is
that a trial starts out with a person saying that they see bubbles
(B). Then 2 seconds later the person says that they see dents (D). How
does this translate to a 2/3 probability of switching out of the
perception of “bubbles” after 2.0
seconds?

Because there are three B -> D events in the example, and for
two of them the bubble phase lasts longer than 2 seconds. List them in
order of how long the bubble phase lasted: 2.0, 3.1, 5.2. Up to two
seconds after switching into the “bubble” phase, the subject
always retained the perception of bubbles. Between 2 and 3.1 seconds,
the subject retained the bubble phase on only 2/3 of the occasions.
And so forth.

At time 3.1

it would drop to {3.1, 1/3}, and at 5.2 it would drop to {5.2,
0}.

Where does time 3.1 come from?

The second fastest B -> D event occurred 3.1 seconds after the
switch into bubbles.

Doesn’t the first switch back to bubbles (B)
occur after 3.3 seconds? And, again, how is the 1/3 probability
calculated?

Becuse in only one of the three B->D events did the bubble
phase last longer than 3.1 seconds.

Maybe I missed it but could you explain what the
participants were actually doing in this
experiment?

Were the subjects asked to fixate on a single
point in the display? It seems like eye movements, leading to
new views of the image, would have a lot to do with when (and whether)
there was a perceptual shift.

Here’s the description, from the published report:

“The Plasticene sheet was viewed directly an binocularly by
the O through a hole in the top of a box about 18 in. deep. An 8-in
diam circular apertured in a mask just above the plasticene defined
the field of view. A hidden horizontal 40W Lumiline light illuminated
the surface of the plasticene from the side below the mask, avoiding
the bias toward bubbles or dents which might be anticipated from top
or bottom lighting. Even so, almost all Os saw the bubble form when
first shown the display. This was unexpected, since the actual
three-dimensinal dented surface, not a flat photograph, was being
observed. Apart from the illuminated surface of the plasticene, the
room was darkened. No fixation point was used, and the Os were
encouraged to allow their viewpoint to rve over the surface. Blinking
was uncontrolled and unrecorded.”

Martin

[From Rick Marken (2004.05.08.950)]

Martin Taylor (2004.05.07 22.13) --

Because there are three B -> D events in the example, and for two of them the bubble phase lasts longer than 2 seconds. List them in order of how long the bubble phase lasted: 2.0, 3.1, 5.2. Up to two seconds after switching into the "bubble" phase, the subject always retained the perception of bubbles. Between 2 and 3.1 seconds, the subject retained the bubble phase on only 2/3 of the occasions. And so forth.

Thanks. Let me see if I understand this.

I take the "mortality" curves (in Figure 11 that you posted) to be plots of the fraction of trials on which the B or D perception has been retained up to that time (on the x axis). So as the curve slopes down to the right, there are fewer and fewer trials on which the perception has been maintained for that length of time. So the downward slope of the curve is proportional to the rate a which the perception "dies off". Is that a reasonable way to look at it?

If so, it looks like, for the first few days, the B perception dies off faster than the D perception for all 4 subjects (I take it that the columns are subjects?). But by the last day the B and D perceptions die off at about the same rate for all.

Is this what the data show?

Best

Rick

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Home 310 474-0313
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[Martin Taylor 2004.05.08.1410]

[From Rick Marken (2004.05.08.950)]

Martin Taylor (2004.05.07 22.13) --

Because there are three B -> D events in the example, and for two
of them the bubble phase lasts longer than 2 seconds. List them in
order of how long the bubble phase lasted: 2.0, 3.1, 5.2. Up to two
seconds after switching into the "bubble" phase, the subject always
retained the perception of bubbles. Between 2 and 3.1 seconds, the
subject retained the bubble phase on only 2/3 of the occasions. And
so forth.

Thanks. Let me see if I understand this.

I take the "mortality" curves (in Figure 11 that you posted) to be
plots of the fraction of trials on which the B or D perception has
been retained up to that time (on the x axis). So as the curve
slopes down to the right, there are fewer and fewer trials on which
the perception has been maintained for that length of time. So the
downward slope of the curve is proportional to the rate a which the
perception "dies off". Is that a reasonable way to look at it?

Correct. Just note that the Y axis is log probability, meaning that
the probability per unit time of a switch can be read off from the
local slope of the mortality curve. (See below for a use of this
property)

If so, it looks like, for the first few days, the B perception dies
off faster than the D perception for all 4 subjects (I take it that
the columns are subjects?).

No. All I posted was the set of fits for the subject with most
variation over the five days of the experiment. The rows are days,
the columns are 9-minute viewing periods.

But by the last day the B and D perceptions die off at about the
same rate for all.

Is this what the data show?

Yes, for this subject. The four subjects behaved differently in that
respect, so we didn't make any generalized conclusions of that
nature. For example, the other subject for whom we fitted the model
shows B and D to be about the same on day 1, with a big divergence on
later days.

You do, however, bring up an interesting point that remains puzzling.

We didn't fit the model to all four subjects, but we did take the
same kind of data from all of them. One subject showed no changes at
all on the first day, and none on the second day until the 18th
minute of the 36-minute trial. All the other subjects started seeing
changes immediately.

The interesting point is that so long as a subject was seeing changes
at all, the rate of changing out of the bubble phase remained
constant from day to day (though not necessarily within the day's
run), and was the same for all four subjects. We used the strange
measure of % changes per quarter-second, for reasons I can't
remember. That was taken from the average slope of the mortality
curve after the latency period.

Using this measure, all the subjects, on all days, had a transition
rate out of bubbles of 10 +-2 % per quarter second averaged over the
whole day's trials, but for all of them the changes out of the dent
phase (the physically realistic phase) increased over time, by
different amounts for different subjects. I still don't know what to
make of that observation.

Martin

[From Rick Marken (2004.05.08.1450)]

Martin Taylor (2004.05.08.1410) --

The interesting point is that so long as a subject was seeing changes
at all, the rate of changing out of the bubble phase remained
constant from day to day (though not necessarily within the day's
run), and was the same for all four subjects.

What were you trying to find out by doing this experiment? I agree that
the results are interesting. It looks like this one subject learned how
to switch perceptions (from B to D to B...) at a pretty regular rate.
My experience with ambiguous figures is that, indeed, switching takes
some learning. So there is an interesting kind of control of
perception that seems to be going on with these ambiguous figures that
involves imagination and/or foveating particular features of the
figure. Is that what you were studying? If so, it seems like it would
have been nice to see where on the bubble/dent pattern the subject was
looking when a shift (B to D and D to B) happened. Didn't Fred Attneave
do a study like this, where he looked at where the eye was looking
during figure reversals?

Best regards

Rick

···

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Richard S. Marken
Home 310 474-0313
Cell 310 729-1400

[From Rick Marken (2004.05.08.1450)]

Martin Taylor (2004.05.08.1410) --

The interesting point is that so long as a subject was seeing changes
at all, the rate of changing out of the bubble phase remained
constant from day to day (though not necessarily within the day's
run), and was the same for all four subjects.

What were you trying to find out by doing this experiment?

We were trying for a definitive proof that the cause of ambiguous
figure reversal was not satiation, fatigue, adaptation, or any other
of those near synonyms. It was a follow-up to the studies I had
earlier done with Bruce Henning on the multiplicity of forms seen in
the other visual and auditory ambiguous (polybiguous?-) static and
moving figures. Those results were strongly suggestive but not
definitive.

We needed some figure that people normally would see in only two
ways, so that we could get the mortality curves. If the tails of the
curves had a shallower slope than the middles of the curves,
satiation would be ruled out, but if the curves continued to steepen,
then satiation would be a viable possibility as an underlying process.

The modelling, and particularly its finding of the integer number of
units, was not initially contemplated. That was the contribution of
Keith Aldridge, who was a geophysics graduate student taking a summer
slumming in psychology. Interestingly, he later used exactly the same
model to look at reversals in the Earth's magnetic field, on the
supposition that the field might have several vortex centres (I
think). I don't know what results he go in that exercise.

I agree that
the results are interesting. It looks like this one subject learned how
to switch perceptions (from B to D to B...) at a pretty regular rate.

None of the subjects did that. If they had, the mortality curves
would have looked more like step functions. The "regularity" was in
the probability of a switch happening in any particular millisecond.
For switching out of B, that probability averaged over a day's run
was about the same for each subject and for each day. Not true for
switching out of D. In that case, the rate went up for each subject
over the five days of the study, and was at a different base rate for
each subject.

My experience with ambiguous figures is that, indeed, switching takes
some learning.

Without prejudicing the term, yes, it takes some time of looking
before switches happen, and I suppose you could call this "learning"
in the widest sense of the term. But one thing we noted in ourselves
and all the pre-experimental trial subjects, as well as the actual
subjects, was that "the stinulus figure has the ... advantage that
the reversals seem to be very resistant to voluntary techniques of
induction. After a minute or two of observation, Os accustomed to
being able to reverse other ambiguous figures almost at will found
themselves unable to influence the reversals of the bubbles and
dents, even by the use of various tricks, such as blinking, fixation
shifts, or the interposition of other objects."

So I don't think the term "learning" is appropriate in its everyday sense.

Something else is happening. It's easy enough to try for yourself.
You could get a chunk of plasticene or its modern equivalent, flatten
it and dent it all over with a pingpong ball, and just look at it.
That might work, without the restrictive box we used, at least if the
direction of lighting was made non-obvious other than being from one
side or the other. I find lunar or Martian crater or canyon
photographs often work, too.

Martin