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A New Reversible Figure 

and an Old One

John F. Kihlstrom

University of California, Berkeley


Someone who saw the title for this paper asked me if I had become a perceptionist. The answer is "no", although I do have some perceptual interests -- chiefly in the phenomena of what I have called implicit perception (Kihlstrom, 1996; Kihlstrom, Barnhardt, & Tataryn, 1992). But I've also been intrigued for a long time in the reversible or ambiguous figures, and talk about them a lot in my teaching of the introductory course. And when I was at Arizona, I collaborated with my then-colleague Mary Peterson on some studies of reversible mental images -- showing, to our satisfaction, that images could be reversed after all (Peterson, Kihlstrom, Rose, & Glisky, 1992). As a consequence of this work, people in both our labs began to notice reversible images everywhere.

002Mobile.jpg (68853 bytes)And that's how it came to be that one night I was lying awake, looking at a mobile of whales that my spouse Lucy and I had hung in our bedroom, and all of a sudden, one of the whales -- a humpback, to be precise -- viewed in darkness-induced silhouette, reversed itself into something else entirely.


            (49455 bytes)Which is the creation story of the Arizona Whale-Kangaroo -- this version created with the help of Elsie Vezey.



In a pilot study, conducted at the University of Arizona, we tried out different versions of the figure, varying in body morphology (fat vs. thin) and orientation (whale's nose pointing at 4:00 vs. 5:00). Our instructions were simple:

"I'm going to show you a picture of an ambiguous figure. An ambiguous figure is a figure that can represent more than one thing. Please look at the picture and then list all the things it looks like to you.

The subjects listed lots of variants on whales and kangaroos: whale, dolphin, shark, seal, fish; kangaroo, fox, dog, rabbit, animal running. These were considered equivalent because they preserved the same object-centered frame of reference (top/bottom, front/back) and general semantic category.  A few subjects saw the whale as an airplane, and the kangaroo as a bird (on a branch). Surprisingly many subjects saw the figure as a chair.

004Pilot1.jpg (52620 bytes)For frequency, there was a significant main effect of percept, and a significant interaction of percept with morphology. More subjects saw the whale than saw the kangaroo, and more subjects saw the kangaroo when it was thin. Most subjects who saw both figures saw the whale first.


Subjects were also asked to rate each of their percepts on a 1-5 scale:

1 = Not very clear, vaguely resembles the object;

5 = Very distinct, clearly resembles the object.

Again, there were significant effects of percept and morphology. The figure is clearly a more convincing rendition of a whale, though the thin kangaroo was better than the fat one.

005Pilot2.jpg (56205 bytes)In a follow-up analysis of the ratings, we considered only those subjects who actually saw both the whale and the kangaroo -- about 57% of the total sample. The rating of the kangaroo improved considerably, though the figure is still a better whale than it is a kangaroo.


For the record, we also did an experiment in which we reflected the thin version of the figure, oriented to 4:00, reflected left to right. There was no effect of reflection on either the frequency of subjects who saw the kangaroo, or on their ratings of the kangaroo.

While it is known that stimulus orientation affects perception, little is known about orientation effects in the perception of ambiguous figures.

In the preliminary study, there were no significant effects of orientation. On the other hand, both the 4:00 and 5:00 versions of the figure were close to what we might think of as the canonical orientation for a kangaroo.

Accordingly, we decided to carry out a more systematic study. Beginning with the whale's nose pointing straight upward, we rotated the figure every 30o right around a clockface.

006CrossNat.jpg (78003 bytes)At the same time, given the nature of the figure, it seemed obviously interesting to compare the performance of North American subjects to subjects from Australia, who have had a lot more experience with kangaroos.


We collected out first Australian sample at Macquarie University, with the help of Kevin McConkey and his students. For reasons that will become clear later, we collected another Australian sample, at the University of New South Wales, with the help of Jacquelyn Cranney (McConkey and Cranney had been sabbatical visitors to Arizona).

Let's start with the North American subjects first.

007AmFreq.jpg (68019 bytes)Every one of the subjects in the new sample saw the whale, or some equivalent percept, at every orientation. But only about 25% of the subjects saw the kangaroo, or its equivalent, and most of those -- more than half of the total -- were at the canonical 4:00 and 5:00 orientations.  There's obviously no effect of orientation on the perception of the whale.  However, the effect of orientation on perception of the kangaroo was significant.

This time, a small minority of subjects saw the kangaroo first -- 5.5% of those who saw the kangaroo. But 5 of these 6 subjects viewed the 4:00 or 5:00 rotation, again attesting to the importance of the canonical orientation.

008AmResem.jpg (66257 bytes)There's a similar story when we look at ratings of the two percepts.  Here we're looking at the ratings made by subjects who actually saw both the whale and the kangaroo.  There's enough variability in the ratings to bring out a small but significant main effect of orientation on perception of the whale, but there's no systematic effect.  With the kangaroo, however, the effect of orientation is both big and systematic: the figure is rated as a better kangaroo when presented in its canonical orientation

009CompFreqWhale.jpg (68677 bytes)Adding in the subjects from Down Under, all the Australian subjects saw the whale, regardless of orientation.



010CompFreqKanga.jpg (58070 bytes)But more than twice as many Australian subjects, a little more than half, also saw the kangaroo.  Similarly, about twice as many Australians, 10.1%, saw the kangaroo first.  There was, again, a significant effect of orientation, with the canonical views eliciting the most percepts, but note that lots of Australians saw the kangaroo at noncanonical orientations.


011CompResemWhale.jpg (65796 bytes)Overall, the Australian subjects gave the whale a somewhat lower resemblance rating than did the North Americans.



012CompResemKanga.jpg (64086 bytes)But, interestingly, they tended to be more accepting of the kangaroo at the noncanonical orientations.



You can see the effects of orientation and experience most clearly by collapsing all the orientations into two categories: canonical, meaning 120 and 150 degrees; and everything else.

013CompFreqCanon.jpg (54182 bytes)Everybody sees the whale, no matter what the orientation.  Both groups were more likely to see the kangaroo at its canonical orientation.  But the Australians were more likely to see the kangaroo, regardless of orientation.


014CompResemCanon.jpg (58567 bytes)Turning to the resemblance ratings, we get a bunch of significant interactions:



Orientation x Percept: Orientation makes a bigger difference to the perception of the kangaroo than to the perception of the whale.
Orientation x Sample: The Australian subjects were less affected by orientation than the American subjects.
Percept x Sample: The Australian subjects thought the whale resembled a whale less than the American subjects did.
And finally, the piece de resistance, the three-way interaction of Sample, Percept, and Orientation (just barely, but it's there): The resemblance ratings of the kangaroo were more affected by orientation for the American subjects than for the Australians.

An analysis by Mary Peterson makes is clear that the Arizona Whale-Kangaroo involves a number of different perceptual transformations:

First, there is a reference-frame realignment, in which the front of the whale becomes the back of the kangaroo.
Then, there are reconstruals of the component parts of the figure:
the whale's flipper becomes the kangaroo's foot, while the whale's tail becomes the nose and ears;
or, even without a reference-frame reversal, the whale's flipper becomes the airplane's wing;
or, again, without a reference-frame reversal, the kangaroo's leg becomes the branch on which the bird sits.
In addition, there are reconstruals of the object as a whole, again without reversing the reference frame:
the whale can also be seen as a dolphin, and the kangaroo can also be seen as a fox.

Unfortunately, it's not clear from our present data whether the subjects actually consider the whale and the dolphin (or the kangaroo and the fox) as two different percepts, as opposed to two different labels for the same percept.

Still, the analysis suggests that there are at least two, perhaps three, different kinds of reversible or ambiguous figures.

Figures that are subject to reference-frame realignments, such as the Necker Cube.
Figures that are subject to figure-ground reversals, such as Rubin's Vase-Faces.
Figures that are subject to reconstruals of the whole or of component parts.

AWK involves a reference-frame alignment and reconstrual, but not figure-ground reversal.

Along these lines, we examined the organization of the subjects perception of the whale-kangaroo figure. First, we classified every percept listed by our subjects as either a reference-frame reversal or a reconstrual. Then, in an analysis modeled on the old literature on the organization of free recall, we examined the clustering of percepts by reference frame.

            (44067 bytes)The American subjects showed a strong tendency to cluster their percepts by reference frame. That is, they seemed to exhaust what they could see within a particular reference frame, first the whale and then other whale-like things, and then -- perhaps -- flip the reference frame, see the kangaroo, and then go on to see other kangaroo-like things.  By contrast, the Australian subjects showed absolutely no tendency to cluster their percepts by reference frame. As a rule, they would see the whale, and then flip the reference-frame, see the kangaroo, and then perhaps flip again to see a whale-like thing, and then flip again. Whereas the American subjects showed very high levels of clustering, the Australian subjects actually showed clustering at levels less than chance.

That difference was so interesting that we wanted to see it again, which is why we collected the second dataset at New South Wales.  Here we see definitive proof of the second rule of experimental research: never try to replicate an interesting effect.  With respect to the effects of orientation, the New South Wales students performed like the Macquarie students had.  But, unfortunately, the New South Wales subjects showed significant levels of clustering. The clustering at New South Wales was still significantly lower than what we observed at Arizona, but not the absolutely null level observed at Macquarie.

So, aside from introducing this new ambiguous figure, we have some interesting differences in perception of the figure between American and Australian subjects.

We tend to think of these as variations on the principle that experience, stored in memory, can affect perception. Australians have more contact with kangaroos than Americans do, and this leads them to see the kangaroo more readily than the Americans do. Think of it as a kind of priming effect -- but a prime that comes from experience, and culture, rather than the immediate stimulus environment.

Ambiguity is not just a property of the stimulus --

it also resides in the mind of the perceiver.

019GypsyGirl.jpg (54577 bytes)Of course, the Whale-Kangaroo is not perfectly ambiguous -- it's a better whale than it is a kangaroo. I suppose we could work on it to make it more equi-ambiguous, but when I consider the amount of effort that Gerald Fisher went to to get a perfectly ambiguous versions of the Gypsy-Girl and other figures (Fisher, 1967a, 1967b, 1967c, 1968), I get tired.


Still, it's interesting to note that many other ambiguous figures are also not perfectly equi-ambiguous.

020GirgusRubin.jpg (54157 bytes)Interestingly, there's not a great deal of normative data on these figures, but recall that Irvin Rock and his colleagues showed long ago that subjects may not reverse even classic reversible figures unless they're told they're reversible (Girgus, Rock, & Egatz, 1977).


021LeeperBoring.jpg (67524 bytes)Consider, for example, Leeper's study of Boring's Wife-Mother-in-Law figure, which found that the Wife occurs much more frequently as the first percept than does the Mother-in-Law (Leeper, 1935).



022JastrowDuck.jpg (83235 bytes)Jastrow's Rabbit-Duck also appears to be imperfectly ambiguous. I've long been interested in this figure, because Jastrow is a special hero of mine. When I saw Jastrow's figure attributed to Wittgenstein in a recent journal article, I dug around in its history a little. Jastrow first published the figure in 1899, in an article in Popular Science Monthly, as an illustration of the constructivist view of perception. 

Read article on Jastrow and the Duck-Rabbit figure.

023DuckSources.jpg (124254 bytes)Jastrow himself discovered the figure in the cartoon page of the old Harper's Weekly (1892), which reprinted it in turn from Die Fliegende Blatter, a German humor magazine.



024DuckVariations.jpg (105373 bytes)Here's Witgenstein's version, from the Philosophical Investigations (Wittgenstein, 1953/1958), which Gombrich picked up in Art and Illusion (Gombrich, 1960).  And also a full-body version of the Duck-Rabbit, created by Walter Ehrenstein, a German psychologist, in 1930 (Ehrenstein, 1930, 1954).


025DuckDiscern.jpg (48212 bytes)On the centennial of Jastrow's original publication of the Duck-Rabbit, Peter Brugger, a Swiss psychologist, tested 12 different versions of the Duck-Rabbit (Brugger, 1999). Neither Jastrow's original, nor Wittgenstein's or Ehrenstein's versions, proved to be perfectly ambiguous. Even when subjects were informed about the ambiguity, they rated the figure a better Rabbit than a Duck.


026DuckEaster.jpg (52587 bytes)Returning to the matter of experience and mental set, Brugger and his wife, Susanne, also did a lovely study in which they asked children what they saw in a version of the Wittgenstein figure (Brugger & Brugger, 1993). When tested in October, the children were more likely to see the figure as a Duck. But when tested on Easter Sunday, they were more likely to see it as a rabbit!


Click on this image for a high-quality JPEG of the Arizona Whale-Kangaroo


Author Note

Paper presented at the annual meeting of the Society of Experimental Psychologists, La Jolla, Ca., March 25, 2006.



Brugger, P. (1999). One hundred years of an ambiguous figure: Happy birthday, duck/rabbit! Perceptual & Motor Skills, 89(3 Pt 1), 973-977.

Brugger, P., & Brugger, S. (1993). The Easter Bunny in October: Is it disguised as a duck? Perceptual & Motor Skills, 76, 577-578.

Ehrenstein, W. (1930). Untersuchungen uber Figur-Grund-Fragen. Zeitschrift fur Psychologie, 117, 339-412.

Ehrenstein, W. (1954). Probleme der anzheitspsychologischen Wahrnehmungslehre [Problems of a holistic theory of perception] (3rd ed.). Leipzig: Barth Verlag.

Fisher, G. H. (1967a). Ambiguous figure treatments in the art of Salvador Dali. Perception & Psychophysics, 2, 328-330.

Fisher, G. H. (1967b). Measuring ambiguity. American Journal of Psychology, 80, 541-557.

Fisher, G. H. (1967c). Preparation of ambiguous stimulus materials. Perception & Psychophysics, 2, 421-422.

Fisher, G. H. (1968). Ambiguity of form: Old and new. Perception & Psychophysics, 4, 189-192.

Girgus, J. J., Rock, I., & Egatz, R. (1977). The effect of knowledge of reversibility on the reversibility of ambiguous figures. Perception & Psychophysics, 22, 550-556.

Gombrich, E. H. (1960). Art and Illusion.  Princeton, N.J.: Princeton University Press.

Kihlstrom, J. F. (1996). Perception without awareness of what is perceived, learning without awareness of what is learned. In M. Velmans (Ed.), The science of consciousness: Psychological, neuropsychological and clinical reviews. (pp. 23-46). London, England UK: Routledge.

Kihlstrom, J. F., Barnhardt, T. M., & Tataryn, D. J. (1992). Implicit perception. In R. F. Bornstein & T. S. Pittman (Eds.), Perception without awareness: Cognitive, clinical, and social perspectives. (pp. 17-54). New York, NY: Guilford.

Leeper, R. W. (1935). A study of a neglected portion of the field of learning -- the development of sensory organization. Journal of General Psychology, 46, 41-75.

Peterson, M. A., Kihlstrom, J. F., Rose, P. M., & Glisky, M. L. (1992). Mental images can be ambiguous: Reconstruals and reference-frame reversals. Memory & Cognition, 20(2), 107-123.

Wittgenstein, L. (1953/1958). Philosophical investigations (G. E. M. Anscombe, Trans. 2nd ed.). Oxford, U.K.: Blackwell.


This page last revised 05/25/11.