David Navon (2002) It Takes two for an Inverse Relationship. Psycoloquy: 13(011) Mirror Reversal (5)

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Psycoloquy 13(011): It Takes two for an Inverse Relationship

Reply to Burgess on Navon on Mirror-Reversal

David Navon



Burgess (2001) discusses, in his words, "the effect of mirror reflection on chirality and handedness". In my view, the known effect of mirror optics on what it shows is part of the question addressed in the target article, not the answer to it. The phenomenon in question is the cognition of mirror viewers that what they see in it in a frontal view reverses position along the horizontal axis of the facet facing the mirror plane. The puzzle is why that is true only of that planar axis GIVEN what we know about mirror optics. Both the account of the phenomenon and the solution of the puzzle are argued to transcend the optics of the mirror. Following that, Burgess' claim that the puzzle is notation-dependent is shown to be false.


spatial cognition, mirror vision, mirror reversal, left-right reversal, perceptual frame of reference, object perception, frontal encounter, enantiomorphs, chirality, handedness
1. The range of stances about the puzzle of mirror reversal is broad enough to encompass a camp of puzzle deniers. Their main theme is that nothing would have looked puzzling had we focused on optics and geometry rather than let ourselves being confused by misleading concepts, especially psychological ones.

2. Burgess (2001) appears to belong to that camp. He puts the full blame on the mirror. To do that, he tells us much about the mirror image. Although he does not describe the optical process, he adduces a nice analogy to describe its product. There is nothing wrong with his description. Sure enough, the object in the mirror differs from the mirrored object. Sure enough, the nature of the difference in a frontal view is "a reversal along the axis perpendicular to the mirror's plane" (Navon, 2001, paragraph 2). Sure enough, whatever gives rise to that reversal is "the optics of the mirror" (ibid). Thus, aside of some terminological niceties, much of Burgess' exposition boils down to about the same as what was posited in the target article, albeit briefly, about mirror reflection.

I. Beyond mirror optics

3. The problem is in implying that since all that is known, there is nothing left to be puzzled about in mirror perception. Note that the issue is not the nature of the difference between any solid object and its mirror counterpart. That is well within the realm of geometry. The issue starts with a pervasive human cognition - that the mirror image gives us the wrong idea about left and right. The source of that cognition is hardly the ex-definitio fact that any object and its mirror counterpart are chiral pair-mates, aka enantiomorphs of each other. People rarely attend to that. They rather usually attend to a particular facet of a mirrored object, the one facing them. They often note that what they see deviates from what they would have seen had they faced the facet of the object itself.

4. Why is that? Replying by something like "because a mirror image is an enantiomorph of the object" just explains the phenomenon away. Worse yet, it acts to divert attention from three observations that are crucial for the real explanation - (a) although an object and its mirror counterpart are ENANTIOMORPHIC pair-mates which by definition differ in intrinsic handedness, the mirror does NOT invert any frontal axis: the facet facing the mirror perfectly overlaps with the corresponding facet of the mirror counterpart, (b) some cross-lateral inversion IS, however, present in the diametrically opposed case, namely when corresponding facets of two IDENTICAL objects face each other, (c) the contrast between case (a) and case (b) entails that the object facet which the viewer sees in the mirror deviates from what she would have seen had she faced the facet of the object itself. That consequence is actually the cognition in question, hence the latter must be due to both (a) and (b).

5. To illustrate, when I put my right hand palm against the mirror, the hand in the mirror is an enantiomorph of my real hand, yet the palm image perfectly overlaps with my real palm. I know, however, that such an overlap is not obtained when my right palm faces any other right palm, hence that my palm image in the mirror differs from how my right palm would look to any viewer in a prototypical frontal encounter. I could easily verify that by just flipping my hand back, but there is no need for that, since that knowledge is embodied in my perceptual system.

6. Now that the source of the cognition is elucidated, let us move on and examine the puzzle. People always relate to the deviation in (c) as left-right reversal, which seems puzzling in view of fact that the mirror does not discriminate between frontal axes. Actually, as stated in (a), the mirror does not invert any of them. It follows that the answer is to be sought in (b). Alas, the answer is well concealed there, because encounters of corresponding facets may vary on planar orientation.

7. The key is to note that the viewer is interested just in one of those orientations, the canonical one. When wondering what she would see were she to face the facet of the object itself she actually means "what would I see were I to face it in a prototypical encounter?" Since a prototypical encounter entails left-right inversion in our environment, the deviation detected by a viewer residing on Earth is regarded as left-right reversal.

8. Thus, the puzzle is not eliminated by knowing that the object and its mirror counterpart are chiral pair-mates neither by understanding why people perceive the "frontal" facet of the latter to be left-right reversed. The word "puzzle", as might be recalled, denotes a psychological state of bewilderment before a comprehensive solution is found. In the case in question, people are puzzled not so much because they cannot explain why they feel that in a frontal view the mirror reverses left and right of the viewed stimulus, rather because they fail to understand why they do not similarly perceive top and bottom as being reversed. The centuries-old debate about how to resolve the puzzle indicates that not only laypersons have been puzzled. Many scholars have found themselves even more puzzled, knowing that the mirror does not optically discriminate between the two axes.

II. A notational artifact?

9. Nonetheless, Burgess seems to suggest that mirror reversal just appears puzzling. In a sense, that is true of any solved puzzle. But Burgess actually means that in a stronger sense - that people are puzzled by what they see in the mirror because they use the "wrong" coordinate system in discussing it: "The mistake is to define the set of axes intrinsically. In this case there is a different set of axes for each object. If the mistake is not realized, one questions why left-right organization appears to have changed" (Burgess, 2001, paragraph 8). Is it so?

10. That prototypical frontal ENCOUNTERS are said to be characterized by left-right inversion follows, of course, from the convenient (and quite prevalent) choice to refer to them in terms of object-centered coordinate systems (as explicated in Navon, 2001, paragraph 17). However, unlike Burgess seems to believe, that choice is immaterial for left-right MIRROR reversal, which is the real issue.

11. Suppose the viewer rather elected to use egocentric coordinates for describing both himself and any frontally encountered person or object. In that case he would say, for example, that the wristwatch worn by his encounter-mate is on her RIGHT (since it is opposite to his own right hand). Yet, by the same logic, when seeing his own mirror image in a frontal view, the viewer would have to say that the wristwatch of his mirror image is on its LEFT (since it is opposite to his own left hand). He must be straightforwardly led then into deducing that his mirror image fails to mimic the spatial relationship with himself held by any real mate of frontal encounter: Its wristwatch is found in the other side of his own midline than is the wristwatch of a typical encounter-mate. Wouldn't he be right in concluding that the mirror image shows him nearly what he would see had he frontally met a copy of himself, except for cross-lateral reversal?

12. It can be easily shown by a similar argument, that the same conclusion would have been reached had the viewer refrained from mentioning the words "left" and "right" and rather used environmental coordinates (e.g., east and west) instead.

13. Hence, regardless of which system of spatial notation is preferred, two claims must be true - (One) "objectively, the spatial relationship between an object and its mirror image differs from the spatial relationship between two objects in a prototypical frontal encounter" (Navon, 2001, paragraph 16), (Two) "in our ecology, [the] axis [perceived to be reversed by the mirror] happens to be the horizontal one" (ibid, paragraph 17). Thus, there is no "correct" way of spatial notation within which the puzzle vanishes, as there is no "mistaken" way that gives rise to it. And that is even before we start to consider cognitive psychology.

14. The claim that the puzzle is notation-dependent, which Burgess shares with quite a few other authors, presumably stems from adopting an overly general frame of reference. The difference between two chiral objects is in their intrinsic structure, not in some spatial relationship between them, since they can be positioned in many ways with respect to each other. On the other hand, there IS a definite spatial relationship holding between facets of two objects viewed from the same angle. A mirror frontal view is analogous to the latter case: A given facet image is being compared with a well-defined, unique anchor - the putative view of that facet had it been frontally encountered in real life. The outcome of that comparison, at least in our environment, is unmistakable - the two are the same except for reversal along the left-right axis.

15. Thus, the issue is real and the puzzle is factual. Since both involve human cognition, no wonder that the solution does.

III. The entire picture

16. An inverse relationship relates two relata. Focusing on just one of them makes sense about as arguing that food scarcity is not due to large food demand, only to small food supply.

17. In the case of mirror reversal of X, the viewer considers two relata: r1, the mirror image of X, and r2, his memory of the image of X when actually encountered. Mirror optics generates a virtual chiral counterpart of X that is reversed to it just on one axis, the one perpendicular to the mirror surface. Hence, r1 is NOT reversed to the facet of X that faces the mirror on any frontal axis. On the other hand, since in a real encounter with X its position is reversed to its position when aligned with the viewer on all axes but one, r2 IS reversed to the facet of X that faces the mirror, hence to r1 as well, on any frontal axis but one. Which axis is not reversed? That depends on what is considered by the viewer as a real encounter for the sake of comparison. In our environment, it is an encounter in which, in terms of object-centered coordinates, top is opposite to top yet left is opposite to right. Accordingly, we feel that r1 and r2 are related by left-right inversion.


Burgess, N. (2001). The effect of mirror-reflection on chirality and handedness can be explained without social psychology: Commentary on Navon on mirror reversal. Psycoloquy, 12(031). http://www.cogsci.soton.ac.uk/psyc-bin/newpsy?12.031

Navon, D. (2001). The puzzle of mirror reversal: A view from Clockland. Psycoloquy, 12(017). http://www.cogsci.soton.ac.uk/psyc-bin/newpsy?12.017

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