Tuesday, March 29, 2011

The Apparent Location of Mirror Images

When I gaze into a mirror, does it look like there's someone a few feet away gazing back at me? (Someone who looks a lot like me, though perhaps a bit older and grumpier.) Or does it look like I'm standing where I in fact am, in the middle of the bathroom? Or does it somehow look both ways? Suppose my son is sneaking up behind me and I see him in the same mirror. Does it look like he is seven feet in front of me, sneaking up behind the dope in the mirror and I only infer that he is actually behind me? Or does he simply look, instead, one foot behind me?

Suppose I'm in a new restaurant and it takes me a moment to notice that one wall is a mirror. Surely, before I notice, the table that I'm looking at in the mirror appears to me to be in a location other than its real location. Right? Now, after I notice that it's a mirror, does the table look to be in a different place than it looked to be a moment ago? I'm inclined to say that in the dominant sense of "apparent location", the apparent location of the table is just the same, but now I'm wise to it and I know its apparent location isn't its real location. On the other hand, though, when I look in the rear-view mirror in my car I want to say that it looks like that Mazda is coming up fast behind me, not that it looks like there is a Mazda up in space somewhere in front of me.

What is the difference between these cases that makes me want to treat them differently? Does it have to do with familiarity and skill? I guess that's what I'm tempted to say. But then it seems to follow that, with enough skill, things will look veridical through all kinds of reflections, refractions, and distortions. Does the oar angling into water really look straight to the skilled punter? With enough skill, could even the image in a carnival mirror look perfectly veridical? Part of me wants to resist at least that last thought, but I'm not sure how to do so and still say all the other things I want to say.

One resolution might be to strip away the specifically sensory, spatial sense of "looks" or "appears", assimilating to cases like "It looks like you're headed for a C" as I gaze over someone's final exam (cases which, in turn, might be assimilated to entirely non-visual cases like "It looks like we might be in Libya a long time" said after hearing a radio broadcast). That maneuver doesn't satisfy me, though: I want, if I can have it, some robustly visuospatial sense in which the Mazda looks like it's behind me and yet the restaurant table looks like it's in front of me.

(See also "Objects in Mirror Are Closer Than They Appear".)


Jonas said...

Very cool post, thank you.

I had never given this phenomenon much thought, but indeed I have noticed the confusion from realizing something was a mirror reflection.

We sometimes tend to make fun of animals not coping so well with mirrors, but in reality we just cover up our own uneasiness with them.

It all starts with the question why left and right are switched. Then there's the phenomenon of showing someone if they have something on their face. Do you show it on the "correct" side or on your mirror side.

Fascinating, thank you!

Anonymous said...

"Does the oar angling into water really look straight to the skilled punter? With enough skill, could even the image in a carnival mirror look perfectly veridical?"

I think the answer to this has to be yes because as I understand it our eyes see a bit of a mess before it is processed by our brains - it is almost as if we are looking in a distorted mirror anyway.

Your difference would be that some things may be more difficult or less important to learn this way.


Arnold Trehub said...

When you look into what you know to be a mirror you see the image in the mirror as a representation of something (your face or something else). However, you see the mirror in front of you as the real thing.

Eric Schwitzgebel said...

@ Arnold: Maybe so. But part of me -- the larger part, I suppose -- thinks that often we don't experience the mirror as a flat surface containing a representation of the object, but rather just see the object as if in a certain location.

Eric Schwitzgebel said...

@ GNZ: That's definitely an appealing view. If I could in good conscience adopt it, lots of other things would fall neatly into line. The problem is, there is part of me that finds it pretty hard to accept.

Arnold Trehub said...

Eric: "But part of me -- the larger part, I suppose -- thinks that often we don't experience the mirror as a flat surface containing a representation of the object, but rather just see the object as if in a certain location."

If I look at a perspective drawing of the interior of a room, I might see a lamp at a certain location. But I experience the lamp at its location in the image as a *representation* of some lamp. When I look at myself in the mirror, I see the parts of my body represented in unusual places with respect to ME. For example, if I raise my right arm, my mirror image raises its left arm. If I hold a round mirror beside my face, I can see what seems to be a multiple succession of round images containing my face becoming smaller as they recede in the perspectival distance. Significantly, it is all perceived in 2D perspective and not with stereopsis. The apparent depth location of objects in rear view mirrors can change because of micropsia caused by fixating a near object (the mirror). The same thing can happen with the moon illusion. If you look at a full moon near the horizon, it looks large; but if you make a loose fist and look at the same moon through the "tube" of your fist it looks tiny. The edge of the "tube" induces micropsia.

Eric Schwitzgebel said...

Thanks for the comment, Arnold! Do you have a good source on stereopsis or its lack in mirrors? Looking in a mirror now, it seems like the focal distance of objects in mirrors is based on apparent distance in the mirror: I dont seem to be able to bring all reflected objects into focus simultaneously by focusing on the plane of the mirror. I'm thinking that vergence too isn't all just to the plane of the mirror. I am definitely open to correction on these points.

Arnold Trehub said...


I don't know much about the physical optics of mirrors but I can offer these observations:

1. When I stand about 3 feet away from a large mirror and turn my head from side to side I see my eyes move together in the opposite direction in relation to the bridge of my nose in the mirror image.

2. When I move my head toward the mirror I can detect no movement of my eyes inward toward the bridge of my nose. This is true even when I bring my nose to within a few inches of the mirror.

So I can detect no evidence of vergence in mirror viewing. Try it yourself. What does this mean to you?

Eric Schwitzgebel said...

Perhaps my comment about vergence was too telegraphic. My impression is the same as yours. This suggests that vergence matches the reflective distance of the target object, not the surface of the mirror. That would seem to be in tension with a simplistic view of the scene as experienced as being on the surface of the mirror. I had thought maybe in your earlier comment you were trying to support the latter view using facts about binocular vision, which didn't seem right to me.