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I'm not sure whether this question belongs here, so I apologize in advance if it does not, however, I think it's worth a try. Also please excuse my poor English, I am not native English speaker.

My question is:

How do people recognize symmetric shapes?

By "symmetry" I mean only reflection with respect to axis in two dimensions and reflection with respect to a plane in three dimensions.

I try to specify what I have in mind.

I don't find strange that one can recognize the same shape rotated in some way, since one has plenty experience "from real life" by which this ability can be justified (If I see the letter "F" written on a piece of paper, after rotating the paper by hand, I still see the same object even though now it looks different). So one could argue that the ability to recognize some shape after a rotation is an evolutionarily developed skill.

However, I don't think that this kind of argument can be applied to reflections. The only experience with this can be obtained by (versions of) observing mirrored images of things. And even though the "skill to recognize a reflection of a tiger on a surface of a pond" can be a good skill contributing to survival, this still does not explain why it is easier to recognize symmetric shapes than recognizing the same shapes, when one of them is rotated in some non-trivial way.

In particular, what I find really puzzling is this: Suppose I know a person with a strangely shaped scar on his left cheek. Someone shows me a reflected picture of that person (so on the picture, the scar is seemingly on the right cheek, etc.) and I still recognize him immediately, and probably I would not even realize the image is reflected. It seems to me that the ability to "ignore" the differences between the original image and reflected image is much stronger than the ability to ignore the difference between an image and the same image rotated.

Are there some explanations of this from evolutionary and/or cognitive science's point of view?

I would also like to stress that this is not a question about the ability to recognize oneself in a mirror.

Also, I would appreciate any references, where similar kinds of questions are addressed.

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I agree this may not belong here. But I also have a guess to offer. So I am going to answer as though it fits.

We are equipped with redundant identical machinery for almost all of our sensory apparatus -- two ears, two eyes, etc. It may be that it is harder to break the symmetry than to allow it. If we want to be able to transfer the acquired skills of the dominant eye easily to the other eye in case an eye goes blind, the easiest way is to set the whole system up symmetrically. In that case it is not work to acquire a sense of symmetry, it is work to create the distinction.

I would conjecture that the less-evolved behavior is not to be able to tell sides apart in memory. I think we see this in folks who have a hard time learning and remembering right from left (myself included). And I think it is also a factor in referred pain, where one limb goes numb and the other one hurts in the same location. Also, some reflexes fail symmetrically, as where you see something peripherally and jerk the wrong way. Further, it is easier, once you know how to write with one hand, to learn how to write backward than forward with your other hand (try it sometime) -- the backward left-handed motions match the forward right-handed motions.

Such failures are more likely to be falling back on the simpler system than to be over-correction by an acquired ability. So there is evidence for the idea that your internal sense of space is originally symmetrical, and you actually do work to keep it lateralized.

Once the sense of symmetry is there, we know that humans use it as a major factor in our measure of beauty, as do other species. Since diseases and other hardships are less likely to affect the stronger side of your body as much as the weaker, good symmetry implies either good immunity from major diseases, or good skills of self-protection. Once deployed, the accidentally afforded ability would never be cleaned up as useless functionality.

  • Thank you for the answer; this really seems convincing to me (for example, it corresponds to the fact that left-handed children tend to write reversed letters from right to left). – PavelC Oct 22 '14 at 20:13
  • Also (sadly for me), there is good evidence that the ambidextrous are less developed than right or left handers on average intellectually, emotionally, etc. mentalfloss.com/article/30667/11-facts-about-ambidextrous. To me that says handedness is work. – user9166 Oct 22 '14 at 20:17
  • We need two ears for stereocopic sound - so not quite redundant! – Mozibur Ullah Oct 22 '14 at 21:21
  • And theoretically, binocular vision matters, too. But both are 90% redundant. We do just fine off alternate cues with one ear or one eye. I am certain most of their survival value is in the redundancy, not stereoscopic/stereophonic processing. – user9166 Oct 22 '14 at 21:45

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