Mirror Image Puzzle

Below is a puzzle I have come across on two different occasions, the latest one being when reading the introduction to Gary Drescher’s book “Good and Real: Demystifying Paradoxes from Physics to Ethics” (which I did not come close to finishing due to boredom, although I may return to it). Based on the amount of exposure I get to puzzles and brainteasers, I’d expect to have come across this one more than twice, as it is a good one. You need no special education at all to understand the question, so no one can claim exemption due to their major or specialty in life!

Puzzle: Why does a mirror reverse the left and right directions, but not the up and down directions? (In other words: Your mirror image wears his watch on his right hand. Why doesn’t he wear his shoes on his head?)

No monetary reward for the solution to this one, as there is (still unclaimed!) for the last one.

Update Tues 7pm: Recommended way of answering: post the answer in the comments, but in a foreign language (ideally one with an alphabet different from English’s), in order to allow readers to browse the comments, and decipher only the answers they’re interested in (you can use an online translator both to encode and to decipher the answers).

Update Thurs 11am: Spoilers in comments

Good and Real: Demystifying Paradoxes from Physics to Ethics

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3 Responses to Mirror Image Puzzle

  1. Tim Olson says:

    This is actually not a physical effect but a psychological one. The mirror shows your body as if you’re seeing it from behind, but you see your front surface not the back. It’s like this: imagine a photo of you printed on thin paper, then hold the paper up to the light and look through the back of the paper. That’s what you see in the mirror: the image of your frontside, as viewed from the back, “through” your body. Now, since the human body has a vertical axis of symmetry, when our brains see the “outside-in” visual in the mirror, they conflate the left and right sides and mentally rotate the mirror object instead of understanding the “outside-in” reflection. Your brain imagines that the image (the front side of the paper) has rotated around to face you. The brain doesn’t play this trick in the other direction because your head doesn’t look anything like your feet. So basically, your brain is falsely flipping left and right because they look the same and your brain doesn’t understand the technicalities of a mirror projection.

    Here’s another related teaser:
    The wavelengths of light in the visible spectrum follows the rainbow: red, orange, yellow, green, blue, purple. When mixing colors together, it may appear at first that our brains average the wavelengths of the component colors. For example, red + yellow = orange (orange is in-between red and yellow), or yellow + blue = green (green is in-between yellow and blue). Now the question is: why do red and blue make purple?

  2. Jonathan says:


    Thanks for the reply. That is an interesting way of thinking about the problem. And you can consider what would happen if in fact your right hand looked very different from your left hand, while your head looked basically like your feet, e.g. suppose your right hand looked like a guitar and your left hand looked like a pencil. And suppose you just define “head” as the part of the body that is to the “left” of the guitar hand (i.e. to the left from the guitar’s perspective), while “feet” are to the right of the guitar hand. Then, you might say “when I move my guitar hand, so does my image, yet when I move my head, he moves his feet. Why is it that the horizontal axis remains intact while the vertical axis is flipped?” So it is a matter of choosing which axis is the “reference axis,” and as you say symmetry biases us towards choosing the vertical axis.

    On your puzzle, I’d say that the wavelength averaging of the first 2 examples is a coincidence – i.e. it is a coincidence that the way we perceive pure orange light is roughly the same as the way we perceive light reflected by a mixture of red & yellow paints. This couldn’t be the general rule, since if you mix 100 different random colored paints (evenly distributed along the spectrum), you won’t get a color that corresponds to the average wavelength, but rather you’ll get a very dark color (i.e. hardly any color). Our eyes only have 3 different color receptors I believe, so they are really not sending full information about the light wavelengths to our brain, but rather just sending some kind of projection onto these 3 axes.

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