The mirror paradox

Have you ever wondered why mirrors flip your image horizontally, but not vertically? It’s one of those curious things that doesn’t actually seem curious at first — it seems perfectly natural. But that’s simply because we’re so used to it. Once you reflect on it (sorry!), it becomes much less obvious why that’s the case.

After all, a mirror doesn’t know or care which way is “up” — in fact, there is no such thing as “up” built into the world. It’s just a term we have for a direction pointing away from some plane we’ve designated as the “ground,” and we only bother to define these concepts because we humans happen to be very concerned with gravity and its effects on us. The light bouncing off of a mirror, one assumes, has no such concerns — it could care less about our concepts of verticality and horizontality. But then why is there this asymmetry in the way a mirror reflects our image, turning us around left-to-right but not top-to-bottom?

The first step towards an answer is to realize that the question is flawed. The mirror doesn’t actually reverse your image either left-to-right or top-to-bottom — it reverses your image front-to-back, that is, along the axis perpendicular to the mirror. Imagine you had a hollow Halloween mask, and you turned it inside out. That’s exactly what a mirror does: it “turns you inside out,” so that you’re facing the opposite direction without having been rotated.

But if the mirror is just flipping our image front to back, why does it look like we’re being flipped left to right? It’s because the left and right sides of our bodies are almost identical. So the inside-out person you see in the mirror looks a lot like what you would see if someone created a clone of your body and rotated it 180 degrees so it was facing you. That’s why you have the strong feeling that the mirror is rotating you in the horizontal plane, even though it’s actually just turning you inside out.

The illusion wouldn’t be nearly as strong if our bodies didn’t have left-right symmetry. Let’s say you had a tentacle in place of your right arm. Then your mirror image wouldn’t look like a 180-degree rotation of yourself, because the tentacle would be on the wrong side. The mirror’s ability to make us feel like an image has been turned around only works with a symmetrical axis.

Another experiment you can do to drive this point home is to try lying down on the floor, on your left side, facing a mirror. Now your mirror-image will be lying on his right side with his left side on top, while you’re lying on your left side with your right side on top, creating the illusion that the mirror is flipping your image vertically, as opposed to when you were standing in front of the mirror and it looked like your image was being flipped horizontally. This proves that the nature of the illusion is different than we’d originally thought: it’s not that the mirror seems to rotate you horizontally rather than vertically, but that the mirror seems to rotate you around your symmetrical axis rather than your asymmetrical axis.

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24 Responses to The mirror paradox

  1. davidad says:

    Nice deconstruction! It reminds me of the old IQ question: if John is looking into a mirror, and touches his right ear, which ear does his mirror image touch?

  2. Barry says:

    Great! I knew the part about the mirror reversing front-to-back, but had never tried the business about lying down in front of the mirror.
    This reminds me of another mirror conundrum: Camel Cigarette packs have (or used to, anyway) the words “CHOICE QUALITY” printed along their sides. We used to slide the cellophane wrapper half-way down the pack so that it covered “CHOICE” but not “QUALITY.” Then we’d tell our mark that the cellophane used on these packages was special — it prevented the writing under it from being affected by a mirror! And indeed, in a mirror, the word “QUALITY” looked all weird, but “CHOICE” was unaffected. You can try it yourself on a piece of paper — just be sure to give the paper a half-turn before looking in the mirror. (And use ALL CAPS!)

  3. Silas Barta says:

    (didn’t go through the first time)

    Well put. This example is also used in Gary Drescher’s Good and Real (and excellent all-around reductionist masterpiece) as an example of how to, and how not to dissolve a paradox.

    (Just surfed in from lukeprog’s announcing of your site.)

  4. Julia Galef says:

    @Silas Barta — I loved Good and Real, and I’ve cited it in several of my essays on other sites. For example: “Definitions don’t prove anything,” and then again in “Newcomb’s Paradox: an argument for irrationality.”

  5. michael says:

    turning us ” inside out” is not really correct. if you turn a latex glove inside out… its exactly that.
    if you turn a human being inside out,.. well… it gets messier. But you get the idea.

    So a mirror turning us inside out, doesn’t seem to be the correct term either.

  6. Kenn says:

    This explanation has never satisfied me — it doesn’t help me understand why text looks flipped left-to-right in the mirror. The text is not symmetrical.

    • Pavitra says:

      Looking at text in a mirror, you see the same thing as if you held the paper up to a strong light and read the text through from the reverse side. It’s reversed front-to-back.

      Also, which way the text appears flipped depends on how you turned the paper towards the mirror. If you turn it around, about its vertical axis, the text appears flipped left-right. If you turn it over, about its horizontal axis, the text appears flipped top-bottom.

  7. Phil Goetz says:

    I have wondered about this – I’ve even tried lying down in front of a mirror before – and this is a new angle on it for me; but I’m afraid it still doesn’t clear it up for me!

  8. Lucette Smoes says:

    A little physics would go a long way here1

  9. Giles says:

    I think the illusion arises not so much due to our near-perfect left/right symmetry, but rather because we are used to people rotating about a vertical axis, but not a horizontal one.

    So for any object we see in a mirror – a human, text, whatever – we (without realising it) first imagine rotating that object about the most “sensible” axis so that it faces us, then compare that with what we see in the mirror and decide that the mirror has flipped it about that plane.

  10. Nick says:

    Interestingly, in general relativity it is possible to take a path through the universe which is spatially closed (returns you to your initial (x, y, z) coordinates) but causes anyone traveling it to undergo a 180 degree reflection (i.e. mirror symmetry). Unfortunately, anyone who took that path would die of starvation once the food he had brought with him ran out; our bodies can only process left handed proteins, because these are the only type that exist in Earth’s biosphere, but after the mirror inversion our returned traveler would only be able to process right handed ones.

    The best cosmological observations so far indicate these paths do not exist in our actual universe, but they have not been fully ruled out.

  11. FAWS says:

    This explanation is simply wrong. It has little to do with symmetry and everything to do with around which axis you expect things you face to be rotated relative to you. If we were asymmetrical, but still usually faced other people when they are rotated around the vertical axis relative to us out mirror image would still look flipped horizontally. On the other hand if we were used to facing people hanging upside down (say living on a space station with corridors in wheel form with inwards facing ladders where you usually meet people when they are on the other side of the wheel going the same way around as you, and you both look inwards) your mirror image (in a mirror inserted into the center of the wheel) would look flipped vertically, even with the same symmetry.

  12. vegan girl says:

    Hm i dont care much for this explanation. the mirror doesnt flip anything, it doesnt turn anyone inside out, the mirror is merely reflective (it is one of its qualities). the way reflections seem to us is of course an illusion. it is a subjective view of the mirror. but if u were a mirror, the object in front of u would be reflected in the way we see things that are in front of us. (imagine if mirrors could see, what would they see? they would see what u see). mirrors dont flip us more or less than we flip people and objects that we see. and if u try to imagine what the person looking at u sees_ BUT FROM YOUR POINT OF VIEW_ u will experience the same illusion. in other words, the mirror reflection that u see of yourself, is the mirror point of view from YOUR point of view. Replace the mirror with any other “observing” thing or a person and there it is – the same illusion (although not visible).

  13. Lucette Smoes says:

    The mirror acts as a plane of reflection. This so-called phenomenon follows the laws of optics.

  14. Stu says:

    This question has interested me for a long time, and I have engaged in an extended debate with Paul Mealing in his blog on the same topic. Paul’s approach is essentially the same as the one given above – but I’m very sceptical.

    What bothers me most is the recourse to “scientific” prescriptions about how we should judge a picture. Surely a reflection is just a type of picture, so to claim that a mirror “really” reverses an image from back to front is like saying that the impression of depth created by a landscape painter is “real” even though the subject-matter on which the image is based may be imaginary.

    In particular, we might consider the reflected image of a signpost with one branch pointing into the mirror, and one pointing to the side.

    If it is necessary to explain the apparent inversion of the branch pointing towards the mirror in terms of a “genuine” reversal, then it is inconsistent to use a completely different rationale to explain the inverted appearance of the left-right facing arm.

  15. Nigel Searle says:

    Gravity defines what is “up” and what is “down.” “Up” means “farther from the center of the earth,” while “down” means “closer to the center of the earth.” A reflection in a mirror does not change what is “up” and what is “down.”
    “Left” and “right” are arbitrarily defined. A reflection in a mirror interchanges “left” and “right.”

  16. It’s tangential to the original post, but I was surprised recently when using the front-facing camera on my iPhone 4S. The Camera app preview shows a reversed image of me as if reflected in a mirror. On taking a photograph, however, the saved image is not reversed, just a normal snapshot from the camera. Not sure what motivated this UI behavior…

    • On reflection (sorry), I realized that if the Camera app preview had shown an unreversed image, rotation of the iPhone about an axis perpendicular to the screen would cause the image to rotate twice as fast in the same direction. After 90 degree rotation from the original portrait orientation, the image would have rotated 180 degrees, making it upside-down in landscape orientation.

    • Max says:

      It’s more intuitive and you can use it as a mirror.

  17. Larry says:

    This is all very interesting… but is it a paradox?

  18. Pingback: Mirroring paradox | Monaschilling

  19. Dave Dubins says:

    This problem has been bothering me a bit. Going out on a limb here. Simple physics – the actual image that goes onto our retina is upside-down. If you’ve ever tried a pinhole camera, or simply hold a magnifying glass close to a wall with a bright window behind it – you will see this effect.

    What I think happens – and I might be wrong – is that the mirror DOES flip our image both horizontally and vertically. Our brains are quite used to flipping images that are upside-down the proper way (right-side up). So our brains take care of the vertical flip, but the horizontal flip isn’t done. It’s our brain’s fault?

    I noticed the iphone front-facing camera flip as well, Chris. Pretty sneaky, Apple! I think they did that to help you compose the shot better.

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