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Ask HN: Why does a mirror show you back to front but not upside down?

10 points by dave_sid ↗ HN
Even if you lie down sideways and look at the mirror it still doesn’t flip you upside down, only sideways.

Unless you stand on a mirrored floor, in which case it makes you upside down.... but facing forward. What’s going on?

9 comments

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db48x
Mirrors only flip in and out, not left and right or up and down.
webmaven
> Mirrors only flip in and out, not left and right or up and down.

This is true, but elides the point that we perceive the flip as left-to-right because we have two eyes arranged side by side.

So, if you want a top to bottom flip, just tilt your head 90 degrees.

db48x
That’s not true. The classic experiment is to write a word on a piece of paper, then show it to a mirror. You have to flip the paper over to show it to the mirror, and most people flip the paper horizontally. Thus the word will appear to be backwards. Flip it vertically instead and it will appear upside down. The key observation is that the mirror reflected the light from the paper back to us, but it didn’t flip anything; we flipped the paper, not the mirror.
a3n
Physics-like answer: There is no flipping at all. Each point on your body is reflected back from the mirror at the location where where the light from that part strikes the mirror.

E.g. draw a "ray" from your left hand to the mirror. It strikes the left side of the mirror and comes back to your left hand. (And another ray comes to your eye, but ignore all but the perpendicular rays.)

Linguistics-like answer: It's because we name our hands etc with directions left and right, but not our heads vs feet.

If we named our hands "writer" and "puncher" we might not suffer from this riddle.

EDIT: Stand in a relaxed hands at your side position. Label the top of the mirror "top," and the bottom "bottom," relative to gravity.

Your head, at the "top" of your body relative to gravity, is at the top of the mirror.

Now pierce your body through the belly button with an axle, and rotate your body 90 degrees. Your left hand is at the "top" of your body, relative to gravity, and so is its reflection in the mirror. No flipping.

FURTHER EDIT: Label the mirror at the top with an arrow pointing up, and the word "north." Three more arrows, with east west and south.

Call your left hand "west." Wave your west hand. What do you see? No flipping.

YET ANOTHER EDIT: Neurologic-like answer. ... I don't know how to do this one, but I suspect there is one.

BjoernKW
A classic puzzle, the answer to which is that the projection takes place along the z-axis rather than x-axis.

Richard Feynman nicely explains this in this video: https://youtu.be/6tuxLY94LXw

pestatije
Because left / right are relative and up / down are absolute.

If you want horizontal absolute coordinates, try north / south / east / west.

If you want relative vertical coordinates, try lying on your side.

jfengel
They don't reverse left and right. They reverse forward and back.

Things on the left side of your body are still on your left as you look at the mirror. You imagine switching places with the mirror image by turning on an axis down your body, because that's how you're symmetric. That also reverses forward and back, but not the way a mirror does, so you get an extra left-right reversal as well.

If you had writing on your chest, it appears reversed in the mirror because it's reversed in front of you. If you looked through a tee-shirt, you'd see that the things seem reversed. The writing is meant to be read by a person looking at you, not by you. The first letter is on your right, so that it's on the left to a viewer in front of you looking towards your back.