The Side the Glass Keeps

Why does a mirror flip left and right but not up and down? It doesn't. A plane mirror reverses one axis only — depth, the direction facing the glass. The famous left–right swap is a half-turn you add, in your head, to read the image as a person.

Stand in front of a mirror and raise your right hand; the figure raises what looks like its left. So we say the mirror swaps left and right. But notice what it leaves alone: your head is still up, your feet still down. Why would the glass meddle with one pair of directions and politely ignore the other?

It doesn't. A mirror reverses the one axis perpendicular to it — the depth axis pointing out toward you — and nothing else. Your left stays on the left; your right stays on the right; up stays up. What flips is front and back. Below you can move the mirror and watch exactly which axis it takes. Left–right is never special — it's just whichever way the glass happens to face.

1 · Move the mirror

Whichever face the mirror presents, it reverses that one direction and leaves the other two untouched. Facing the glass, the axis it leaves alone includes left–right — so the everyday sentence "it swaps my left and right" is, taken literally, false. The reversal is real, but it's front-to-back.

2 · So why does writing come out backwards?

Hold a printed word up to the mirror and it reads backwards — left-to-right reversed. Surely that's the mirror swapping left and right? No. A flat letter has no depth of its own, so the mirror simply shows you its back. Whether the back looks mirror-written or upside-down depends on one thing the glass has no say in: which edge you turned the page about to face it.

Same mirror, same letter — turn the page about its vertical edge and the image is mirror-written (the left–right reversal everyone names); turn it about its horizontal edge and the very same glass gives you the letter upside-down, not reversed. The glass only ever shows the back. You chose the axis.

That choice is the whole illusion. When you imagine your reflection as a person and ask "which of their hands is raised," you mentally turn yourself around to face them — a half-turn about the vertical, because that's the turn a standing, two-sided animal makes without thinking. Add that turn to the mirror's honest depth-flip and the arithmetic comes out as a left–right swap. Imagine instead a forward somersault — a half-turn about the horizontal — and the same reflection would read as up–down reversed. The mirror never picked left–right. Your body did.