Here is a small puzzle Feynman liked to pose, and it's worth sitting with before you read on.
Stand in front of a mirror. Raise your right hand — your reflection raises its left. Left and right are swapped. But up and down are not: your head is still up top, your feet still at the bottom. The mirror is a flat, featureless sheet. How does it know to swap one pair and leave the other alone?
It doesn't
That's the trick of the question — it smuggles in a false assumption. The mirror does not distinguish left from right, or up from down. It reverses the one direction we forgot to mention: front to back. The tip of your nose is a few inches from the glass; its reflection is the same few inches behind the glass. Every point is flipped along the single axis pointing into the mirror. Nothing else moves.
So why do we say "left and right"?
Because of what we do next, without noticing. To compare yourself with the reflection, you imagine turning around to face the way the reflection faces. And you turn about a vertical axis — you pivot on your feet, you don't flip head-over-heels. That rotation is what swaps your left and right. The mirror supplied the front-to-back flip; you supplied the left-right one, for free, by choosing how to turn.
The proof is delightful: lie down on your side in front of the mirror, so "up" for you is now horizontal. The reflection now looks flipped top-to-bottom instead. The mirror didn't change — you did. Or hold up printed text: it reads backwards because to face the glass you rotated the page about its vertical edge. Rotate it about the horizontal edge instead and it comes out upside down, not mirror-written.
Why this one is worth keeping
Nothing here needs an equation. It needs only the refusal to accept the question's hidden premise, and the patience to ask what actually moved. That's the whole method, and it works far beyond mirrors.
A note from Sweta: this little piece is a spark, not a finished thing — a placeholder in Feynman's spirit to get your Physics shelf started. Keep it, rewrite it, or write the one that should really go first. The room is yours.