Timmy stood with his back to the wall. He picked up his name tag, the one that read TIMMY. He peeled off the protective backing paper and attached the tag to the front of his shirt. Did it look all right? He turned around so that he could see himself in the mirror on the wall.
Timmy raised his right hand with a question. In the mirror, my name tag says YMMIT. Why is that? And why does my reflection have its left hand raised?
More generally, why does a mirror swap things left-for-right?
And, come to think of it, why it does it not swap things top-for-bottom? Why should the X dimension behave differently from the Y dimension?
The dimensions don't behave differently, of course. But we interact with them differently. It all comes down to gravity and the way we stand on this planet.
If we want to turn around, it's easier to rotate our bodies this way (keeping our feet beneath us) than this way (turning ourselves upside down).
Who swapped Timmy's name tag left-for-right? The mirror didn't do it. Timmy did it himself, by pivoting from his left to his right with his name tag attached. When he turned to face the mirror, he did it the easy way, rotating like this .
He could have done it the hard way and turned from top to bottom. To do so, he would have had to lower his head to the floor so he was looking between his legs at the mirror, then stand on his hands with his feet in the air. That would have been much more difficult.
Actually, a mirror doesnt reverse things either left-for-right or top-for-bottom. It reverses things front-for-back!
However, the mirror hasnt flipped the letter around. I have.
The reversal, dear Timmy, is not in our mirrors but in ourselves.