I think the mirror explanation is unsatisfactory, because it is bad. It’s true that back-front flip is a correct description of how the mirror-image could be recreated. However the same image could be created with a left-right flip followed by a 180 degree rotation. Flips and rotations form a group, after all, so the same transformation can be composed in many ways. The second explanation is longer, but more intuitive. It is not wrong, as you seem to imply.
I propose that the real explanation of mirror images is that we understand and detect left-right and up-down flips in fundamentally different ways.
Good point! We only think the left-right flip is isolated from the rotation (and therefore breaks symmetry) because our brains do (specifically) the rotation around a vertical axis so naturally that we don’t even notice it. Mirrors don’t seem to flip things vertically because our brains don’t intuitively do the rotation around the horizontal axis without us noticing.
In fact, this suggests an example. Imagine a person (I’m imagining my nephew) is lying on their side looking at the mirror, and you’re standing behind them standing upright. When you look at this person and their reflection, is their reflection (intuitively) flipped horizontally, or vertically?
I think the mirror explanation is unsatisfactory, because it is bad. It’s true that back-front flip is a correct description of how the mirror-image could be recreated. However the same image could be created with a left-right flip followed by a 180 degree rotation. Flips and rotations form a group, after all, so the same transformation can be composed in many ways. The second explanation is longer, but more intuitive. It is not wrong, as you seem to imply.
I propose that the real explanation of mirror images is that we understand and detect left-right and up-down flips in fundamentally different ways.
Good point! We only think the left-right flip is isolated from the rotation (and therefore breaks symmetry) because our brains do (specifically) the rotation around a vertical axis so naturally that we don’t even notice it. Mirrors don’t seem to flip things vertically because our brains don’t intuitively do the rotation around the horizontal axis without us noticing.
In fact, this suggests an example. Imagine a person (I’m imagining my nephew) is lying on their side looking at the mirror, and you’re standing behind them standing upright. When you look at this person and their reflection, is their reflection (intuitively) flipped horizontally, or vertically?