seems stranger than left and right swapping, but both happen and so this again fails to explain why left and right swap but top and bottom do not.
There are other possible answers, i.e. it is perhaps worth the reader considering what they think the answer is before reading on. However, rather than discuss them all, I will instead state what I believe is the correct answer, which involves symmetry and rotations, plus, not surprisingly, reflections and also, perhaps more surprisingly, a little bit of gravity. I believe that the key insight is that when we are asked to consider which is the image’s ‘left hand’ we picture ourselves moving around to where the image appears to be, possibly picturing ourselves literally walking around to it, and standing where the imagine is, that is, we effectively picture ourselves rotating around a vertical axis which runs down the middle of the mirror. We do this for two reasons. The first is due to the very simple fact that a human body, roughly speaking, has a vertical line of symmetry. This means that when we picture ourselves having rotated around to where the image is standing, we match up pretty well with the image. Of course, we don’t match up exactly, e.g. if we are wearing a ring on our left hand and we picture ourselves moving around, then the ring ends up on the right hand. The reply may come back: okay, so suppose we had both a vertical and horizontal line of symmetry, e.g. suppose that we were like a starfish, but with only four arms in the shape of a cross, and just one round eye in the middle. Wouldn’t we still look at ourselves in the mirror and see left going to right but not top to bottom? This is where gravity plays a part too – we see things in the way just described because when we line ourselves up with the image we still picture ourselves moving around as before, rotating around a vertical line, doing this now because this is what we have to do on earth. If we picture ourselves like a cross shaped starfish but in the sea we might actually find it just as easy to swim ‘over the top and down’ to line ourselves up with the image facing back, i.e. to rotate around a horizontal line through the mirror. We see now that in this case, our top and bottom have swapped, but not our left and right. It is hard to picture this because we are unused to turning around like this, and we end up literally ‘upside down’, which we don’t usually encounter. However, considering this gives what I believe is the correct answer to the original question, namely that left and right swap first of all because, due to our vertical line of symmetry, we fit ourselves so much better if we picture ourselves rotating around a vertical line to match up with our image, and secondly because this is much a much more natural movement on earth. If neither of these are the case, e.g. the cross shaped starfish in the sea, then it is just as easy to swap top and bottom as it is to swap left and right.
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