Apr 4, 2023, 7:59 PM
Confession: I've had a confusion for a long time. And I think that it makes me sound stupid.
It's got to do with that old question, "why does a mirror swap left and right, but not up and down?"
I understand that the question doesn't really make sense. I know that it's not something weird about mirrors, just something weird about our brains and perception. But if asked to explain why we see it this way, I would probably just mumble something about symmetry. This morning, it was stuck in my brain for some reason. This post is what my mind went through as I overly dwelled upon this. Mind you, I could probably find a decent article that explains this a lot better, but I thought that the gyrations my mind went through were pretty interesting, at least to me.
So you have a right hand. Viewed from your back, that hand is oriented in a clockwise position from your head. And your left hand is over there in a counter-clockwise location. When you look at another person head on, things are reversed. Their right hand is counter-clockwise from their head and their left hand is clockwise. But when you look in a mirror and move your right hand around, the hand that moves in the mirror is clockwise from that person's head. And what you know is your left hand is counter-clockwise.
The question of why doesn't the mirror swap up and down makes no sense because it's not going to put your head on the bottom and your feet in the air. OK, some mirrors might do that, but we're talking about an ordinary flat mirror. Because we have left-right symmetry, we can see that left and right get swapped from how we usually see people, but not up and down.
So I figured there must be some thought experiment I could do that would cause the same issue on the other axis. What if we had two heads? One that faced downwards and one upwards. And our arms just stuck out of the middle of our bodies and we kind of floated in the air. And we had an even number of fingers so that our hands were up-down symmetrical?
It still wouldn't work. You'd look at yourself and say, "my up head is still up and my down head is still down, but my left and right hands are swapped. So it's not just symmetry.
I started thinking that it's got to do with the fact that we have an absolute orientation of up and down. Up is always towards the sky and down is always towards the ground. At least experientially. But left and right are always relative. You point to the right and it's one direction, but if you turn around, then right is in the other direction.
Another thought experiment I did:
First, imagine lying down on some kind of platform facing a mirror. You'd still see your right and left hands swapped, but they would be swapped vertically this time! But you wouldn't think your head and feet were swapped, even though they extend to the left and right. We fixed the mirror! Or at least changed how it was seemingly not working right.
Now, say we were the same as we are now, but we floated along on our sides like fish. Say the way we floated was always such that what we call our right hand would always be up in the air, and our left hand would be down toward the ground. We'd probably call our left hand our "down hand" and our right hand our "up hand". Then, whenever we faced another person, their feet would be near our heads and vice versa.
But if we floated by a mirror, it would be a very different experience. The person we saw in the mirror would be all wrong. Their down hand would still be down and their up hand would still be up. But their head and feet would be flipped. So now we've proven that it's not even about symmetry at all! The symmetrical part of our body didn't get flipped, but the unsymmetrical part did. Amazing.
So this is way more about frame of reference and psychology, which I already knew, but I think I understand it more. But at the same time, it's still confusing.
As I was writing this though, I thought of another way of thinking about it. When you look at another person face to face, it's because they turned around to look at you (considering you were initially facing the same direction). Thus, their right hand is now on our left, and their left hand is now on their right. Since most of us see other people more than we look in mirrors, that's what seems normal. We forget that they rotated 180 degrees on their own y-axis. And the mirror doesn't do this. Because we always rotate on our y-axis, it's only our left and right parts that cause this cognitive dissonance. If we were walking in one direction and wanted to turn around and go back and then flipped upside down and walked on our hands, then I think our mirror experience would be very different. I guess.
Again, there's probably some Youtube video that explains this in a much more logical way. I bet it touches upon some of these same things. But I like banging away on them myself.