If you look in the mirror........?

Question

.....left become right and right becomes left. So why isn't the top and bottom reversed as well?

Answer 1

The answer to this question depends upon our physiology! (NOT !! --- see "POSTSCRIPT, WEARING SACKCLOTH AND ASHES," below.)

I'll first assume you're an upright kind of guy.

The "left and right" behaviour is different from the "top and bottom behaviour" because OUR EYES ARE ON THE LEVEL!

When left and right are "switched," our originally left ear is still at the same height that it was to start with; similarly for the other one.

Now imagine that you do this lying horizontally as you look at the mirror.

One eye is now higher than the other. Now, the left-right switch also changes the height of what you call the left or right ear, and in fact involves an "Up-down flip" that was absent before. It mixes up "left-rightness" in a way it didn't before.

So it really matters that normally, you're a guy on the level rather than a lying .... (Well, I'd better not finish that!)

Live long and prosper.

POSTSCRIPT, WEARING SACKCLOTH AND ASHES:

Jack B. Nimble's answer is clear and succinct; I've given it a thumb's up. It sent me back to confront myself in the mirror once more; as a result, I take back my original answer, and now offer the following analysis.

Looking in the mirror with my recognizable bathroom and bedroom beyond "in its depths," I imagined myself being the person in the mirror examining how all things were treated as they appeared in or were "transformed" in the "mirror world." Walls, floor, ceiling all continued into the mirror world, but the things furthest behind me in my world were now the furthest in, in mirror world.

It's like holding out an infinitely thin sweater by the sleeves, front upwards, and then turning it iside out, away from you. The right sleeve becomes the "left" one and vice-versa --- try it! And yet the front of the sweater, held flat, upwards, remains upwards during this process. So, the left-rightness of this "mirror inversion" appears to "switch left and right," but doesn't affect "up" and "down," in this EXPLICIT, practical example.

I think this is the nub of the answer, but there are further implications found by examining mirror world a bit more carefully.

If you now start looking around in mirror world, you notice a remarkable thing: the left-right interchange is not just for your own mirror image, it's true for EVERYTHING. Looking straight into the mirror, this is hardly surprising: the edge of a picture I could just see through the door, behind my real world left hand, was now behind the "right-hand" of mirror man (MM).

I then turned, to look to the side, parallel to the mirror. In the real world, there was my toilet, just beyond and below the far edge of the mirror. (You may not wish to know that.) A corner shelf was to my right.

Mirror man disagreed, and pointed out in rather strong and critical language that I had it all wrong. He asked me to look at the situation from his point of view. I had to reluctantly agree. His toilet was to the right; his corner shelf was to the left!

This meant that no matter in what direction mirror man looked, while standing on the projection of my floor, EVERYTHING had a left-right switch, no matter in which direction he turned.

I confess that I found this remarkable. It meant that the "sweater-like inside-outness" applied to everything, to depth in the mirror, sideways, in fact turning around and looking in any direction. It's an INTRINSIC property of mirror world, without altering the way gravity operates --- that still pulled mirror man to the floor.

I decided to take what mirror man had told me lying down, on my right side, parallel to the mirror. Gravity pulled me to my "right"; but it pulled mirror man to HIS left, though physically it was still downwards.

What did all this mean, mathematically?

It meant that if a set of coordinate axes (O, x, y, z) in my world had their origin O in the silver reflecting surface of the glass mirror, with Ox horizontal to the left, Oy straight out at me, and Oz vertical, then in mirror man's world those same axes, for him, would be Ox', - Oy', and Oz'. The - Oy' is the mathematical consequence of the "sweater inside out effect" perpendicularly to the mirror surface. It's the ONLY one that's changed.

In my world, my axes form a "right-hand screw set (RHSS)." It's responsible for advanced physics students screwing up their hands and faces as they try to imagine which way a vector cross-product points, the direction of the Coriolis effect, in which direction a tipped-over gyroscope will precess, or which way a moving particle will be deviated in a magnetic field.

But mirror man lives in a world governed by a "left-hand screw rule." When I stand, doing my physics student thing in front of the mirror, my right-hand screw rule demonstration becomes mirror man's left-hand screw rule demo. I do it with my right-hand; he does it with his "left-hand."

So: ALL of the strange effects described come about from just one simple transformation, the "flipping" of all the coordinates normal to the mirror so that y ---> - y'. This DOESN'T change the direction of the x- and z- axes, but it does imply a change from an RHSS world into an LHSS world, or an "everything horizontally inside-out" world.

And THAT'S finally WHY: When you look in the mirror ... left becomes right and right becomes left ... but the top and bottom aren't reversed as well.

THANK YOU VERY MUCH FOR SETTING THIS QUESTION! It's been most thought-provoking and educational.

Live long and prosper.

Answer 2

There is an important difference between left/right and top/bottom: the direction of left or right depends on what direction you're currently facing. But top and bottom are in the same direction regardless.

Answer 3

Neither of those is true, actually: the direction that is reversed is front-to-back. The reason we perceive this as a left-to-right transformation is because, to see that view ourselves, we quite foolishly TURN AROUND. We usually turn around horizontally, but if you did a backflip and viewed the scene upside-down you would find it just like the scene you were viewing in the mirror, except upside down.

Answer 4

think about your reflexion as another person. It's the same concept. Your left is their right, and the other way around, but your up and down is the same as theirs.