### Mirror Magic Revealed

My brain panics every time I see a flipped AMBULANCE sign on a car driving in my direction. I feel like an Alice-in-Wonderland who falls into the world of my little kids' beautiful drawings, with their names scribbled from right to left.

It is intended to look correct in the rear view mirror when the ambulance is driving behind us, but looking at it straight on is disorienting. Someone, please come up with a creative, non-confusing solution that works both ways!

The masterpiece of reflection is a flat mirror. Every ray of light is elegantly bouncing back at exactly the same angle it came in, creating a virtual image identical to the one in front of a mirror. Or is it? Doesn't the image in a mirror look like it is a right-left flip of the original figure? Don't we see ourselves with our right hand being left and left hand being right in a mirror? And if this is true, why do mirrors only flip right-left and do not transform up-down?

I tend to agree with those who believe that mirrors have never pretended to do a right-left transformation. With its parallel reflection, a mirror is flipping our image in the depth dimension (Z axis). Your right hand stays on the right and left hand on the left, top on top and bottom at the bottom. We are basically looking at a Xeroxed copy of ourselves.

But our brain is unsure. Much more often than seeing ourselves in a mirror, we are used to seeing other people in front of us. Standing, sitting or pictured with their faces toward ours, with their right hand in front of our left hand and their left in front of our right. When comparing such a figure with our own mirror image, it does look right-left flipped.

Right-left flip comes out of intuitive comparison to something we are accustomed to seeing. But why should we be comparing? If we constantly saw gymnasts on the bar rotated upside down, we might want to compare them to our mirror image and it then would look up-down flipped.

So, let's stop blaming the innocent mirror for confusing us. It does only one thing, and it does it very well: object reflection in depth, aka Xeroxing. It has never pretended to do left-right or up-down flip. The flip is our brain's desperate attempt to make sense of a virtual object we see, by matching it with something we know well.

And as for visual confusion with the mirrors, it is my excuse for skipping mirrored aerobics rooms. There are too many lefts and rights there.

Like it? Try more math adventures in home ownership by The Math Mom: Pythagoras vs my husband... or You put a dirty plate in, you take a clean plate out. And you repeat it all around.

1. Reminds me of a Richard Feynman interview on that topic, in which he explains things so delightfully:

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2. Bonny Smith from cadsmith.com wrote to me and pointed that horizontal mirror will indeed flip up and down. Take a look at any flat surface of water reflecting the land on the opposite shore.

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4. I agree that you can actually compare that act to what gymnasts do to go upside down. I can't think of how it works in the mirror, but I'm glad you described it.

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5. Suppose someone puts my guitar down facing a mirror. I see my guitar in the mirror, but i don't realize the mirror is there. So i think the guitar is upside down. Based on that perception, I notice that the strings are reversed in the up and down direction. So the guitar does look backward top to bottom. However, if I knew the mirror was there, I could not perceive the guitar as backwards top to bottom because the top points up. I would think that the mirror changed my right handed guitar into a lefthanded guitar. Invariably, people will compare an upright mirror image to an upright direct image and see it as backward left to right.

6. I was wondering.. What we see in the mirror... Is that what other people see or?

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