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Reflection

You may notice in a mirror that words are backwards in the reflection, but it's actually more than words that are reversed; it's everything!

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You may notice in a mirror that words are backwards in the reflection, but it’s actually more than words that are reversed; it’s everything!

You may disagree, citing that if you lift your right hand and the reflection of you in the mirror also lifts her right hand, but does it?

People sometimes get confused between what mathematicians call “reflection” and “translation.” Let’s see if we can sort it out.

Imagine an identical twin standing facing you, who does everything you do. You raise your right hand. She raises her right hand. Now, which side is it on? She raised her right hand, but from your perspective, that hand is on your left side. Try it and see!

This is what mathematicians call a translation of you, that is, your twin is essentially you, just moved to another location in space.

A reflection of you is different. What happens when you raise your right hand in front of a mirror? Does the reflection raise it’s right hand or left hand? Well, to avoid confusion, let’s say that the reflection of your hand comes up on the same side as your hand does. Since a mirror is nothing more than a surface that bounces back the light that hits it, this has to be the case.

Notice, though, that the person in the mirror, if it existed, would be raising it’s left hand. In that sense, your reflection is doing everything backwards!

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