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Through the Looking Glass (Posted on 2004-01-29) Difficulty: 4 of 5
When one looks into a mirror, one see an image of himself....

When raising one's right hand, the image raises its left. When raising one's left, the image raises its right.

So, why is it that the mirror reverses left and right, but not top and bottom? Why does a mirror appear to invert the left-right directions, but not up-down?

See The Solution Submitted by SilverKnight    
Rating: 3.6667 (6 votes)

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Solution solution | Comment 2 of 13 |
Physically and mathematically the only distinguished direction with regard to the plane of the mirror is the direction perpendicular to the mirror, toward or away from it, either in front or in back. And in fact this is the only direction in which the mirror reverses.

When it is said that the mirror reverses left and right that is a semantic distinction based on the perceived characteristics of the fictitious person "in" the mirror, that is, your reflection. In fact, the reflection of your own right hand is still on your right. If you are facing north into the mirror, your right hand is to the east and the reflection of that hand is also to the east. The only thing is, that you look at that reflection in the mirror and say that that reflected right hand is a left hand, that is, the left hand of that fictitious person in the mirror. Why do we say this?

A good way of defining left and right (which actually can't be done from scratch) for purposes of this description, is that side which is clockwise relative to the front of the body, as seen from above.

As mentioned in the first paragraph, up and down are not changed, so "above" is still "above". But front and back have been reversed. So now, clockwise from your front is not the same direction as clockwise from the reflection's front. That is why, semantically, we call that reflection of your right hand, that is still to your own right, a left hand, as it appears to be attached to a "person" who is facing the opposite direction.
  Posted by Charlie on 2004-01-29 16:00:52
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