Wiki-woman wrote:The question is sometimes asked, "Why does the mirror reverse left to right and not top to bottom?", and it is worth thinking about. The counter-intuitive answer is that it actually does. Imagine you had a complete copy of your body that you could manipulate into different positions, and imagine that it is directly in front of you and facing the same direction as you, so that you are looking at its back. If you twist the copy around the vertical axis, as if it were turning to face you, and then compare that with your reflection in the mirror. The reflection will be different from the
model because everything that should be on the left will be on the right.
But imagine instead that you twist the
model about a horizonal axis, as if it were doing a handstand. The
model would be upside down, facing you. If you compare this to yourself, and the reflection, then left and right are all correct. Your wedding ring, eye patch, and false leg are all on the correct side, be that east west north or south, but something is glaringly wrong about the reflection compared with the
model, the reflection's feet are down at the bottom, where its head should be! Or, you could just keep the
model in front of you so that you are looking at its back, and compare that with the reflection. Now left, right, up and down are all correct, but the reflection has its back where its front should be.
The
model represents the way the 'real you' ought to look. If some other person looks at you, what would they see?. So you compare the reflection against what you think you 'ought' to see. If you think you ought to see what you look like when you're doing a handstand, then the reflection is upside down, and if you think you ought to see your own back, then the reflection is flipped front and back. But most people want to see themselves from the front, whilst standing up, they think their reflection ought to look like they would look if they turned around, and they think that left has been flipped with right.
In some sense what has 'really' been flipped is front and back. If you were to describe the body with co-ordinates, east/west north/south up/down, and the mirror has been facing south whilst you are looking north, then the difference is in the north/south direction; front and back. So I don't think my reflection looks a bit wrong because left has flipped with right, I think it looks hideously deformed because it has a face where the back of its head should be.
The mathematical or geometrical version of the question is: "why does a chiral object (such as a right hand or glove) appear as an object of opposite chirality (left hand or glove) in the mirror?" The answer is that chirality of the three-dimensional space is dictated by the choice of the directions of the three axes. When the direction of one axis is reversed, as is the case in a mirror image, the chirality (or "handedness") of space changes to the opposite one. If two mirrors are set side by side (with, say, a 90° angle between them), the axes in the doubly reflected image are inverted twice and the "handedness" of the image is not changed. In such a double mirror, a right hand looks like a right hand. This set-up lets you see how you really look, but most people find it very difficult at first to use a mirror like this for shaving.
Posted: Sun May 14, 2006 4:24 am
Bob.
