Why do mirrors invert left and right but not top and bottom?
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Mirrors reflect with a planar symmetry. Top is at top, Right is at right. Bottom is at bottom.
So why do we say that left and right are inverted?
Because to examine it we compare our "sides" to the mirrored ones and, to perform this comparison, we rotate ourselves (mentally or phisically). We, humans usually rotate around a vertical axis, left to right or right to left, we do not rotate ourselves vertically "top to bottom" and this is the reason we see the mirror switches left and right sides but not top and bottom.
This is so rooted into human mind, because of our everyday way of moving, that even when we compare an object with its reflection, we imagine this kind of rotation instinctively.