This question has a surprisingly intriguing answer. The truth is, mirrors don’t really switch left and right, let alone up and down. Rather, they reverse the image of the world you see from front to back.
Left and right are the only directions that are defined based on the observer’s perspective. In contrast, up and down (as well as north, south, etc.) are not influenced by the direction you’re facing. When you glance in the mirror, up, down, east, and west remain unchanged.However, you read printed text from left to right not east to west, which is where the confusion with ‘mirror writing’ comes in.
A mirror doesn’t actually reverse left to right, as you can see with an asymmetrical object. Picture the mirror as one of those toys with a bunch of pins that pop back when you touch them, keeping the 3D shape. Now, imagine pressing your body against it and stepping back. The trick is that, since we are generally symmetrical, it seems like there’s been a left/right flip. But in reality, your right side is still on the right side of the image.
Mirrors don’t flip left to right, they flip front to back. When you see yourself in a mirror, it looks like your reflection is another person who resembles you, standing behind a piece of glass, at the same distance from it as you are, and facing you. To make sense of this, you might think that person walked behind the glass and turned 180 degrees around the vertical axis to face you. So, their left hand should be where your right hand is, and the other way around. But that assumption is incorrect. Your reflection didn’t turn 180 degrees, it was simply reversed front to back without any rotation. Your brain subtracts the 180-degree turn you think must have happened from the observed front-to-back reversal.
The mirror doesn’t flip images from left to right, it actually flips them from front to back in relation to the mirror’s front. Stand in front of a mirror and point to one side. You and your reflection are both pointing the same way. Now, point straight ahead. Your reflection is pointing the opposite way. When you point up, you both point in the same direction. Now, turn sideways to the mirror and do it again. This time, when you point sideways, you’re pointing in opposite directions. If you place the mirror on the floor and stand on it, you’ll find that when you point up, you’re again pointing in opposite directions, while your upside-down reflection points down.
In every scenario, the direction only reverses when you point towards or away from the mirror. This all comes down to the fact that a reflection isn’t the same as a rotation. Our bodies are pretty symmetrical left to right, and we tend to think of the reflection as a rotation around a vertical axis. We picture the world in front of the mirror as having been rotated 180 degrees around the mirror’s vertical axis, ending up behind the mirror where we see the image. This rotation would place the head and feet where we expect them, but it would switch the left and right sides of the body compared to how they appear in the reflection.
However, if we think of the world being rotated around a horizontal axis that runs across the mirror, it would leave you standing on your head but keep your left and right sides in their usual spots. The image would then be inverted top to bottom, but not left to right. So, whether you perceive the image as left-right inverted or top-bottom inverted, or even inverted around any other axis, really depends on which axis you mistakenly imagine the world has been rotated around.
If you lie down on the floor in front of a mirror, you can see both effects simultaneously. The room looks like it’s flipped left to right around its vertical axis, while you perceive your body as flipped left to right along a horizontal axis that runs from your head to your feet.
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