pgimeno wrote:watching a mountain reflected in a lake: the mirrored mountain is upside down, because we compare the images by looking up and down (thus turning the eyes over an horizontal axis).
The mirrored mountain is upside-down because the lake flipped the image vertically; the vertical axis was the one perpendicular to the reflecting surface. Because mountains don't have top-bottom symmetry, there's no way to mistake this for any other kind of flip.
Some mountains do have approximate left to right symmetry, yet we don't perceive that the image flips their left and right, which was your implication. The mirror's normal doesn't have to be vertical to give an appearance of vertical inversion; the trick is over what axis you compare and perhaps mentally rotate the images.
ThirdParty wrote:Look, take a book, hold it up to a mirror in the usual way (face toward the mirror, top pointing upward). The cover will appear to have been flipped left-to-right. Then, without changing the orientation of your eyes, rotate the book ninety degrees (face still toward the mirror, top now pointing rightward). Now the cover of the book will appear to have been flipped high-to-low.
I don't hold books that I read that way. I hold them in front of me, almost horizontally. When I look at them, the letters are upright. If I am in front of a mirror and look at the book's reflection, the letters will have left and right in the same place, but will have up and down flipped. I guess Kit agrees, judging by the explanation given.
When you hold the book the way you propose, you are setting up the scenario for mentally rotating the image (or physically rotating the book to face the mirror, or physically rotate your eyes or your neck or your waist etc. to look at both images) over a vertical axis in order to compare both and decide which side is flipped. If you are in front of the mirror and hold the book open vertically with the text facing you, in order to make it face the mirror to look at the inverted image while keeping the letters pointing up, you have to rotate the book over a vertical axis, which is the axis that preserves up and down, and preserving up and down is the invariant you implicitly postulate in your framing.
It's been said in the thread: mirrors invert front and back. But rotating the image over certain axes converts the front-back inversion into something else, which is what gives the illusion that a different axis is inverted. Our tendency to compare the mirror reflection with the original by rotating over a vertical axis is what gives the illusion that left and right are what is inverted.
Yes, symmetry can play a role, in that it's mentally easier to match a figure with left and right inverted than with up and down or front and back inverted, because of the similarity of both sides. But you can get out of that prejudice by asking yourself: what aspect would I have if my left and right were preserved, but my top and bottom were inverted? And what aspect would I have if both were preserved by my front and back were inverted?
After getting rid of that prejudice, the axis over which you rotate to compare the original image with the mirror one is what decides the inversion axis.