Ground as in electronics. You’re telling me after all this algebra and whatnot that in order for it all to work I have to stick one end in the ground? Magic!
And this:
I’m standing 2 feet from a mirror. How much work do my eyes need to do to properly focus my image (depth of focus perhaps?) I know it’s 2 feet, but stubbornly believe it’s 4 feet.
I thought the electrons had to be able to get back home? Sticking one end in the ground wouldn’t always provide that, would it?
I call it “brain damage”. In one of the neuroscience classes I took in college, we discussed the interesting fact that in addition to taking away the ability to do something, it also takes away the ability to figure out that you can’t do that thing–or that you used to be able to do it–or that anyone can do it. Something like that. So when I intellectually know that something is true, but can’t accept it on an instinctive or emotional level, I call it “brain damage”.
Speaking of which, every once in awhile, it will occur to me that things in a mirror appear reversed left and right but not top and bottom. I have to stop whatever I’m doing and think through an entire line of reasoning to convince myself that that is indeed the correct case.
Um, it IS 4 feet. You’re focusing on your image, not the surface of the mirror.
It’s simple: Things in a mirror appear reversed left and right but not top and bottom if you twirl them around a vertical axis (i.e., yaw) to face the mirror. They’ll appear reversed top and bottom but not left and right if you twirl them around a horizontal axis (i.e., pitch) to face the mirror. If you wrote “8M0” on a piece of paper, held it up to face you, then twirled it, bottom to top, to face the mirror, rather than the usual twirling of left to right to face the mirror, you’d see “8W0” rather than the “expected” “0M8”.
Really, the mirror doesn’t reverse anything except depth; the other reversals arise from the rotations one uses in combination with that.
Also, I concur with Q.E.D.; the optics of a mirror act as though it were simply a window into a depth-reversed copy of the world in front of it. You don’t focus on the window; you focus on the action behind it. If things were otherwise, it wouldn’t be possible to have significant depth-perception with respect to the image in a mirror/window.
You wanna mess your head up? Install a closed-circuit camera and a monitor right next to it so that when you look up at the camera, you see yourself in the monitor. A lifetime of conditioning has left me unerringly creeped out by seeing myself as if I’m looking in a mirror but not mirror-reversed.
I’ve noticed that my cell phone’s camera, when configured to take a self-portrait, reverses the image it shows you on the little screen so that you are spared this: until the moment the picture is taken you essentially are looking in a mirror.
Crap. So much for getting any work done this afternoon.
Woosh.
“Woosh”? How so?
(Perhaps prefacing that with “It’s simple” struck some as a joke, but that wasn’t my intention. I may have worded it poorly, but the example at the end with the paper should demonstrate that it really is simple, the underlying concept here; the mirror doesn’t reverse anything except depth. The reason we feel it reverses things horizontally is because we usually twirl things in that way in order to face the mirror, but the mirror itself isn’t responsible for that)
If I’m understanding your methodology correctly, it has absolutely nothing to do with top-bottom reversal: if you were to stand between the paper and the mirror, you’d see that the top and bottom are not reversed, but the left and right are.
It doesn’t matter where you stand (as far as the image on the mirror is concerned)… all that matters is how you orient the paper in getting it to face the mirror.
Suppose there’s a mirror on the north side of a room. I stand on the south side of the room and write something on a piece of paper and hold it up to read it. Well, the paper is facing me right now; it’s facing to the south. So what I see in the mirror is just the empty backside of the paper. Not very interesting. So now I have to turn the paper around to face the north, in order to get the side with writing to appear in the mirror rather than the empty backside. Well, I have several means of carrying out this switch in the orientation of the paper now. The means I choose will determine what kind of “reversal” the image of the writing in the mirror will manifest.
I could twirl the paper around a vertical axis to get it to face the north, in the usual way, in which case the top edge of the paper remains on the top and the bottom edge remains on the bottom, but the edge which was formerly on the east is now on the west and vice versa. In this case, the writing will appear horizontally, but not vertically, reversed in the mirror. Alternatively, I could twirl the paper around a horizontal axis to get it to face the north, in which case the edge which was on the top moves to the bottom, but the edge which was on the east remains on the east. In this case, the writing will appear vertically, but not horizontally, reversed in the mirror.
I’m puzzled by this. All sorts of electronic devices work without any connection to the ground.
Rotating it along the horizontal axis changes the top edge to the bottom edge, as you said. Look at the side with the writing on it and the M will be a W there, too. It doesn’t have anything to do with the mirror.
Our brains interpret images upside down to begin with. So if our brains weren’t automatically rotating the image in the first place, we’d see ourselves upside-down in a mirror.
If we could interpret the image being directly transmitted to our eye, if we stood in front of a mirror and waved our right hand, we’d see ourselves upside down, waving what appeared to be our left hand.
So the mirror does indeed reverse up and down, our brains just put it back!
Look at the side with the writing on it by pivoting your own body around a vertical axis to be able to face the re-oriented paper, and yes, the M will be a W there too. Look at the side with the writing on it by pivoting your body around a horizontal axis (so that your head is now on the floor but your right arm remains on the east side of the room where it started), and the M will remain an M. If you say this flipping of M to W doesn’t have anything to do with the mirror, that’s correct, but it’s correct in the same sense that the flipping of “<p<” to “>q>” in a “mirror image” doesn’t have anything to do with the mirror.
That is, to restate your post with words added and substituted:
Rotating it along the horizontal axis changes the top edge to the bottom edge, as you said. Look at the side with the writing on it (by pivoting your body around a vertical axis (yaw) to face the re-oriented paper) and the M will be a W there, too. It doesn’t have anything to do with the mirror.
Rotated it along the vertical axis changes the left edge to the right edge, as you said. Look at the side with the writing on it (by pivoting your body around a horizontal axis (pitch) to face the re-oriented paper) and the p will be a q there, too. It doesn’t have anything to do with the mirror.
Actually, there’s a more important point to be noted here which has been obfuscated by picking ‘M’. Suppose we wrote ‘p’ on a piece of paper, held it up to face us, then rotated it across a horizontal axis (taking the previously top edge to the bottom) to face a mirror. What will we see in the mirror if we look at it right now? We’ll see ‘b’; vertical inversion but not horizontal inversion. What will we see in the paper if we keep it oriented as is and walk around to the other side in the usual manner (i.e., pivoting our bodies around our vertical axis to face it anew)? We’ll see ‘d’; vertical AND horizontal inversion, one from the way we rotated the paper, the other from the way we rotated ourselves. (And, of course, if we move to view the re-oriented paper in an unusual fashion, by pivoting our bodies around a horizontal axis rather than a vertical axis, the two rotations (of the paper and of ourselves) will cancel out, and we’ll just see the original ‘p’ on the paper).
It was glib of you to originally say “Look at the side with the writing on it and the M will be a W there, too.” as though this was somehow completely disconnected from what goes on when people think of mirrors reversing text left-to-right. Had the original paper had a ‘p’ on it rather than an ‘M’, you could not say “Look at the side with the writing on it and the p will be a b there, too”; no matter how we look at the paper, we’ll never see a ‘b’ on the paper; however, we will be able to see one in the mirror, when we do the appropriate thing to have the mirror appear to reverse top-bottom but not left-right, the appropriate thing being just to face the paper to the mirror by rotating it around a horizontal axis rather than the (conventional, but not actually special in any relevant way) vertical axis.
Mirrors don’t have magical abilities to tell up-down from left-right (they’re not tapping into gravitational effects…); the only reason they appear to reverse one of these dimensions and not the other is because we follow one convention and not another in turning objects (paper, our own bodies) before looking in the mirror. The only thing a mirror actually reverses is depth; all the other effects arise from this by our own doing.
I get what you’re saying, Indistinguishable, but it is very hard to explain, since our frame of reference is defined by the very same parameters.
I think people might find it easier to understand if you place your theoretical mirror on the floor. It eliminates an aspect of the confusion. Actually, using a chiral structure such as a hand would be helpful, too: lay a mirror on the floor, and imagine a hand palm up, thumb pointing away from the mirror, then rotate the hand so that is palm down with the thumb pointing at the mirror. (The thumb demonstrates the illusion of the up-down myth. Clearly, up and down are “reversed” if you put the mirror on the floor.) The orientation with respect to your eyes of what you end up seeing in the mirror depends entirely on how you flip your hand over. However, it will structurally always appear the same, regardless of orientation (as the enantiomer of the hand you use).
On this we can agree.
Your original post sounded entirely too much like the “watch me turn this dollar bill upside down just by folding it” trick, and I thought you were pulling someone’s leg by telling them that turning a piece of paper upside down would magically change the actual facts of how a mirror works. Let’s just let it go at that.
‘‘Ground’’ is an electronics concept; a car, or a battery operated radio has a gound, or ‘‘common’’ where the electrons go after they’ve passed through the various circuits. VERY LOOSELY you could think of it as the place where all the pachinko balls collect. In the case of houses and such ground is the actual earth
my contribution:
Record players, 2 points on the album, they’re rigidly connected yet moving at different velocities. It kept me up long before Calvin and Hobbes came along.
