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dogfriend_ltk
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mirror optics
« on: Mar 9th, 2003, 12:40am » |
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First of all I would like to make sure that everyone knows what a corkscrew is used for. It is used for opening wine bottles and/or deducting physical laws. So, if one chooses to rotate a normal corkscrew from left to right he will witness that it(the screw) tends to go forward, a feature that we shall heceforward call "the screw law". That being asserted, let us return to the riddle in question.
What happens if I try to experiment the screw law inside of a mirror? Will it work the same? I believe not, and thus hereby assert the second screw law, which I shall call "the counterscrew law" stating that, upon rotating a normal screw inside of a mirror from left to right, not only will not it go forward, but, alas, it will move backwards.
Well, what has all this got to do with the actions of my mirrored alter-ego? The connection is very simple - inside the mirror 'left' will become 'right' and 'right' will become 'left' for the second time. When I raise my left hand, my relection will rise what APPEARS to be his left hand, but what in fact is, physically speaking, his right hand. So my reflection is in fact doing exctly what I am doing.
The End
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Icarus
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Re: mirror optics
« Reply #1 on: Mar 9th, 2003, 11:45am » |
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There is already a good discussion of what mirrors do here.
The mirrored corkscrew switches from a right-handed thread to a left-handed one. (Threads on any type of screw are called right-handed if when you curl the fingers of your right hand in the direction the screw is turned, the screw will advance in the direction pointed to by your right thumb.) Turning the screw clockwise will cause an ordinary right-handed screw to advance. But CW motion is turned into CCW (counter-clockwise) motion in the image. The CW turning of the "original" RH screw causes it to advance. In the mirror image, the CCW turning of the LH screw causes it to advance. So both screw and reflection advance when turned.
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ybr
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Re: mirror optics
« Reply #2 on: Apr 14th, 2003, 10:59pm » |
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I think the mirror does not 'reverse left and right' at all. It shows left on the left and right on the right, as well as up up and down down.
It's just that when we look in the mirror, we interpret left as right and right as left. They question is, why?
The answer is our the learned programming of our brains. If you stand in front of a person, facing away from him, your left and his are on the same side, much like in a mirror. The same goes for the other 'edges'. But you can't see him - because you're looking away!
In order to see him, you have to turn around, around a vertical axis, thereby reversing your left and right. Having seen this effect from when we're infants, we learn to recognize views of peers with left and right reversed, accordingly.
If our rotation method (for facing our peers) were somehow always on a horizontal axis, I suppose we'd learn to interpret mirror images as 'upside down'.
Any thoughts?
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Icarus
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Re: mirror optics
« Reply #3 on: Apr 15th, 2003, 6:29pm » |
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Not quite - The difference is seen in exactly that screw. If you look at the mirror image of an ordinary right-handed screw, you will see that were the image to be made solid, it would be a left-handed screw. Similarly, if something is rotating clockwise, its mirror image is rotating counter-clockwise. Reflection causes an image to undergo a "chirality" change. Our anthropomorphic mind-set determines how we perceive this change (i.e. as a reversal of right and left), but the change itself is inherent within the reflection.
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ybr
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Re: mirror optics
« Reply #4 on: Apr 16th, 2003, 11:40am » |
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Cool. I see your point. I think I remember this from organic chemistry, I believe it's called optical resolution or something like that; you have left- and right-handed molecules, like gloves - identical, but cannot be overlapped as they are 'mirror'-images!
But the neat thing is, I'm right (ugh! a pun!) too - but only for two dimensional objects, like a picture of a person, with left side, right, up, and down. The reason I'm wrong for a 3D object is that I missed the fact the there is a difference between the view from the mirror and the view from turning 180 degrees around a vertical axis, and that is that the mirror also reverses distance to the viewer!
In other words, if I look at a person from the back, I see left left and right right. And If i look at a mirror in front of him, I see left left and right right (unlike if I go to his front, turn 180-degrees and look at him). But in the mirror, his FRONT is closer to me, whereas in the 'real' person, his BACK is closer to me (I am behind him). So the mirror effectively flips front and back of the image, but not left right, thereby achieving the effect you describe with the corkscrew.
And again, we are used to seeing the right of a person's who is facing us (because we've rotated on the vertical axis) on the left side (and vice versa); for example we expect his heart to be on the right side of our view, not the left. So when see the person (or ourselves) in the mirror, we consider it 'wrong', or 'switched'.
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Icarus
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Re: mirror optics
« Reply #5 on: Apr 16th, 2003, 8:42pm » |
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Actually, your are not quite correct about 2D either: Consider the 2D shape to be something irregular, such at the outline of a dog. Look at its reflection, and you will see an image that is the reverse of the orginal. Rotating the reversed image in its plane will never get you something that matches the original. The only way of doing that is to lift the image up out of its plane, and flip it over.
Reflection in any number of dimensions is equivalent to such a flip in a higher dimensional space.
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ybr
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Re: mirror optics
« Reply #6 on: Apr 17th, 2003, 7:52am » |
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About 2D, I said:
If I look at a mirror in front of him, I see left left and right right (unlike if I go to his front, turn 180-degrees and look at him)
My point is that we think the 'wrong' thing with the mirror is that it is left-right reversed is because we normally turn around on a vertical axis to look at one another.
If our norm was to stand on our heads to converse (etc) with our peers, my sentence would have been:
If I look at a mirror in front of him, I see up up and down down (unlike if I go to his front, spin head over heels 180-degrees and look at him)
Is the outline of the dog identical to the image in the mirror? If you bring outline to be against the mirror, they will overlap. But we feel that that does not count, as we expect to first turn in our 3D space (or turn it thus), around the vertical or horzontal axis.
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Icarus
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Re: mirror optics
« Reply #7 on: Apr 17th, 2003, 7:08pm » |
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No, they are not identical. Think of it from the point of view of a two-dimensional observer in the same plane. When he travels around the original, keeping it on his right, he sees first the head, the back, tail, legs and belly, and returns to the head. Now he looks at the reflection. This time he must travel in the opposite direction, keeping it on his left, to see the parts of the dog in that order.
For every natural number N, there is a sense of "handedness" or as scientists call it "chirality", that applies to object in an N-dimensional space. That chirality goes away once we tack another dimension on. So my 2D picture dog comes in right-handed and left-handed versions as long as he is kept in 2 dimensional space. It is only when I am allowed to pick him up into the third dimension that he can be flipped over and changed from a RH dog to a LH dog, or vice versa.
But, in adding the third dimension, I also get 3D objects which have a handedness. If I had access to a 4th spacial dimension, I could flip my left shoe in it, and have two right shoes! Flipping my foot to match would be rather painful, so I better flip my right shoe so it becomes a left one. Then I can walk around with my right shoe on the left foot and my left shoe on the right, with no one the wiser (certainly not me, to waste such a neat trick on a pointless exercise!) 
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ybr
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Re: mirror optics
« Reply #8 on: Apr 17th, 2003, 10:46pm » |
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Wow, this is getting complicated! You seem to know about this a lot more than I do, so I apologize if I'm being fully seeing it eye to eye with you. Well, I am, but it depends on which eye is seeing which... 
I agree and love your explanations of chirality. I do not fully understand the dog explanation, as I'm not sure where his 'right' is ('keeping it on his right').
It seems to me that the mirror is acting as a 4th dimensional device to 'flip' the object in our space from left-handed to right-handed. Specifically, it is doing so by reversing it's front to back and back to front - only.
What I mean by 'only' is that we too can 'turn' an object back-to-front and front-to-back (i i.e. reverse which of the front or back sides is closer to us), without the higher-level dimension / mirror, by walking to it's other side. But then, to see / face it, we must turn either on a vertical or horizontal axis. This second fact keeps it from losing its 'handedness'.
So the mirror is not reversing left and right. It is reversing it's front-back-ness, by the laws of physics of light and reflection, etc. But we interpret this reversing as a reversing of left-right, because it's equivalent to having gone to the other side of a opposite-handed object (person), and turned our bodies 180 degrees. If we could design a trick mirror (like in a funhouse) that reverses front-back like a regular mirror, but also somehow really reversed left-right, the object would now appear to be correct-handed. But if instead of (the normal front-back and) left-right light-beam reversing it did (the normal front-back and) up-down light-beam reversing, it would also appear to use correct-handed!!
Hence my point that the mirror is not reversing left and right. It is reversing front and back, and we are interpreting it as reversing of left-right.
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redPEPPER
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Re: mirror optics
« Reply #9 on: Apr 18th, 2003, 4:43am » |
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I agree with you ybr when you say that a mirror inverts front and back, and nothing else. When you're facing the mirror, that is.
on Apr 17th, 2003, 10:46pm, ybr wrote:| If we could design a trick mirror (like in a funhouse) that reverses front-back like a regular mirror, but also somehow really reversed left-right, the object would now appear to be correct-handed. But if instead of (the normal front-back and) left-right light-beam reversing it did (the normal front-back and) up-down light-beam reversing, it would also appear to use correct-handed!! |
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Well guess what? Such a mirror exists. It's actually two mirrors. One for the front/back inversion and one for the left/right inversion. Put these two mirrors at a 90° angle. Face the first mirror. In it you can see a regular reflection. This mirror inverts your front and back, perpendicularly to the mirror plane. Now turn your head right towards the second mirror (we'll assume this one's on the right). You'll see another reflection. Even though this reflection has the same "chirality" as the first one, it was produced by inverting your left and right, perpendicularly to the mirror plane.
Now look towards the angle between the mirrors. There's also a reflection there, that is produced by light rays bouncing on both mirrors before coming back to you. So it could be said that this image is inverted front/back (by the mirror in front of you) and left/right (by the mirror on your right). Lo and behold, this image has the same "chirality" as yourself! Raise your left hand and the image will raise its left hand too.
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ybr
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Re: mirror optics
« Reply #10 on: Apr 18th, 2003, 7:49am » |
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Now, if you arrange the two mirrors one over the other at a 90 degree angle, instead of beside each other (i.e. the mirrors are in vertical axis arrangement, rather than a horizontal one), you will reverse up-down (as well as front-back). The double-mirror image will have the same chilarity as the original, but will look as though it was flipped front-back, we walked to it's other side, and turned 180 degrees head over heels to face it (as opposed to having turned around a vertical axis to face it)!
In the real (3D) world we cannot flip an object front-back without also flipping it left-right or up-down. The mirror does, however, so we interpret that as flipping it front-back and left-right (which we take for granted), then flipping it left-right again! It's that last one that stands out, so all we 'see' is that the mirror flips objects left-right, which was the original observation that we were supposed to explain.
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Icarus
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Re: mirror optics
« Reply #11 on: Apr 18th, 2003, 9:30pm » |
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There are a number (well, that number is 3) of ways to interpret what the mirror does. All of them are actually equivalent.
Concerning traveling around the dog and keeping it on the right, consider this: if you were squished flat, you would still have a right side and a left side. The concept of two sides, and always turning the same direction is still there in 2D, just as it is in 3D.
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WOUF
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If you put the mirror on the ceiling, or on the floor, up and down will be reversed, and so will be right and left.
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jackper
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Re: mirror optics
« Reply #13 on: Jun 25th, 2003, 5:30am » |
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well, i'm on ybr's side on this. his/her thesis of a "preferred axis of rotation" seems sufficient to explain mirror images and our impressions of them.
consider the dog outline: draw the outline on an opaque piece of paper. now, how are you going to view the mirror image?...you have to hold the paper up to the mirror, which requires that YOU rotate the paper to face the mirror, and you can choose to rotate the paper around a vertical axis, or a horizontal axis, or any other axis. YOU do the rotation, whether physical in this case, or simply mental. [if you draw the outline on a transparent piece of paper, you can see a mirror image WITHOUT turning the paper... and the mirror image is identical with the original...because YOU didn't rotate the image.]
The examples of the corkscrew and right-left handed molecules are just examples wherein our preference for one particular axis for rotation is less obvious.... much like the word 'AMBULANCE': most people will write the mirror image as a right-left reversal because we tend to want to keep letters 'right-side up'.
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Icarus
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Re: mirror optics
« Reply #14 on: Jun 26th, 2003, 8:16pm » |
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Take a LH threaded screw (if you can find one) and hold it up to the mirror. Examine closely the mirror image: Suppose that the image were to magically become solid, and that you could reach in the mirror and grab it. You then take your two screws over to a block of wood and start screwing them in. Lo and Behold! You have to turn them in opposite directions! Your original screw was a LH thread. The new screw is RH. This has nothing to do with our preferences. It is a fundamental property of reflection. Hold your left shoe up the mirror. If you could reach in and grab its reflection, it would fit comfortably on your right foot.
You have also missed the point of the dog outline discussion entirely. Your dog outline is in three dimensions, so yes you can rotate it around to get the reverse outline. If you will read the earlier posts again, you will discover that I said so.
It is when you are restricted to 2 dimensions that there is a difference between a right handed and a left-handed dog (or any other irregular shape). A 2-D mirror is just a line on that page. The reflection is obtained by taking each point of the original shape, finding the perpendicular from that point to the "mirror-line", and choosing the point on the other side of the mirror-line that is the same distance away. All such points together make up the reflection.
Within the confines of the page, you cannot rigidly move the reflected image in such a way as to make it identical to the original. It is only when you are allowed to move the image into the third dimension that this becomes possible.
So you have a 2-D sense of chirality which disappears when a 3rd dimension is added. But in doing so you pick up a 3-D sense of chirality, which is the one we are so familiar with. We could get rid of it by adding a 4th dimension, allowing us to turn right shoes into left shoes and vice-versa. But we would also pick up a 4-D sense of chirality, which would require a 5th dimension to lose, but then ...
(There is also a 1-D sense of chirality that goes away in 2-D.)
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RiddleGuy
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Amusingly enough, no one answered this question at the low level I did when I read it -- referring to light optics and how light would strike an object, bounce off of the mirror, and be received by eyes.
In any event, Icarus thanks for your edifying discussion of chirality. When I read about the concept of chirality in other dimensions, I was left wondering "What about 1-D" and then I saw you mention it in your final post. Can you elaborate on 1-D chirality? I was trying to think of how a point could have some sort of "handedness" and I couldn't come up with anything.
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James Fingas
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Re: mirror optics
« Reply #16 on: Aug 29th, 2003, 7:28am » |
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The 1D chirality is probably direction. Picture a line with an object sitting on it:
----0--00--------
The object needs to have more than a single point to be recognizeable.
Now mirror it:
----00--0--------
Moving it in just one dimension can't make this the same object we started with.
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Icarus
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Re: mirror optics
« Reply #17 on: Aug 30th, 2003, 10:50am » |
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Yes - Objects in 1-D are generally 1-D, (just as we are 3-D). And the points that make them do not have to be homogeneous. So consider a line segment that is blue on one end and green on the other:
______
In the plane, it is trivial to rotate it so that the green is on the left. But if it is trapped in a line, no such rotation is possible. So in 2-D there is no difference between the two segments
______ ______
But in 1-D they are distinct.
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John_Gaughan
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Re: mirror optics
« Reply #18 on: Jan 14th, 2004, 5:50am » |
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If my eyes were oriented one over the other but I still saw things with "down" in the same direction (i.e. I am not just turning my head 90 degrees), would a mirror flip things upside-down?
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towr
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Re: mirror optics
« Reply #19 on: Jan 14th, 2004, 6:30am » |
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Since it is irrelevant to the problem wether there are one or two eyes, I'd say no.
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Icarus
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Re: mirror optics
« Reply #20 on: Jan 14th, 2004, 7:29pm » |
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If we were built symmetrically for up & down, but asymetrically for right to left, we would interpret the image as having its right to our right & left to our left, but with its' top and bottom sides reversed from ours - as opposed to having top and bottom matching but right and left reversed, as we normally perceive it.
If we were asymmetric in all 4 directions, we would perceive the reflection as having its right to our right, left to our left, top to our top, bottom to our bottom, with no flipping at all - but we would also perceive the image as not being a good representation of us, since it four sides will be in the wrong order.
We interpret the image we see as being what we look like when facing the opposite direction, because that is the natural way we see other people. But this is not true, since the reflection has everything on the opposite side from where we would if we were facing the other way.
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John_Gaughan
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Re: mirror optics
« Reply #21 on: Jan 15th, 2004, 1:22pm » |
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Thanks Icarus, I get it. I always understood the "what" of mirrors but not the "why." I guess I should have stayed awake during Physics class :-D
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Kyle Bennett
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Left and right are defined only within the context of our point of view. Up and down are defined relative to a context outside our point of view. The mirror reverses our point of view, thereby redefining everything defined within it, but it does not change anything defined outside of that context.
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Murali Mohan Saginala
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The counterpart of 'left' in a mirror is 'right' and vice-versa. But the counterpart for 'up' in a mirror is 'up' and for 'down' it is 'down'.
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icecoldcelt
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Re: mirror optics
« Reply #24 on: Mar 5th, 2010, 1:55pm » |
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And what if we were symmetric front to back(only)?
What if we were symmetric front to back and left to right?
What if we were symmetric front to back and up to down?
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