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BNC
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Mirror inversion  
« on: Jan 21st, 2003, 9:38am »
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The following is not really a riddle. It is, however, a question Iíve been trying to figure out for some time now, unsuccessfully, and I hope that some of the brilliant people here may help.
 
Iím also not convinced itís ďhardĒ, but as I said, I couldnít figure it out, although (on the surface) itís an optics question, and I have a PhD in optics. I asked many colleagues of mine, some of which are University professors, and they donít have the answer as well. So maybe itís not an optics questions after allÖ
 
So, after the long introduction, here is the question:
 
Stand in front of a mirror. Look at the reflected image. Now, raise your right hand. The reflected image seems to raise its left hand. Raise your left hand. The image raises its right. So, the mirror inverts left and right.
 
Now, move your head up and down. The image will move up and down. So, the mirror does NOT invert up and down.
 
Why is the inversion not symmetrical? Why invert left-right and not up-down?
 
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Re: Mirror inversion  
« Reply #1 on: Jan 21st, 2003, 10:35am »
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actually, my mirror image just moves the hand which is on my right when I move my hand on my right..
 
try placing a mirror underneath yourself, or overhead, on your top will no longer be your mirrorimages' top either..
For instance, take a ball, and lay a mirror on the floor, drop the ball on the mirror.. What do you see? A ball in the mirror image falling up..
Take a standing mirror, throw the ball at the mirror. What do you see? A ball in the mirror image moving towards you..
 
The problem is non-inversion, rather than inversion.. For people standing on the same plane, up is in the same direction. But if we face each other our left and right are in opposite directions.. They change as we move..
But consider the people on the other side of the world do have a different 'up' and 'down' from us..
 
A mirror is, unlike us, not antropocentric in its directions. Our up is its up, our left is its left, etc..
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Re: Mirror inversion  
« Reply #2 on: Jan 21st, 2003, 10:55am »
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Yeah, what towr said.
 
A nice, easy way to put it is: when you're standing in front of it, a mirror doesn't invert left and right any more than up and down.  It simply inverts front and back.
 
As left and right are relative to the front, it will seem that your mirror image raises its left hand.  But not because left and right were inverted.  They were not: your reflection's raised hand is still on your right.
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Re: Mirror inversion  
« Reply #3 on: Jan 21st, 2003, 10:59am »
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The solution I heard to this problem was: Because your eyes are positioned on the left and right sides of your face and not the top and bottom.
 
Which isn't a terribly great answer, but it's good for provoking thought. Smiley
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Re: Mirror inversion  
« Reply #4 on: Jan 21st, 2003, 11:27am »
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"Now, move your head up and down. The image will move up and down. So, the mirror does NOT invert up and down."
 
If you move your head left, the image moves it's head left.  It does not invert left and right either.  I've heard this phenomenon explained as the misperception that your image is facing you and that it's "right" hand is to your left.    
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Re: Mirror inversion  
« Reply #5 on: Jan 21st, 2003, 5:08pm »
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Oh yeah. Damn me for having an incomplete memory.
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william wu
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Re: Mirror inversion  
« Reply #6 on: Jan 22nd, 2003, 2:30pm »
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FYI, this puzzle was listed in the Microsoft section as Mirror Optics, but no one has posted a thread on it yet. Yeah, I knew someone who was asked this puzzle during an interview.
 
The solution I heard was that physicists have never agreed on an official answer, although that may have changed. If I recall correctly, this puzzle is discussed in the last recorded Feynman lecture at Caltech, in the series on which the famous Lectures on Physics books are based. Feynman suggested this phenomena has something to do with a fundamental and unexpected asymmetry in nature, and cited experiments recent to that era. It went over my head but I'll listen to it again. I have an MP3 recording of it and I'll upload it for you guys later. It's a fantastic lecture, humorous, philosophical, and extremely interesting. Should make good discussion!
« Last Edit: Jan 22nd, 2003, 2:36pm by william wu » IP Logged


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Re: Mirror inversion  
« Reply #7 on: Jan 23rd, 2003, 1:16am »
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I think this 'effect' occurs simply because people get confused between the 'reflection' function and the 'rotation' function.
 
If you look at an example on an X-Y graph, and say that the mirror is on the Y axis, the mirror just does Fmirror(x,y) = (-x,y).
 
However, when you meet people and look at their left/right hand, the actual function is Fmeet(x,y)=(-x,-y) which is a rotation function.
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Re: Mirror inversion  
« Reply #8 on: Jan 23rd, 2003, 6:29am »
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If you take two mirrors, and place them at a 90 degree angle, then you do get rotation.. Which is a nice effect as well.. But not really any more helpfull if you're trying to comb your hair or something..
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Re: Mirror inversion  
« Reply #9 on: Jan 23rd, 2003, 8:15pm »
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To express it another way:  People are roughly symmetric, so when we look in a mirror, we see something that looks like a person.  If that actually were a person over there on the other side of the glass, it looks like it would have its left hand on the same side as our right hand, etc.  But it's not actually a person.
 
If people had up-down symmetry, instead of left-right symmetry, then we would think that mirrors reversed up and down.  And if people had no symmetry at all, then we wouldn't have this problem at all, because that thing in the mirror wouldn't look like a person at all.
 
Yet another way to think about it:  Think about north, south, east, west, instead of left, right.  When I look in my bathroom mirror and raise my north hand, my image also raises its north hand.
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Kozo Morimoto
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Re: Mirror inversion  
« Reply #10 on: Jan 25th, 2003, 2:40am »
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There are a couple of interesting experiments listed at howstuffworks.com.
 
You write your name on a piece of paper, which is slightly transparent so that you can see what's written from the other side.  
 
If you present your name to the mirror, it looks reversed in the mirror. (unless you have an unsual name which is both palindromic and reflection symmetric, like TOOT or AIMIA etc)  But if you look at the back of the paper, you see your name backwards, just like in the mirror. [incidentally, my MIT t-shirt spells TIM whenever I look in the mirror and always gives me a chuckle or two]
 
If you present the back of the paper to the mirror, the reflection will show your name properly, just like how the piece of paper you are holding also shows your name properly.
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Re: Mirror inversion  
« Reply #11 on: Jan 25th, 2003, 12:28pm »
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On the planet Gzimmerdell live three intelligent species. All three possess bodies consisting of round disks, featureless except for an eye in the center, and four appendages equally spaced around the diameter. They travel by pulling in the appendages and rotating about their axes. Each has little to do with the others, though they share a language.
 
The Humpelts have an eye on only one side. Their appendages consist of a fusnel, for eating, breathing, speaking, and hearing; and opposite it is the lensuf, for excretion and sex. The remaining two appendages, called rebbets, are identical and used for standing and for manipulation. Facing a Humpelt, the rebbet one finds as one passes clockwise from lensuf to fusnel, is called the venticle rebbet, while the other is the resticle rebbet. When two Humpelts stop to have a conversation, they rest on a rebbet facing each other with their sole eye, but it is considered extraordinarily rude to align your lensuf with the other's fusnel. (Would you want someone sticking their butt in your face?) When Humbolts look in a mirror, they see their reflection properly lined up with them, lensuf to lensuf and fusnel to fusnel. But when a Humpelt waggles his venticle rebbet, the reflection waggles his resticle rebbet. Why is it, they wonder, that mirrors reverse top to bottom, but not side to side?
 
The Gerfas have differentiated rebbets, one (which they call the resticle) for standing only, the other (the venticle) for manipulation. The Gerfas are also the only race to have an eye on both sides of their disks, (so the definition of venticle vs resticle used by Humpelts does not apply, since the Gerfas have no well-defined front or back). Gerfas call the side which when faced shows the venticle, fusnel, resticle, and lensuf in clockwise order the lusan side, while the other is called the nasul side. When a Gerfa looks in a mirror with his lusan side, he sees his reflection, but what is clearly his nasul side! How is it, he wonders, that though the mirror does not reverse top and bottom, nor side to side, how is it that it manages to show him the side he has facing away from the mirror?
 
Like the Gerfas, the Broubats have 4 differentiated appendages. Like the Humpelts, they have an eye only on one side. The Broubats are split into two factions: those with their eye on the lusan side, and those with the eye on nasul side. Lusaners and Nasulers hate each other with a passion, each viewing the other side as the very embodiment of evil. The only thing on which they agree is that mirrors are the most vile thing in creation. For when a Lusaner looks in a mirror, he sees himself, but as a horrible Nasuler. And no Nasuler can dare to view himself as a dastardly Lusaner. How is it, they wonder, that these wicked instruments, which do not reverse top and bottom, or side to side, or front to back, how is it that they manage to reverse good and evil? Huh
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Re: Mirror inversion  
« Reply #12 on: Jan 26th, 2003, 12:06pm »
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If you have a right handed system of x-y-z axes and look at it in a mirror it becomes a left handed system. This occurs no matter the orientation of the axes relative to the mirror. This can be verified by expressing the axes as vectors in some absolute coordinate system, creating the reflected coordinate system by using symmetry about the plane of the mirror, and computing cross product of any two axes.
 
We define top and front independently of the handedness of coordinate system. For example, the top of my head is the direction opposite from my neck, and front of my head is the side with my face on it. However, we implicitly define left and right in terms of the handedness of the coordinate system: right is the direction defined by cross product of the front and top directions. Since the refection has a left handed coordinate system, cross products have opposite signs, so left and right get reversed.
 
If instead, left is defined without reference to handedness of the coordinates system there is no reversal. If I define left arm as the one closest to the heart, then when I raise my left arm, so does my reflection.
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Kozo Morimoto
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Re: Mirror inversion  
« Reply #13 on: Jan 26th, 2003, 11:31pm »
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I thought that the heart was centered in your chest cavity...  Its just that the bigger chamber was situated on your left.
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Re: Mirror inversion  
« Reply #14 on: Jan 29th, 2003, 10:49am »
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Instead of looking at your hand in the mirror, look at the room behind you. Now when you turn around and look at the room directly, everything is switched left/right. But that's because you turned around by turning left or right. If instead you bend over and look at the room between your legs, then left and right are still right where they were in the mirror, but everything's upside down. It's how you turn around that inverts things, not the mirror.
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Re: Mirror inversion  
« Reply #15 on: Jan 29th, 2003, 7:42pm »
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Phil, are you saying the mirror is not inverting anything, except the direction that the reflection is facing? What if you stand with your body turned 90 degrees from the mirror (with your left arm close to the mirror and right arm furthest from the mirror).  If you raise your right arm, the reflection still raises its left arm even though both you and your reflection are facing the same direction and top of your heads are in the same orientation.
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Re: Mirror inversion  
« Reply #16 on: Jan 30th, 2003, 1:55am »
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If your body is turned 90 degrees from the mirror, the mirror DOES invert left and right, because your left/right axis will be perpendicular to the mirror plane.  
 
When you're facing the mirror, it inverts front and back because your front/back axis is perpendicular to the mirror plane.  As left and right are relative to front and back, that gives the impression that left and right are inverted, while they are not.  
 
Proof: when facing the mirror, if you throw something to your right, your reflection will throw something to its left, but to your right.  Left and right were not inverted.  When at a 90 degrees angle, throw something to your right and your reflection will throw something to its left and to your left.  Left and right were really inverted.
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Re: Mirror inversion  
« Reply #17 on: Jan 30th, 2003, 5:39am »
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Yes, I meant that the mirror inverts front and back. When I look into a mirror and I'm facing west, I see someone facing east. It's too hard to imagine the body turning inside out and the eyes, nose, and mouth passing through the body to end up on the other side, so when we look in the mirror we always either imagine the things in the mirror having been turned around, or we turn around ourselves to compare what's in the mirror with reality. In either case, you always turn around left/right, rather than by turning upside down, unless you enjoy looking at the world between your legs.
Stand perpendicular to a mirror and your right and left hands will be inverted because of the front/back inversion. But now if you've got a really good imagination, imagine the guy in the mirror either having his face morph to the back of his head, or having his face drop straight to his feet turning him upside down without moving his hands. Either inversion will give you a normal person with his right and left hands on the correct side of his body.
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Re: Mirror inversion  
« Reply #18 on: Jan 30th, 2003, 11:00am »
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I think that we agree so long: the mirror doesn't (invert left and right).
Left and Right are subjective only.
The mirror reflects the beams of light entering back to the viewer; if they stem from the right hand or the foot: they will 'return' there.
If you are lying on a bed with a mirror in a horizontal plane above you, of course you'd perceive you to be above that mirror, respectively looking down onto your bed, while actually you are looking up. So don't tell us, that a mirror doesn't 'invert' (see above) up and down.
Furthermore, it projects a 3D-space into a plane, and we can never ever retrieve the 3D-scene from a plane. Think of those perspectives of cubicles, where you can easily 'swap' the subjective impression if you look at them from top or bottom.
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Re: Mirror inversion  
« Reply #19 on: Jan 30th, 2003, 7:41pm »
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So many confusing explanations. I think part of the problem is that people are using different definitions of what right and left are.  
 
There is nothing subjective about the appearance of a right and a left hand. They are distinguishable from a each other by looking at relative positions of thumb, fingers, and palm.  The reflection of your right hand in a mirror looks like a left hand no matter its orientation relative to the mirror.
 
See my post from Jan 26. Nobody seems to have read it, but I think it explains it all.
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Re: Mirror inversion  
« Reply #20 on: Jan 30th, 2003, 8:01pm »
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MY point seems not to have been taken either, even though it is not truly mine but another way of saying the same thing as has been said before by several respondants.  
 
Mirrors reverse the chirality of what they reflect, as SWF has said without the high-dollar word.
 
The interpretation of that reversal as exchanging side-to-side and not up-and-down is strictly a cultural thing, brought about by the symmetry of our bodies. Other beings, with differing circumstances, could interpret the reversal in other ways (though I admit it is unlikely that any smart enough to make mirrors would be stupid enough to mistake what the mirror showed them as their opposite side!)
« Last Edit: Feb 8th, 2003, 3:21pm by Icarus » IP Logged

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Re: Mirror inversion  
« Reply #21 on: Jan 31st, 2003, 3:10am »
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on Jan 30th, 2003, 7:41pm, SWF wrote:
There is nothing subjective about the appearance of a right and a left hand. They are distinguishable from a each other by looking at relative positions of thumb, fingers, and palm. †The reflection of your right hand in a mirror looks like a left hand no matter its orientation relative to the mirror.

 
As you said, the appearance of the hand depends on the position of the fingers relatively to the palm (i.e.: it's subjective).  If you hold a hand with the palm facing the mirror, then the mirror will invert the palm with the back of the hand, perpendicularly to the mirror plane.  Left and right were not inverted.  Front and back were.
 
Take a right hand glove.  Turn it inside out.  Now the thumb is on the other side of the palm.  Does that mean it's now a left hand glove?  That's what happens in the mirror: the reflection of your right hand is not a left hand, it's a right hand turned inside out along the axis that's perpendicular to the mirror plate.
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Re: Mirror inversion  
« Reply #22 on: Jan 31st, 2003, 11:21am »
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Somebody up there mentioned Feynman. In that same lecture (mostly), Feynman asks us to imagine that we have discovered intelligent life and are communicating with them. Once the language barrier has been sorted out, we explain to them how we look like.
 
How tall ? Uh....So and so many hydrogen atoms.  Generally bilaterally symmetric body shape.....The heart is located slightly on the "left" side.
 
ALIEN:  Duh ? Left ?
 
Is there any way of objectively defining left and right ? Or clockwise and anti-clockwise for that matter. I do not think so. It's mere convention.  
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Re: Mirror inversion  
« Reply #23 on: Jan 31st, 2003, 12:49pm »
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A quick google search tells me that only left-handed subatomic particles and right-handed antiparticles partake in weak interactions. And circular polarized light destroys one type of helical molecules more than the other, which is supposedly the reason why enzymes on earth are left-handed and sugars are right-handed. So alien dna might have the same handedness as ours. There may be other physical distinctions that would let us define the terms.
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Re: Mirror inversion  
« Reply #24 on: Jan 31st, 2003, 3:06pm »
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on Jan 31st, 2003, 12:49pm, Phil wrote:
So alien dna might have the same handedness as ours. There may be other physical distinctions that would let us define the terms.

 
Interesting, but there are other configurations of DNA that have been observed, and theorized, some of which can be more compact than ours.  We couldn't assume that their DNA is the same as ours.  I think there was actually an X-files where Scully's "proof" of alien DNA was a base other than C,T,G,A, or U.  
 
I would think there are other natural systems of fixed chirality (for lack of a better term) that are not biological, but none come to mind.
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