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        riddles >> hard >> Mirror inversion
        
(Message started by: BNC on Jan 21^st, 2003, 9:38am)

Title: Mirror inversion
Post by BNC on Jan 21^st, 2003, 9:38am

The following is not really a riddle. It is, however, a question I’ve been trying to figure out for some time now, unsuccessfully, and I hope that some of the brilliant people here may help.

I’m also not convinced it’s “hard”, but as I said, I couldn’t figure it out, although (on the surface) it’s an optics question, and I have a PhD in optics. I asked many colleagues of mine, some of which are University professors, and they don’t have the answer as well. So maybe it’s not an optics questions after all…

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?

Title: Re: Mirror inversion
Post by towr on Jan 21^st, 2003, 10:35am

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..

Title: Re: Mirror inversion
Post by redPEPPER on Jan 21^st, 2003, 10:55am

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.

Title: Re: Mirror inversion
Post by Garzahd on Jan 21^st, 2003, 10:59am

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. :-)

Title: Re: Mirror inversion
Post by prince on Jan 21^st, 2003, 11:27am

"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.

Title: Re: Mirror inversion
Post by Garzahd on Jan 21^st, 2003, 5:08pm

Oh yeah. Damn me for having an incomplete memory.

Title: Re: Mirror inversion
Post by william wu on Jan 22^nd, 2003, 2:30pm

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!

Title: Re: Mirror inversion
Post by Kozo Morimoto on Jan 23^rd, 2003, 1:16am

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.

Title: Re: Mirror inversion
Post by towr on Jan 23^rd, 2003, 6:29am

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..

Title: Re: Mirror inversion
Post by Chronos on Jan 23^rd, 2003, 8:15pm

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.

Title: Re: Mirror inversion
Post by Kozo Morimoto on Jan 25^th, 2003, 2:40am

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.

Title: Re: Mirror inversion
Post by Icarus on Jan 25^th, 2003, 12:28pm

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? ???

Title: Re: Mirror inversion
Post by SWF on Jan 26^th, 2003, 12:06pm

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.

Title: Re: Mirror inversion
Post by Kozo Morimoto on Jan 26^th, 2003, 11:31pm

I thought that the heart was centered in your chest cavity... Its just that the bigger chamber was situated on your left.

Title: Re: Mirror inversion
Post by Phil on Jan 29^th, 2003, 10:49am

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.

Title: Re: Mirror inversion
Post by SWF on Jan 29^th, 2003, 7:42pm

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.

Title: Re: Mirror inversion
Post by redPEPPER on Jan 30^th, 2003, 1:55am

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.

Title: Re: Mirror inversion
Post by Phil on Jan 30^th, 2003, 5:39am

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.

Title: Re: Mirror inversion
Post by udippel on Jan 30^th, 2003, 11:00am

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.

Title: Re: Mirror inversion
Post by SWF on Jan 30^th, 2003, 7:41pm

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.

Title: Re: Mirror inversion
Post by Icarus on Jan 30^th, 2003, 8:01pm

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!)

Title: Re: Mirror inversion
Post by redPEPPER on Jan 31^st, 2003, 3:10am

on 01/30/03 at 19:41:54, 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.

Title: Re: Mirror inversion
Post by jabhiji on Jan 31^st, 2003, 11:21am

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.

Title: Re: Mirror inversion
Post by Phil on Jan 31^st, 2003, 12:49pm

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.

Title: Re: Mirror inversion
Post by prince on Jan 31^st, 2003, 3:06pm

on 01/31/03 at 12:49:31, 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.

Title: Re: Mirror inversion
Post by udippel on Feb 1^st, 2003, 2:19am

Now we seem to drift off, somehow ?
I do agree with redPEPPER (if he doesn't mind) on the subjectiveness of 'handedness'.
Standing in front of my course, when I move to the right of the stage, the students have to turn (at least their eyes) to the left. For them it's left where I'm heading. Do I walk up the stairs to the last, uppermost row, at least everyone perceives me going 'up'; irrespective if the students sit below or above the row that I've just reached.
The very moment I'll see my image (actually it is not an image!) in the mirror in the morning raising the left hand when I raise my left hand - that is the *other* side ! - I'll definitively stop taking booze. *That* would be inverting left and right, right? But as long as my left hand still shows up on my left side, even 'in' the mirror, I'll be fine.
And my mirror at least doesn't fail me here even if I turn the horizontal orientation of my eyes by 90°. Don't know what your mirrors do, but mine still shows the - then - upper hand to be upper; just like the left hand earlier was still the left hand. So the mirror in this household at least does *not* treat left/right different to up/down.

Title: Re: Mirror inversion
Post by Chronos on Feb 3^rd, 2003, 5:31pm

Quote:

A quick google search tells me that only left-handed subatomic particles and right-handed antiparticles partake in weak interactions.

Yes, but then you have to tell them which are the particles and which are the antiparticles. It can still be done, though, since there are subatomic processes such as the decay of the long-lived K meson which do make a very slight (on the order of one part in a thousand) distinction between matter and antimatter.

The bit about light degrading certain chiralities of molecules more than others, though, I would suspect is a myth. Chirality preference only shows up in the weak interaction, which is almost completely negligible in chemistry.

Title: Re: Mirror inversion
Post by Bored to Death on Feb 8^th, 2003, 10:10am

My goodness.

Why do we all get into this sort of discussion? The reference point of the reflected image is meaningless. (Its left, right, up, or down.)

If you are not convinced, read the post by udippel.
And think hard. Very hard.

I’m sure there are other posts, but I don’t think the puzzle deserves any more attention. So, I didn’t bother to read them all.

Title: Re: Mirror inversion
Post by Interesting... on Jan 21^st, 2004, 11:08am

I found another good example when I was thinking about this, and before I read this page and forum:

Look a text in a mirror, than rotate the text 90 degrees. The mirror inverts the text in exactly the same way, and thus makes no difference between up/down and right/left. Purely cultural.

Title: Re: Mirror inversion
Post by deoBRAT on Feb 6^th, 2006, 11:45pm

Hey, seems there is a lot of heated discussion going on. I have a fairly simple explanation (though I am not sure if its enough)

A mirror, by definition inverts the plane perpendicular to it and leaves the one that is parallel to it.

If we stand in front of the mirror, Vertical plane will remain unchanged, but the horizontal plane gets rotated 180 degrees.

Thats the reason why right seems to be left (becuase its in the horizontal plane, and it gets rotated 180 degrees) and up remains up (cause its in the vertical plane) in the mirror.

Title: Re: Mirror inversion
Post by rmsgrey on Feb 7^th, 2006, 6:00am

on 02/06/06 at 23:45:56, deoBRAT wrote:

There are an infinite number of planes perpendicular to most mirrors - including at least one vertical one. If you have a mirror that isn't itself vertical, then there is no horizontal plane perpendicular to it; if the mirror is actually horizontal, then all the perpendicular planes are vertical.

And the one thing a (single, plane) mirror definitely does not do is rotate anything.

If you hold something between you and a mirror, you see the near side "live" and the far side reflected - the mirror doesn't change left and right or up and down, but does switch front and back.

A simple experiment to demonstrate this is to take an arrow and a mirror, and see how the direction of the arrow compares to that of its image in the mirror - I find that an arrow pointing up, down, left, right or anything in that plane parallel to the mirror points in the same direction in the mirror as in real life, while anything pointing towards the mirror points away, and vice versa

Title: Re: Mirror inversion
Post by Grimbal on May 16^th, 2006, 4:57am

In fact, the mirror doesn't reverse anything. The mirror is a tool that lets you see around a corner, so to say. If you think you see "through" the mirror, you haven't really understood what it does. What you see is yourself, located on this side of the mirror. If you don't locate that image correctly, if you think that what you see is behind the mirror, and as a result label "left" what is in fact "right", it is your own mistake.

The day you really see a mirror for what it is, you see it as opaque as a wall.

Title: Re: Mirror inversion
Post by alien on May 16^th, 2006, 6:25pm

Just turn your back to the mirror and the mirror will, for once, reflect the way it should. Maybe the mirror is gay.. If so, I am not turning my back to it. No sir, not a chance.

Title: Re: Mirror inversion
Post by uk9raine on Dec 1^st, 2006, 9:45pm

I'm really sorry, but, did I read that you have a PhD in optics? ....And this has been troubling you?..... :o ....And your professor friends couldn't explain this to you either?....??? WOW ! Here's one for you then, fella!...

"If your body's core temp is 98.6F ..... then why do we sweat when its only 80F outside, yet, we'd get hypothermia if we were in 80F water for too long?"

Title: Re: Mirror inversion
Post by THUDandBLUNDER on Dec 2^nd, 2006, 5:37am

on 12/01/06 at 21:45:54, uk9raine wrote:

. "If your body's core temp is 98.6F ..... then why do we sweat when its only 80F outside, yet, we'd get hypothermia if we were in 80F water for too long?"

Air is a poor conductor of heat (hence string vests in winter), water is not.

Title: Re: Mirror inversion
Post by Grimbal on Dec 4^th, 2006, 1:58am

80°F = 26.6°C
98°F = 37°C

makes it much clearer ;)

Title: Re: Mirror inversion
Post by towr on Dec 4^th, 2006, 2:32am

I don't think I'd get hypothermia any time soon in water with a temperature of 26.6 C (80F)

also

Quote:

Expected Cold Water Survival

Temperature Fahrenheit-------------------------Exhaustion/Unconscious------------------- --Expected Survival

32.5------------------------------------------------------------ <15 min. ------------------------------------- 10 to 45 min.
32.5 - 40------------------------------------------------------ 15 - 30 min. ------------------------------- 39 to 90 min.
40 - 50--------------------------------------------------------- 30 - 60 min. -------------------------------- 1 to 3 Hours
50 - 60--------------------------------------------------------- 1 - 2 Hours -------------------------------- 1 to 6 Hours
60 -70---------------------------------------------------------- 2 - 7 Hours --------------------------------- 2 to 40 Hours
70 -80---------------------------------------------------------- 3 -12 Hours --------------------------------- 3 to Indefinitely
Over 80-------------------------------------------------------- Indefinitely --------------------------------- Indefinitely

(http://www.walrus.com/~belov/hypothermia.html)

Title: Re: Mirror inversion
Post by BNC on Dec 4^th, 2006, 6:59am

on 12/01/06 at 21:45:54, uk9raine wrote:

I'm really sorry, but, did I read that you have a PhD in optics? ....And this has been troubling you?..... :o ....And your professor friends couldn't explain this to you either?....???

Yes, yes, and yes.
surprised?

Quote:

WOW ! Here's one for you then, fella!...

"If your body's core temp is 98.6F ..... then why do we sweat when its only 80F outside, yet, we'd get hypothermia if we were in 80F water for too long?"

I beleive the answer was provided, but do tell: how does it relate to original question?

Title: Re: Mirror inversion
Post by Bobishkindaguy on Oct 7^th, 2007, 7:56pm

I've been reading all the explanations, but I'm not sure I understand it yet.

Standing in front of the mirror, it's true, you move your left hand and the hand of the "guy in the mirror" that is on your left also moves.

It's also true that front-to-back are "reversed". That is, point everywhere and the image points to the same place, except when you point toward the image, and in that case, in that plane of pointing, the image reverses and points, not in the direction you are pointing, but back at you.

And yes, if you rotate things on their horizontal axis instead of their vertical axis, then the imaginary "reflection" that results would be "waving the same hand" as you are.

BUT I cannot escape the simple truth that if I'm a gas station attendant named "Bruce", (which is a legal name, even outside of Australia), (no offense, just kidding; monty python silliness), and I stand in front of the mirror, my image in the mirror's name on his name label on his chest is BACKWARDS.

How about this hypothesis:
The "world" inside the mirror has an opposite frame of left-right reference to "our world". This sounds ridiculous, but think about it: There really is no "person" there, anyway, right? The "world" in the mirror is imaginary anyway, so we have to "invent" a set of laws of physics for that "world".

I know, I know. But Biff is my supervisor, so I just can't stand this level of confrontation with my mirror image. I'm afraid this puzzle has driven me crazy la la la la la la

Title: Re: Mirror inversion
Post by blacksabbath8907 on Oct 22^nd, 2007, 11:02pm

Alright I'm sorry if this is wrong or incomplete or anything but I thought about it and so far no one has proved this wrong. So here is my idea.

To help you understand what is happening, you must understand the two events that are occurring. First there is a mirror image made, second that image is moving while you move. I will first explain how the motion works.

What you must first consider is what the mirror is actually representing. To explain what it is representing, I will first explain to you how the mirror is working. The mirror can be considered a two-dimensional plane existing in a three-dimensional universe. Before you can understand this concept it would probably be easier to imagine a one-dimensional mirror in a two-dimensional world.

Imagine an x-axis and a y-axis on a graph. This will be our two-dimensional world. Now imagine that there is a mirror that runs parallel to the y-axis and perpendicular to the y-axis. An example of this in the real world would be a wall mirror and your floor, negating the width of the mirror. The floor will be our x-axis and the wall with the mirror will be our y-axis. Now pretend that there is a ball on the floor that can only move towards and away from the wall and up and down. This is our two-dimensional system. Now pretend that the ball is moving away from the mirror. In the mirror it appears that the ball is moving opposite of the direction our ball is moving, but also moving away from the mirror on its side, in other words the motion is inverted. This is a simple property of light; as an object moves away from the observer it appears smaller because less light waves are able to hit it and bounce back towards our eyes and this is how we are able to perceive things in three dimensions. This is what happens when an object moves perpendicular to the reception of the light. Now when the ball moves up, instead of the ball in the mirror moving down it moves up as well. This is because the distance between the observer and the ball remains constant, but it is a matter of placement within this constant distance that changes, it is because motion is in the dimension parallel to the mirror. This explains why it is that the mirrored movement is not universally related to the movement of the object.

Now that you have understand the concept of a two-dimensional system with the one-dimensional mirror all you need to do is add in one extra dimension. Now we have the x-axis, the y-axis and also the z-axis. We are now going to find out why the three-dimensional actions are exhibited in the way they are. Pretend that our one-dimensional mirror is now a two-dimensional mirror, with an x-axis and a y-axis, as our mirrors are. Rather than it just being a line up and down, it now has width and we can consider this a plane. Now we are looking at this two-dimensional plane from its z-axis, a two-dimensional object in a three dimensional world. Now what we have is another axis, z, perpendicular to our mirror. Based on our knowledge of how a perpendicular axis relates motion in the world to that of its reflection, we can determine that the motion of the z-axis will be inverted on the mirror. The x-axis and y-axis, however, are both parallel and therefore will not be influenced by the reflection (see image 2.)

Now that you understand how motion works, there can still be a question about how the image is made on the mirror. An assumption people make is that when you see into a mirror, you are seeing the z and the y or x-axis flipped, but cannot explain why the other axis isn’t flipped. (If you don’t yet see this problem pretend that you are cut into half, keeping only your left half. Now on the mirror your reflection will have the right half of its body. Your heart will still be on your left, but the reflection will have it on its right side.) The problem is that you are not actually flipping anything, rather you are inverting it. To better understand this, pretend that you can see every particle on your body. Now in order to make a perpendicular reflection, rather than flipping anything left to right or top to bottom, you take each particle and move it to a depth on the mirror equal to the depth from you to the mirror. Rather than the reflection moving in a normal three-dimensional world though we can say that it is moving in a negative three-dimensional world (however this is only an illusion because the mirror is two-dimensional.) The mirror can actually represent negative space, which is why things appear to be flipped on one axis, but not the other. If you are having difficulty understanding why it is that the mirror represents a negative space, think about the z-axis. It protrudes out towards the observer from the mirror. When you come into contact with the mirror, you are zero spaces from the mirror and there is no light. You are now on unit zero on the z-axis. In order to move in positive units you go out from the mirror, but on the mirror it actually moves the opposite way (toward the negative space.)

This also can explain your problem about the name tag. The backward name tag is merely an inverted image, nothing is flipped or rotated. It is inverted.

Again I'm sorry if this is restating anything or wrong, its just something I thought up. I'm not even sure if it is appropriate to call it "negative" virtual space (I don't consider it actual space it is sort of a representation) but its what made sense to me.

Title: Re: Mirror inversion
Post by towr on Oct 23^rd, 2007, 1:22am

on 10/22/07 at 23:02:12, blacksabbath8907 wrote:

as an object moves away from the observer it appears smaller because less light waves are able to hit it and bounce back towards our eyes

If it were merely that fewer light particles hit the eye, the image would seem dimmer, not smaller. It appears smaller, because the angle under which the rays of light are perceived is smaller.

Quote:

(see image 2.)

Title: Re: Mirror inversion
Post by Iceman on Oct 23^rd, 2007, 6:19am

The mirror is treacherous. Don't trust the mirror. Don't trust anybody and don't trust anything. Open your heart and meditate..

Title: Re: Mirror inversion
Post by Grimbal on Oct 23^rd, 2007, 6:49am

That is a deep reflexion.

Yeah. Mirrors. When I take a picture and turn it around, it is upside down. If I take a mirror and turn it upside down, it is not! There must be some piece of lead inside the image that pulls the bottom of the image down, just to confuse us.

Title: Re: Mirror inversion
Post by blacksabbath8907 on Oct 23^rd, 2007, 9:49am

sorry the smaller thing I didn't pay attention to and when i wrote that up I had a couple of pictures which didn't paste onto here and I forgot to remove all the "see image" deals... other than that though does it sound right?

Title: Re: Mirror inversion
Post by malchar on Jun 27^th, 2008, 8:06am

on 10/07/07 at 19:56:50, Bobishkindaguy wrote:

How about this hypothesis:
The "world" inside the mirror has an opposite frame of left-right reference to "our world". This sounds ridiculous, but think about it: There really is no "person" there, anyway, right? The "world" in the mirror is imaginary anyway, so we have to "invent" a set of laws of physics for that "world".

Many years ago, I saw an episode of Goosebumps the TV series, or some rip-off of that series. In the story, a kid finds a magical mirror and his reflected image trades places with him or kills him or something like that. The image was left-handed where the original kid was right-handed, and the words on his shirt were backwards too.

Anyway, I had this same mirror debate with some relatives a few years ago. I ended up concluding that the mirror reverses front-back, which basically turns the image inside-out. It has all been said before, but a mirror just reflects back the light that hits it. Consider how a small hand-held mirror works when you use it to reflect light around a dark room.