The weirdest and most puzzling problem I've ever encountered

[ManDay]

...what would that be? Please listen, and don't laugh before you have finished reading all I have to say about it. On the one hand its embarrasing, but on the other, I can't keep that to myself any longer. Usually, I don't ask questions of such "triviality" to others, but instead prefer pondering on them until I figure them out - and then, I wouldn't be asking a question.

But in this case, I think the problem is so weird (and maybe proof for my utter misconception of the world), that it deserves being asked before filed in the "problems I've solved" section of my brain. I'm on the best way to arrive at a final explanation, but until then: Enjoy (in case that you are just as stunned by this as me, I won't give you any hints what I've thought so far).

So, what is it? The question is as trivial as the above introduction suggested. Maybe you see the solution at a first glance. I think you wont. However, don't make the mistake to put the problem just aside for being apparently trivial, unless you are really sure that you understand what it is.

Why does a mirror swap Right and Left, but doesn't so with Up and Down? One may argue that the mirror doesn't actually swap left and right - since you see your left in the left side of the mirror, but consider the following:

You see yourself in the mirror and you raise your left hand. Your counterpart raises his/hers right (in his/her reality). You move your head left while your counterpart moves it right. You move it up, however, and your counterpart complies.

Still not convinced that there is an error in the universe? Imagine that (or just try it, your mirror won't lie to you):

Stand in front of a mirror: Raise your left arm and describe a large circle arround your upper body. When your arm is left to yours, your counterpart has his/hers right to him/her. Same with right to you.
The only point where you and your counterpart would agree on where your arms are, is when it's excactly up, down respectively.

What is it that makes up perceive that? Gravity? The symmetrie of the human body? One may easily be tempted to say "yes" to one of the former. But that's not enough. Provide a thorough explanation or admit, that you don't know the answer to the absurd mirror problem.

 

[berkeman]

It's because your two eyeballs are separated left-right, and not up-down. Lay on your side, and the effect is different, right?

 

[ManDay]

It's because your two eyeballs are separated left-right, and not up-down. Lay on your side, and the effect is different, right?

I'm sorry, that is not the kind of reply I expect from a proper scientist (or anyone truly interested in science). Think about it again and don't, as I said, put the problem aside as "trivial". Because (althought I naturally can't allege that you don't know the right answer/mean the right thing):

1.) That's not a "thorough explanation", as I stated.

2.) So you claim a person with only one working eye (or let it be Leela from "Futurama") would dissent from my description of things. Also, your insufficient answer (because your eyeballs are aligned horizontally) would imply, that viewing something through a camera, would differ from this perceiption, which, apparently, is not true.

 

[NoTime]

Your head is reflected at the position your head is at.
Your feet are reflected at the position your feet are at.
It's the same with both hands.
It is only your mind that wants to do the rotation on the vertical centerline.
You get exactly the same effect using a video camera.
No mirror required.

 

[mgb_phys]

It's a purely psychological effect - you intepret a reflection as a rotation.
Your brain is wired for dealing with the case of meeting another human head-on so it process the visual data into that circumstance.

 

[ManDay]

Right. Mgb, I just came to the same conclusion. In fact, when we "interpret" our counterpart raising the left hand it raises its right hand - which we usually don't realize because we focus solely on our counterpart which makes us think it was rotated, where we neglect to consider that the reference system would have had to be rotated too, which it isnt.

 

[flatmaster]

Here we go. Immagine your 3D axes. Put the y and z axes parallel to the mirror, and the x-axis coming out perpendicularilly to the mirror. What a mirror does is takes any given object at positoon (x,y,z) and produces an immage of that object at the position (-x,y,z). This is consistent with every position of where something is expected to be in the image. The reason your immage's right had is you left is because your image is now esseentially in a left handed coordinate system. IE, the new coordinate axes for you image no longer obey the right-hand rule.

 

[natives]

If you know the answer why bother asking...First ironically YOU HAVE NO COUNTERPART,its not human<I know you know,am just pointing out>...you should know,people had querried into that lots of ages ago,thats why they came up with the idea of REFLECTION...am not taking it simple,its what it is,they thought it too...but technically its just a matter of optical projection,affected by the brain not able to process the data which is provided from 2 different reference planes and opposite eyesight directional vectors[this inability<I think!>,was purposeful,after all I do believe we are not just discrete energies,and not so much into revolution and solid on the metaphysical phenomenon of GOD!]...Take it "simple",its called REFLECTION!...its not even a matter of physics,or biology or mathematics,its simply a proof of the idea of "the simple human and the superior GOD"...dont know if you get me!

 

[OAQfirst]

Mirrors don't "know" left or right. They only reflect what is directly in front of them. When your hand moves left to right, the image remains directly in front of it. When you move it up or down, the image is still directly in front of it. You're imposing the concept of left and right / up and down. There's nothing absurd about it.

 

[Vanadium 50]

I'm sorry, that is not the kind of reply I expect from a proper scientist (or anyone truly interested in science).

That's the answer. I don't think insulting the people who give you an answer you don't like is the mark of a "proper scientist" either.

As pointed out, the mirror reflects what is directly in front of it (i.e. it doesn't swap left and right - the image of your left hand is on your left), and perceptually we impose a leftness-rightness upon that image based on our own left-right bilateral symmetry.

 

[Danger]

I don't think insulting the people who give you an answer you don't like is the mark of a "proper scientist" either.

Agreed. Berkeman didn't earn the honour of being a Mentor by being a shoddy scientist. He is one of the most reliable sources of information on this site, with a ready willingness to assist others to the best of his ability. It was a totally inappropriate response to his explanation.
Additionally, a forums search would show that this issue has been addressed extensively in the past. Bad ManDay.

 

[ManDay]

No Berkeman was not right. And confirming his false answer just because he has proven to be a "reliable source of information" in the past actually doesn't put you in a good light, either.

It is not because our eyeballs are aligned left right - and I have to wonder why you argue that since we have come to the correct explanation already. Plus, his answer is exactly what I asked not to receive: 20 words short, neither grasp, nor thorough and superficial.

After I spend a few sentences on expressing that this is right the kind of answer I would not like to see, I cannot confirm that Berkeman has lived up to his reputation of being the one "with a ready willingness to assist others to the best of his ability" - unless he really depleted "the best of his ability" for this response - which is what I doubt since I have indeed seen good responses from him.

Plus, there is no insult in my reply that his answer is not what I would have exspected from a true scientist. It's a plain fact that doesn't at all imply that he wasn't a scientist.

After four paragraphs argueing your attitute (irrespective of the actual content, the above remains), let me just spend one last on Berkeman's explanation:

The example that lying on the side diminishes the effect of interpreting a right and left into the virtual image is true. But since this on its own is even less close to an explanation then the other senctence, I didn't consider it at all when replying to him. The reason for this is not, as he alleged, the eyes being aligned left right. I'll forgo argueing this now, I got to leave soon. You will have to go with a counter example (which I actually already gave) as a proof that his assumption is wrong:

A camera has only "one eye" - so does a one-eyed person (I repeat myself, but take "Leela" for example). You thus get a one-eyed picture from both. Yet, you can lay the screen on which you see the picture or yourself on the side, and you still have the same effect. You may just as well imagine yourself being "Leela" - same here.

(Berkeman, please don't take this as another submission against you - I'm hereby argueing those, who insisted that your post was correct and I had "insulted you"...)

PS: Vanadium: Did you notice that "I don't think insulting the people who give you an answer you don't like is the mark of a 'proper scientist' either." that in you stated that in your opinion I don't appear like a proper scientist, which is an insult compared to mine saying that "the answer he gave is not what I had expected from a proper scientist"?

Now since you insulted me, I think YOU aren't a proper scientist!:D ...oh dear, if we go on like this we won't have any more scientists left on PF in a day ;P

 

[rcgldr]

Why does a mirror swap Right and Left, but doesn't so with Up and Down?

A mirror doesn't swap left/right or up/down, a mirror swaps forwards and back (depth). If you hold up an object in front of you, the back (far) side of the object will appear to be the front (near) side in the image, because the far side of the object is closest to the mirror.

 

[Danger]

confirming his false answer just because he has proven to be a "reliable source of information" in the past actually doesn't put you in a good light, either.

Well, I guess that I'll just have to slink off to a corner and die because I don't meet your standards.

 

[HallsofIvy]

Agreed. Berkeman didn't earn the honour of being a Mentor by being a shoddy scientist. He is one of the most reliable sources of information on this site, with a ready willingness to assist others to the best of his ability. It was a totally inappropriate response to his explanation.
Additionally, a forums search would show that this issue has been addressed extensively in the past. Bad ManDay.

Yes, Berkeman has given good responses. Which makes the fact that he gave such an obviously incorrect answer to ManDay surprizing. And ManDay only said that was not the kind of answer he expected from a scientist. In effect, he was calling Berkeman a "scientist". Is that an insult?

 

[gabbagabbahey]

Yes, Berkeman has given good responses. Which makes the fact that he gave such an obviously incorrect answer to ManDay surprizing. And ManDay only said that was not the kind of answer he expected from a scientist. In effect, he was calling Berkeman a "scientist". Is that an insult?

Agreed; I think ManDay's comment was misinterpreted by some. Also, Berkman's reply is incorrect (at least if you interpret it to mean "the orientation of our two eyes is directly responsible for the effect"-- After all, one may argue (convincingly or not) that our mind evolved to interpret things this way based on the orientation of our eyes)...you need only close one eye while looking in the mirror to realize that the effect persists even without using two eyes.

The effect is not just in the mind however: as a light ray coming from your left enters your eye, it strikes your retina to the right of center and vice versa. The same thing occurs for up and down, but in that case the brain compensates. It's a combination of how light is absorbed by the eye, and how the mind interprets it.

 

[Andy Resnick]

.<snip>

Why does a mirror swap Right and Left, but doesn't so with Up and Down? One may argue that the mirror doesn't actually swap left and right - since you see your left in the left side of the mirror, but consider the following:

<snip>

Mirrors swap the 'in' and 'out' direction.

http://math.ucr.edu/home/baez/physics/General/mirrors.html

 

[HallsofIvy]

A mirror does NOT swap left and right- and that's why it looks as if it does. When I look at another person, standing opposite me, because he has to turn to face me, his left is to my right and vice-versa. When I look at myself in a mirror, precisely because a mirror does NOT swap left and right, it doesn't look right- the left and right sides seem to be reversed from what I am used to seeing when looking at other people. Similarly, if I were holding a book up to a mirror and want to read it, I have to turn it around so I can see it. I have "swapped left and right" (and not top and bottom when doing that). The mirror does NOT "swap" and so it appears strange to me.

 

[natives]

Its all a matter of REFERENCE...the mirror effect is an issue of the 2 reference planes...While the answer and its way of answer just depends on the reference views of the reader...We are right AND we are all wrong,what determines this is who views these ideas i.e what is the reference...I don't know if you see,but you should see,in REFERENCE to me,see!

 

[Danger]

Yes, Berkeman has given good responses. Which makes the fact that he gave such an obviously incorrect answer to ManDay surprizing.

It appears that there's more than one misinterpretation at work here. Berkeman's original post seemed to me to conform to the common PF practice of opening a dialogue with the 'student' by offering a single bit of information to start with, to encourage him to work through it, rather than just lay the whole solution out.
While he was incorrect about the separation of the eyes, I took it to be just a minor brain-fart wherein he was in fact referring to the orientation of the optic 'plane' in the head. His next sentence supports that, and is correct. The apparent effect in a mirror rotates as one's head is tilted. When you lie down, the mirror's 'top' and 'bottom' become your 'left' and 'right'. Establishing that seemed like a good starting point for examining the phenomenon.

ManDay only said that was not the kind of answer he expected from a scientist. In effect, he was calling Berkeman a "scientist". Is that an insult?

Maybe I've become overly sensitive due to exposure to a few rude (mostly banned) members in the past. My take on it was that he was saying that Berkeman is not a scientist because he didn't provide a spoon-fed explanation. If that's in error, then my apologies to ManDay and anyone else who I might have offended.

 

[cabraham]

It's because your two eyeballs are separated left-right, and not up-down. Lay on your side, and the effect is different, right?

But if we close one eye and view the mirror, the image is still swapped left/right. It can't have anything to do with our eyes being horizontally separated rather than vertical.

I was asked this question in the early '80's. My answer then was the same as now. A mirror does not reverse right/left nor up/down. We reverse right/left in our mind when we establish a reference frame then flip it for the image. When I raise my right hand, the mirror's image of me raises its --- **right** hand as well! "Right hand" meaning referred to MY frame of reference, not that of the reflected image of me. Right and left do NOT reverse.

Another example is viewing a car in our rear view mirror and noticing the "FORD" logo on the grill apparently reversed. The mirror did NOT reverse the Ford logo. Given the orientation of the letters and the direction we're facing, the letters are ALREADY REVERSED. To clarify, write the word "cat" onto a transparent slide using a marker. If you hold the transparency in front of you, the image is either forward or reversed. Holding it in front of a mirror **changes nothing**! If the image is already reversed, it will still look reversed in the mirror.

The mirror does not reverse anything. The left/right thing is just an artifact of our spinning the reference frame in our mind. The mirror conveys exactly what is going on exactly where it is going on. We do the reversing ourselves. Do I make semse? Peace.

Claude

 

[TVP45]

A mirror doesn't swap left/right or up/down, a mirror swaps forwards and back (depth). If you hold up an object in front of you, the back (far) side of the object will appear to be the front (near) side in the image, because the far side of the object is closest to the mirror.

Good answer. It's the reason TV repairmen (when there were TV repairmen) kept a large mirror on their workbench.

 

[TalonD]

an even more striking example is when you hold written text up to a mirror and all the sdrawkcab era sdrow but not upside down. !

 

[lol1986]

I think the answer should be like this:

We only have (our body) left/right looks symmetrical while our up/down and front/back are not symmetrical,

hence when we moving up/down and front/back the mirror will same with us while moving left/right will be opposing us.

Is this answer satisfy you?

 

[lol1986]

Imagine we have two eyes, one at the front and one at the back? We will going crazy to be confused by left and right. (^_^)

 

[TVP45]

As Jeff and Andy pointed out, the reversal is front to back (or in/out). To see this, rename your body parts. Stand facing north and look in a mirror directly in front. Touch your west ear; the image touches it's west ear. Touch your "up" end; the image touches it's "up" end. Touch your north face; the image touches it's south face.

 

[Sjorris]

It's simply a case of symmetry (due to the light propagation in straight lines), the mirror is a plane of symmetry between you and your 'counterpart', or reflection. If a mirror was instead a line of symmetry (say, in the vertical direction), then it would exert the behaviour like you described, if you move your arm to the right in your frame of reference, then your reflection would also move his arm to the right in his frame of reference (so, to your left). You could even make the mirror a point of symmetry, in which case everything would be flipped, up and down, and left and right. Sadly, line and pointmirrors don't excist because they have no area.

Or, more basic, your reflection has nothing to do with you. It's simply the path rays of light follow (in the science of optics) to return to your eyes, which your brains process in a normal way, and then, because you 'know' that it's you in the mirror (which it's not, it's your reflection), but 'you' are not doing exactly what you (yourself) are doing that you think something inconsistent is going on, where in fact nothing special happens.

When you look at a mirror, and someone throws a ball past it from left to right, wouldn't you be very surprised when you saw the ball reflected moving from right to left? I know I would.

 

[agamemnon]

It's not a physics problem, it's a linguistic issue.

"up" and "down" are absolute, "left" and "right" are relative.

Notice that when you look in the mirror and raise your "east"
hand, the reflection also raises his/her "east" hand.

 

[Sjorris]

'Up' and 'down' are also relative, however they are the same in both frames.

 

[rcgldr]

If you hold up a piece of clear glass or plastic with text written on the piece of glass or plastic, so that you can read the text on the glass, you'll also be able to see the same text in the refelction, left and right are not swapped. If you were to stand outside a store with a neon sign, and could look inside to see a reflecion of the neon sign on a window inside the store, the reflection of the sign would not be reversed, again an example of left and right not being reversed.