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The weirdest and most puzzling problem I've ever encountered

  1. Nov 17, 2008 #1
    ...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 wont 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 wont 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.
  2. jcsd
  3. Nov 17, 2008 #2


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    It's because your two eyeballs are separated left-right, and not up-down. Lay on your side, and the effect is different, right?
  4. Nov 17, 2008 #3
    I'm sorry, that is not the kind of reply I expect from a proper scientist (or anyone truely 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.
  5. Nov 17, 2008 #4


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    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.
  6. Nov 17, 2008 #5


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    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.
  7. Nov 17, 2008 #6
    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.
    Last edited: Nov 17, 2008
  8. Nov 17, 2008 #7
    Here we go. Immagine your 3D axes. Put the y and z axes parallel to the mirror, and the x axis comming 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 consistant 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.
  9. Nov 17, 2008 #8
    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!
  10. Nov 17, 2008 #9
    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.
  11. Nov 18, 2008 #10

    Vanadium 50

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    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.
  12. Nov 18, 2008 #11


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    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.
  13. Nov 18, 2008 #12
    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 aswell 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 wont have any more scientists left on PF in a day ;P
    Last edited: Nov 18, 2008
  14. Nov 18, 2008 #13


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    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.
  15. Nov 18, 2008 #14


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    Well, I guess that I'll just have to slink off to a corner and die because I don't meet your standards. :rolleyes:
  16. Nov 18, 2008 #15


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    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?
  17. Nov 18, 2008 #16


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    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.
    Last edited: Nov 18, 2008
  18. Nov 18, 2008 #17

    Andy Resnick

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

    http://math.ucr.edu/home/baez/physics/General/mirrors.html [Broken]
    Last edited by a moderator: May 3, 2017
  19. Nov 18, 2008 #18


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    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.
  20. Nov 18, 2008 #19
    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 dont know if you see,but you should see,in REFERENCE to me,see!
  21. Nov 18, 2008 #20


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    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.

    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.
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