Martin Gardner covered this back in the 70s or 80s in his Scientific American column Mathematical Games, the topic being “Why do mirrors reverse left and right but not up and down”. What [flat] mirrors actually do is reverse back and front (which is all they can do, reverse the plane they themselves are in); notice that your east-most hand (say) is also your reflection’s east-most hand (or, your hand holding a spoon is directly opposite your reflection’s hand holding a spoon), but you face north whereas your reflection faces south.
True, dat.
Confused. You’re a charter member responding to column from the 80’s today? Curiouser and curiouser…
The column on concave mirrors reflecting upside-down was the column of the day Oct. 25, 2012.
Martin Gardner first tackled the mirror question in SciAm back in the 1950s. And whether or not a flat mirror reverses an image is a question of definitions, not of verifiable objective truth. Anyone with the ability to reason and the ability to use his eyes can see what the fact is.
I disagree that it is merely a question of definitions, but, even if it were, nearly everybody in the world with an opinion on the matter, almost all of whom have the ability to use their eyes and to reason, will assert it as objective fact that a mirror reverses left-right. It is far from a triviality to point out that they are wrong.
Also, I very much doubt whether Martin Gardner was the first person to write about the subject.
Incidentally, Mr Kennedy, I hope you will not think me impolite to ask, but I have been wondering for some time why it is that you seem never to venture out of this sub-forum (where you post quite frequently, and often make interesting and useful points) onto the wider board.
I agree. Mirrors reflect light. They don’t reverse anything but the direction of the light hitting them.
Actually it uses 2 flat mirrors placed at 90 degrees: http://www.truemirror.com/
Details: http://www.truemirror.com/Moredata.asp
As was stated above, the mirror only reflects light, it is *you *who must reverse left and right to match the image in the mirror.
For example, if you are standing directly in front of a mirror while you are facing North, the image you see in the mirror is yourself, facing South. Most people, in order to match the image and face South, would turn their bodies either to the left or right 180 degrees until they were facing South. In this case, your right hand is now where your left hand was, and vice versa. Ergo, the mirror reversed left and right.
But if you stand on a mirrored floor tile, your head is pointed UP, and your feet are pointed DOWN. Your reflection, however, has your head pointed DOWN and your feet pointed UP. Clearly, then, the mirror has reversed UP and DOWN.
If it were the usual practice for people to turn and face the opposite direction by—instead of turning left-to-right 180 degrees—standing on their head, we would notice that our right hand after turning is on the same side as the right hand of the reflection, and likewise our left hand, but now our head is where our feet were in the reflection, and our feet in the place of our head. Clearly, the mirror has reversed TOP and BOTTOM!
I submit the issue is entirely dependent on one’s definitions, and the mirror, itself, is completely indifferent to our choice of Left-Right, Top-Bottom, Up-Down or whatever.
It is impossible to prove them wrong, because they are not wrong, unless you select a sufficiently narrow definition of “reverse”, and provide some kind of proof that that definition is somehow uniquely correct—an extremely difficult thing to do with definitions (by definition, so to speak).
I did not say that he was. I merely observed that he tackled the issue long before “the 70s or 80s”.
Time.
NM.
And here I thought the comment-worthy pull quote was this one:
I realize Cecil was looking for cool uses of curved mirror, but the effect described here has been available for a long time from flat mirrors.
I believe the arrangement is called an Extrospective Mirror, and it consists of two flat mirrors connected by hinges. When properly arranged, the mirror on the left is not showing you your own reflection, but rather a reflection of your reflection in the mirror on the right, and vice-versa. The result is that the image had been flopped (right and left reversed). Raise your right eyebrow and you will see the person in the mirror raise the one on your left, his right.
And I have heard the benefits of such a mirror described by that very same quote from that very same poem; that it is a mirror that allows us to see ourselves as others see us.
They’re not hard to find, or at least didn’t used to be. Go to clothing stores. They have those three panel corner mirrors. The mirrors are such you can see a reflection of your reflection. Used to do that all the time as a kid.
Now that I think about it, I haven’t seen those mirrors in a while.
Yes, but a two-panel mirror at 90˚gives the illusion of being a non-reversing single flat mirror. The three-panel store mirrors give a great many partial images (which is more useful for trying on clothes).
I give this problem to students all the time because it involves an object that they are extremely familiar with and yet challenges them to articulate their thoughts in a coherent fashion.
I usually frame it as follows:
Q1
A mirror switches left and right but not up and down. What can you do to an ordinary plane mirror to make your image appear upside down?
Answer
Put the mirror on the ceiling.
If the student gets that, then I move on to the next question.
Q2
If I face a mirror on the wall it reverses my left and my right. It also reverses front and back (me and my reflection are facing different directions), but it does not reverse up and down.
If I stand side on to a mirror on the wall it reverses left and right but my reflection faces the same direction as i am and it is the same way up.
If I place a mirror on the ceiling, left and right are switched. Up and down are reversed, but the reflection still faces the same way that I do.
In light of this, why is left/right always switched. Why does the mirror switch two things when on the ceiling or when I am facing it, but only switch one thing when I stand side on to it?
It is all to do with definitions and frame of reference.
We use an external frame of reference when speaking about front/back inversion, up/down inversion, north/south inversion.
We use ourselves as a frame of reference when speaking about left/right inversion. Hence my reflection has a mole on the left side of its face whereas I have a mole on my right.
A more consistent analysis of the situation is to say that the mirror reverses in the direction perpendicular to its plane and that in the process any clockwise sequence of points becomes anticlockwise.
Now THAT is a mirror that reverses left and right. Look at the relative positions of the handles on the cup.
Seriously, I’ve never understood the logic of people who say mirrors reverse left and right. Stand in front of a mirror and place your right hand out to your side. The reflection of your hand is also out to your right side. It hasn’t magically been flipped over to appear in front of you on the left, as it would if the mirror was reversing left and right.
If your reflection was not a reflection but another person to whom you were speaking, it would be that person’s left hand. That’s what people mean.
Powers &8^]
And that’s only because humans happen to be (mostly) bilaterally symmetric. Because we’re symmetric, a reflection of a human still looks like a human, and so we picture it as such.
Or indeed if you hold a printed or written piece of text facing the mirror, it looks like it has been reversed left to right (although of course actually, this is because you’re already turned it to face away from yourself)
It is difficult to confirm them incorrect, because they are not incorrect, unless you decide on a completely filter meaning of “reverse”, and provide some type of evidence that that meaning is somehow exclusively correct—an incredibly hard thing to do with explanations (by meaning, so to speak).
If you use clear plastic or some type of paper you can (partially) see through (i.e. tracing paper) for the paper-in-the-mirror trick, you’ll see right away that the writing in the mirror looks just like the writing as seen from behind.