2 - Savoring The Mirror Reversal Paradox

[MikeO]

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Why do mirrors SEEM to reverse left and right, .BUT not up and down?



How does a common mirror, in the common configuration, reverse left and right, and not up and down?




It would seem that the mirror doesn't have the wherewithal to discriminate between horizontal and vertical.


The image of yourself in your bathroom mirror has its heart on the wrong side, yet it's not upside down. Why?

If, in a mirror, we watch a tennis match between two right-handed players we will see two left-handed players,
yet they will not be playing upside down. Why the asymmetry?


***


In 1969 I was a Physics major in college, and I loved the science very much. One day, while taking a break from my studies and half watching a re-run of “Leave It To Beaver” on TV, an eventful challenge was presented to me. I have never forgotten this, and it has deeply affected my life. In this old TV sitcom (even THEN it was old!) I first heard this mirror riddle which has defied clear and complete explanation for centuries.

This chance viewing of a serious paradox in a comic presentation was a very long time ago, and my memory of many of its surrounding details has dimmed and distorted. This in itself is a fascinating subject, that human memory is far from immune to alteration. However, the heart of the matter presented on the TV show is still very clear. I’d love to verify the small details someday, and get a peek at the competition between accurate memories and confabulated distortions.

I’ve never again seen this TV episode, but that may change soon as more and more such material is becoming available via the Internet. When I do again see that show, it will be a unique opportunity to compare my 40 year old memories (including any distortions) with the original presentation. Before that happens, I want to document the details of my probably inaccurate memories.

Here’s the best of what I can recall. The Beaver and Wally were brushing their hair, standing side-by-side in front of the same mirror. Beaver turns to his brother and casually asks, “Hey, Wally. Why does a mirror reverse left and right, but not up and down?”

As all the Physics student circuits in my brain awoke with a start, Wally looked in the mirror with a quizzical face, then turned to the Beaver and said nothing.

He then looks back in the mirror with greater perplexity, and then turns to the Beaver again, this time with a scowl on his face. “Shut up, Beaver. We’re going to be late for school,” he commands, resuming his hair brushing, determined to brush off Beaver’s perplexing riddle as well.

By this time I was fully awake and poised to hear the answer, but there was none. The issue was dropped by the Beaver and Wally, and so was my jaw.

Mentally I was cranking away answers, thinking this question could very well someday end up on an Optics exam. But I did not like the few pseudo answers that were forthcoming; I was stumped!

Through the commercial, I thought hard on the problem, but stayed glued to the TV set in case it came up again. It DID come up again! But again, it wasn’t answered, just posed for the comic effect. A third time it came up, and again, the puzzlement it caused was milked for the comic effect, but the Physics of any answer was absent.

I don’t think it was the Beaver who asked the question its second and third times. It dimly seems that Ward Cleaver, the Beaver’s father, was involved in the later incidents. It was passed on from Beaver to Wally and then to Ward. It was contagious. I too caught the curiosity with which this mirror question seems packed.

The years past, I tinkered with the problem from time to time, and gradually found the answer.

[MikeO]

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But this particular thread is not about the answer; it's about savoring the question. The answer has it's own thread here.

I've seen and heard many, many attempts to answer this riddle. It's an odd little puzzle that's defied clarity.

A HUGE number of people have asked the question at Yahoo Answers in many, many different wordings. The WWW and the real world are strewn with it, and often in the oddest places, one being the "Leave It to Beaver" TV show. Many scholars have offered their theories in an almost equally HUGE pile of attempts. In my opinion, most of it is utter confusion.

I've spent many years working on this mirror issue, and it's led me into many rich side issues.


***


Going to Yahoo Answers anyone can see that there are many pages of incidents where people have asked this same question, but in many different ways. Many answers are offered too.

Here's what I found in just the first ten pages after typing "mirror reverse" into the search box:

If a mirror reverses things from left to right why doesn't it reverse things from top to bottom?
How come mirrors reverse the image horizontally but not vertically?
How is it that in a Mirror, everything is reversed right to left, but not top to bottom (or upside down)?
If a mirror reverses left and right, how come it doesn't reverse up and down?
If a mirror reverses right and left, why doesn't it reverse up and down?
If a mirror reverses the image side-to-side, why not top-to-bottom?
If a mirror reverses things from left to right why doesn't it reverse things from top to bottom?
If you look in a mirror, you see a reverse image, what would happen if your eyes were one above the other?
Is the mirror a reverse of what others look at me?
Since a mirror reverses the reflected images from left to right, why doesn't it appear upside down as well?
Stand in front of mirror facing it. Why the mirror appears to reverse left and right, but not up and down?
When facing the mirror, the left & right sides reverse places_ but why not the up & down?
When I look in a mirror my image is reversed-left to right_ Why am I not upside down as well?
Why do mirrors reverse an image horizontally and not vertically?
Why do mirrors reverse right and left, but not up and down?
Why do you see yourself reversed in the mirror only horizontally, but not reversed in the vertical direction?
Why does a flat mirror appear to reverse image left to right, but not up and down_?
Why does a mirror appear to reverse an image in only one plane?
Why does a mirror on reverse left and right, not up and down?
Why does a mirror reverse an image (make it back to front) yet not turn it upside down?
Why does a mirror reverse an image from left to right but not top to bottom?
Why does a mirror reverse images horizontally (lef-right), but not vertically (up-down)?
Why does a mirror reverse left and right and not up and down?
Why does a mirror reverse left and right but not up and down?
Why does a mirror reverse my arms when I stand up, but not when I lie down?
Why does a mirror reverse our image from right to left, but not up to down?
Why does a mirror show a person in reverse left to right but not reverse up to down?
Why does a mirror show an image in reverse, but not upside down?
Why does a plane mirror reverse left to right, but not top to bottom?
Why does flat mirror appear to reverse the person looking into the mirror left to right, but not up and down?
Why does mirror reverse right and left but not up and down?
Why in a mirror does left and right reverse but not top and bottom?
Why is it that mirrors reverse images from right to left and not from top to bottom?
Why is it, that one sides in a mirror are reversed but not top and bottom?
Why is the image formed in a plane mirror laterally inverted or reverse?
Why is the image in a mirror reversed horizontally but not vertically?
Why isn't everything reflected in a mirror the reverse image?


It's sort of interesting to see them all laid out this way.

Then I typed "mirror flip" in the search box and found these in the first ten pages:

Anyone know why a mirror seems to flip images horizontally Words flip backwords but not upside down?
If a mirror flips your image from left to right, why doesn't it flip your image from top to bottom too?
If the lens in the eye flips the image from top to bottom, why does a mirror flip right to left?
Why do mirrors flip your reflection from right to left and NOT top to bottom?
Why is it that a mirror flips images from left to right but not upside-down?
Why mirror reflection is flipped along the vertical axis and not along the horizontal axis?


I also tried typing "mirror switch" in the search box and found these:

Why do mirrors switch left-right and not top-bottom?
Why does a mirror always switch left and right but not up and down?
Why does a mirror switch left and right and not up and down?
Why does a mirror switch right and left?



I also found a few funny variations like these:

At what stage of inebriation do you look at yourself in the mirror and use reverse psychology?

If you talk in a mirror and you make the reflection talk back will it talk in reverse?




***


The main aim here is to get to the riddle's ultimate answer, and there is much learning in this task.

But there's more. With so many people offering their answers to the mirror riddle on the Internet, collecting these answers can lead to new understandings in Cognitive Science as to what constitutes a human theory, and what seems to satisfy people in the way of explanations.

There are many unenlightened answers that seem to quickly satisfy the simple minded, and there’s learning enough just in understanding why these blunt theories satisfy some.

It also mystifies me as to how many scientists and intellectuals of the highest caliber can be content in employing strategies which simply deny the left/right reversal.

[MikeO]

As a hint to the solution, ask yourselves "WHY is it a riddle in the first place."


The riddle's power of attracting our attention is in the asymmetry it seems to proclaim. This is what we MUST have settled to consider the riddle answered: Why the asymmetry? Either that, or have symmetry restored.


It would seem that a mirror does not have the assets necessary to distinguish the difference between two directions in space. A mirror has no batteries, no microchips, no sensors, no actuators, or anything like that. How could it perform the discrimination between horizontal and vertical? How could it "know" to reverse only left and right, but not reverse up and down?


So that's why it's a riddle, and symmetry restoration is what we need to fully solve it.

[MikeO]

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Probably the main reason this was never fully solved over the centuries is because there is so little direct practical application to the actual answer. There's plenty of INDIRECT applications as we will eventually see here, but this question never seems to have popped up needing solution for some gizmo to work or for some theory to make better sense.

It just seems no one ever really needed the answer.

Even if it was fully solved by someone in the distant past, to where would they post the solution? It seems that the question only comes up in a context of idle curiosity. Not until the Internet could such an inapplicable answer be well distributed.


***


So why did I spend years trying to solve this puzzle?

I would not call it idle curiosity. I think there's deeper value in answering it than that. From what I understand, the ultimate value of a college education is NOT the actual learning of facts that were taught in its pursuit, but the learning how to learn in the process. This mirror puzzle has all the attributes of being a great education in problem solving.

A college diploma demonstrates for future employers that the recipient was able to successfully jump through a complex set of hoops that the school set up. The employer figures that if the diploma holder could jump through the college’s hoops, then maybe they can jump through the hoops that a job site will demand of the applicant.

As a college education is an exercise and is preparation, so is this mirror riddle. When this riddle is properly understood, though it has little direct practical application, the hoops it requires us to jump through will help us think more clearly about other difficult situations.

And the side issues it all brings onto play may very well have useful applications, as we shall see.

[MikeO]

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For reasons we'll explore later, this riddle has defied solution for a long time. I hear the ancient Greeks pondered it thousands of years ago.

It's resistance to solution has been noted by several top scholars (documentation forthcoming) who have dabbled in this. I've seen many answers to the riddle on the Internet and in scholarly journals, but these answers usually are several pages long and very dense reading. Often they merely deny the Left/Right reversal.

You'll be amazed at how simple this whole thing gets when it's solved. PLUS, there are huge ramifications tied up in that solution. I'm talking about sociological insights and political breakthroughs! This is not an exaggeration. The solution is extremely enlightening.

[MikeO]

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