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This thread is titled "Generating THE Answer" and is a little bit wordy.
If you can't wait, and want a real quick answer, there are three attempts at abbreviating the answer on the thread titled "Concise Summary of the Riddle's Solution."
This thread aims to lead towards, or generate, or derive the answer, and will take a little more time. After reading it through, please check out the concise answers also available here.
Ok.
Here's THE answer.
Bartenders and Mirrors
A benchmark for deeply understanding any subject is seeing if its explanation can be made sensible to a reasonably intelligent person in a bar while sipping a favorite beverage. Such a setting makes for friendly and informal explanations, and can help filter out longwinded academic expositions. Several times in this kind of environment I’ve offered my solution to the mirror riddle in under two minutes. However, if possible, I prefer to take a little longer so that the listeners (myself as well) can explore its depth. It’s a great way to meet people.
Often a bar will have a mirror behind its rows of bottles, so this setting is a contextually rich one for the mirror riddle.
Bartenders hear many different things from all sorts of people, and can be excellent sounding boards for brief theories on anything. When business is slow, it can be a good opportunity in which to ask the mirror riddle. This demands brevity in order to finish before another customer eventually orders a drink. Plus, I must quickly get to the point before the bartender gets bored.
When the time looks right I ask, “Hey, bartender, have you ever wondered why this mirror behind you reverses left and right, but not up and down?” If he looks intrigued I add, “It seems to me the mirror shouldn’t be smart enough to be able to tell the difference.” I will then wait for his theory before offering mine. I’ve heard a lot of mirror reversal theories, some amazingly elaborate, and some quite amusing.
One of the prime reasons this has been such a tough riddle is because it LOOKS so much like a science question... but it is not. A little science can help in getting the answer, but too much science can actually get in the way. Science has helped to HIDE the answer to this riddle for centuries.
The mirror riddle is actually a PEOPLE puzzle, and not one of the science of mirrors and bouncing light rays. It’s a people issue, involving the way people use words. There is one word in the puzzle that’s very slippery. Can you guess which one it is? Which word eludes simple definition? It’s the word “reverse.”
When we see that there are three very different ways to define this word, then the riddle will melt into nothing and everyone will be satisfied. To get to the point of clearly seeing these three definitions of “reverse” we will need to borrow one small scientific idea from Einstein: that of using an operational definition.
We could talk for hours about why “reverse” is slippery but the bartender would throw us out, so onward quickly with the three operational definitions of “reverse.”
***
The first operational definition is the most popular one, and the one most scientists seem to latch onto as well.
It’s my contention that when most scientifically minded people explain the mirror riddle, they do so by denying or disproving the reversal of left and right. In essence they shove the mirror riddle under the rug by their skilful use of this first definition.
They don’t seem to care that this leaves the rest of us hanging, wondering why we ever thought in the first place that a mirror DID reverse left and right. It seems to be satisfying to the scientist, but not to any of the rest of us who can still sense a left/right reversal lurking in there, even though it seems impossible to prove it.
***
What it means to use an operational definition is this: we must specify the operation, or the procedure, or the formula, the recipe, whereby we might detect (or not detect) “reversedness” in the mirror setup.
The procedure for definition Number One is extremely simple:
We will compare an object and its mirror image AS IS,
not allowing either to move in any way.
To some, this may seem too obvious to bother stating, but trust me, it helps enormously to explicitly state it. It will be useful later.
A good "object" for our discussion can be the man sitting next to me at this bar, to my right, facing the same mirror I am, the one behind the bartender. This customer next to me is holding up his right arm after he overheard my question to the bartender. Luckily, this raised arm is directed away from me, and hence not able to spill my drink. In the mirror his image also has an arm raised, also directed away from me. Both arms are pointing in the same direction: away from me.
Comparing this man with his mirror image AS IS, there seems to be no reversal of left and right. Moreover, both the image and the object obviously have their heads facing up, so up and down are also not reversed. The scientist now shoots back his drink and wants to say “Game over!” thinking it has been proved that mirrors don’t reverse left and right at all. His attitude is one of “to hell” with the strong feeling many people have that mirrors DO somehow perform this quirky left/right reversal. My suggestion is to say, “Let’s keep the game going and move on to operational definition Number Two.”
The scientist also likes to point out that (in using definition Number One) the image and the object are facing each other, and thus pointed in opposite directions. He says the mirror reverses front and back, and not left and right at all.
I agree with all of the scientist’s points except the “game over” idea. I’m willing to concede that when we adopt definition Number One of “reverse,” then mirrors reverse front-to-back and that’s all. So, now let’s see what happens when we adopt operational definition Number Two of this slippery word “reverse.”
***
In operational definition Number Two, we again must specify the operation, or the procedure whereby “reversedness” is going to be detected (or not detected) in the mirror situation. Previously we held the image and the object still and compared them AS IS, looking for something that was reversed. This time we are NOT going to compare them “as is” and I’ll explain the reason why. This is going to be the core issue in the mirror paradox.
When people want to compare two nearly identical objects,
how do they usually do it?
If you were going to buy a car and had to choose between two nearly identical models located on the same lot, how would you like to have the two cars parked? Most people would want them facing in the same direction, or something like that. Then the comparison process is easier. Having one car pointed North and the other pointed East just wouldn’t do. It’s much easier to line the two cars up and then compare.
Have a friend compare two nearly identical pens by holding them up in front of him. Would you hold up one of the pens vertically and the other horizontally? No, you’d hold them both in the same way, FACING IN THE SAME DIRECTION. For brevity, let’s invent the word “isodirectionality” to refer to this normal human preference of moving things to face the same direction when we want to compare them.
I believe
the core issue in the mirror riddle is that many people want to compare the object and its mirror image in this way, by somehow getting object and image to face the same direction. I’ve seen people do it, or attempt to do it, in front of mirrors while pondering the mirror riddle.
RIGHT NOW, at this very minute, I see the guy sitting to my right in this bar trying to do it!
He had earlier raised his right arm while looking into the bar mirror, and now he’s trying to twist around 180 degrees to face away from the bar, but it’s not working and he looks frustrated.
He's trying to rotate his body, shoulder and arms around, while still looking at the mirror. Not only is it a difficult body maneuver, but his mirror image is also twisting halfway around, and that’s seriously complicating the comparison he’s trying to do between himself and his mirror image.
So, I’m going to help him. It’s a good thing I picked a slow night for this, because otherwise I’d never get the bartender’s cooperation.
I have a crayon in my pocket, having prepared for this, and I get the bartender’s permission to lightly sketch the other customer’s outline in the mirror with his raised arm. This freezes the mirror image. Now he can totally swivel around on his barstool easily, arm still raised, and we can all compare image and object for reversal.
Well, what do you know! The comparison is easy and obvious, now that isodirectionality has been achieved.
The customer is facing in the same direction as his crayon frozen mirror image, in the same direction the bartender usually faces. Both image and object are standing with heads up, BUT they have opposite arms raised.
The mirror has “reversed” (using operational definition Number Two)
left and right but not up and down.
I am sure this is exactly what a sizeable portion of the population is subconsciously doing in their heads when they perceive a left/right mirror reversal, but it’s SO COMPLICATED they can’t verbalize it very well. I’ve seen Physics professors claim to be getting an headache when they try to unravel this and clarify this natural internal rotation that the brain unconsciously does.
It’s a lot to do in the head: freezing the image, rotating it 180 degrees, and then comparing. Add verbalization to all that and headaches are the common result. It took me about five years to do it!
***
Insisting on isodirectionality and moving things around is a natural thing to do for subtle comparisons, but so also is holding the scene still and comparing things “as is.” Both are useful ways of trying to understand something that’s complicated, so both methods are used by people. It’s just that the second method in this mirror setup is much more subtle and much more difficult to verbalize.
So,
it’s not the mirror that chooses what to reverse, but PEOPLE make the choice. People choose whether to apply definition Number One and have front to back reversed, or to apply definition Number Two and have left and right reversed.
It’s a people thing, not a mirror thing. The mirror does the same action in both instances, but people select which operational definition they want to apply.
Sometimes people apply
both definitions, or
drift from one definition to the other, and this confusion helps make the riddle even more difficult.
Keeping all the steps
unspoken in definition Number Two, tucked away in
vague mental images, is the heart of the riddle's resistance to solution.
***
Summarizing what we've seen so far:
A mirror reverses front-to-back when operational definition Number One for "reverse" is used,
AND it reverses left and right when operational definition Number Two for "reverse" is used.***
The mirror riddle is now relatively solved, but there's still more to the story.
1. - There's yet the issue of Up/Down not being reversed to explain.
2. - I said earlier that there are THREE ways to define “reverse” so what’s the third one all about?
3. - And how is it that science tends to hide the answer so well?
4. - There’s a much deeper issue to consider. How many OTHER common words lend themselves to multiple definitions, and hence to riddles, puzzles, complications, confusions, and even arguments and fights? This mirror riddle with its solution can lead into many more things to think about.
...to be continued
