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Mirror puzzle - solution?

What follows is my own suggested solution to this puzzle - scroll down for the puzzle (I note several of you offer much the same solution)

We noted before that, in a sense, mirrors don’t reverse anything. So why do we say they reverse left-to-right, but not top-to-bottom? Well, if the mirror before you was replaced by a sheet of glass, and you were to stand behind the glass in just the position your mirror-self seems to stand, then while your head would still be at the top and your feet at the bottom, your left hand would be over to the right, where your right hand appears in the mirror, and your left hand would be to the left, where your left hand appears. That is why we say the mirror reverses left-to-right, but not top-to-bottom.

But notice that we have just taken something for granted: the axis about which we rotate you when we imagine you over there behind the mirror. When we turn something round, we rotate it about an axis. A spinning top, for example, rotates around a vertical axis. A car wheel rotates around a horizontal axis. When we imagine you over there in the position your mirror-self seems to be in, we mentally put you there by rotating you about a vertical axis. But what if we were to get you over there not by rotating you around a vertical axis, but a round a horizontal axis? Then you would be stood on your head. And, compared to your mirror image, your left and right sides would not then be switched round. Your left hand (the one with the watch in the diagram) remains to the left. Which is also where your left hand appears in the reflection. But top and bottom are now reversed. Your head appears where your feet are in the image.

It seems the reason we say mirrors reverse left and right but not top and bottom is due to the fact that we take for granted a particular axis of rotation. But we could just as easily choose a horizontal axis. Then it would be true to say that a mirror reverses top to bottom but not left to right.

So yes, it is true to say mirrors reverse left to right, but only if we choose a vertical axis of rotation. Choose a horizontal axis and they then reverse top to bottom.

Of course, this raises the question of why we take the vertical axis for granted. The answer, presumably, is that people are not in the habit of flying through the air like birds and settling on their heads. When people normally rotate, it is almost always about a vertical axis. So we just took for granted a vertical axis of rotation in this case too.

So this puzzle about why mirrors do what they do is generated by our not noticing what has been taken for granted. To solve the puzzle, we need to take a step back and start questioning what we took for granted.

When only philosophy will do

Notice that, if this solution (or part solution) is correct, we certainly didn’t have to any scientific research into how light and mirrors behave. Nor did we have to investigate how our brains work. Even if we had done that sort of scientific research, it still wouldn’t have solved the puzzle. In order to solve this puzzle, we need to stop doing science and start doing philosophy. It is a puzzle that is solved just by thinking.

People sometimes assume all questions can be answered by science. They would assume that the mirror puzzle must have a scientific solution. But it turns out that the mirror puzzle is a puzzle that science cannot solve. It seems that, sometimes, only philosophy will do.

The Door Puzzle

There is similar puzzle about doors. Walk though a door that opens on your left and turn round to come back through it, and the door now opens on your right. But pass through a door that opens at the top (like a cat-flap) and turn to come back through it and the door still opens at the top. Why does passing through a door reverse the way it opens from left to right, but not from top to bottom? What explains the difference?

The solution is much the same as for the mirror puzzle. When you pass through a left-opening door and turn around to come back through it, you would normally rotate about a vertical axis. But what if you were to rotate about a horizontal axis, and you floated back through upside down? Then the door that opened on the left would still open the left on the way back though it, but a door that opened at the bottom would now open at the top. We say that left and right are reversed but not top and bottom only because we take for granted a particular axis of rotation.

In space, where we are weightless, the axis of rotation about which we choose to rotate when turning to come back through a door is less likely to be the vertical axis. You could just as easily spin about a horizontal axis instead. So, after years in space, it might seem as natural to you to say that a door that opens at the top opens at the bottom when you come back through it as it does to say that a door that opens on the left opens on the right when you return though it.

For creatures that live in a weightless environment, where it is as easy to rotate about one axis as the other, perhaps neither the mirror puzzle nor the door puzzle would even be puzzles.


Larry Hamelin said…
Interestingly enough this question was put to me by my high school (11th grade) physics teacher. It took me a couple of years to work it out, and another couple of years to be confident of the answer.

But this question seems—contrary to your earlier post—to be very atypical of the sorts of problems raised in the philosophical canon, in that it has an actual solution.
Mithrin said…
"For creatures that live in a weightless environment, where it is as easy to rotate about one axis as the other, perhaps neither the mirror puzzle nor the door puzzle would even be puzzles."

This last sentence is the key for me.

Most humans have a poor intuition for certain concepts in mathematics (probability being the most obvious example).

A reflection is not the same transform as a rotation, and I think because the human psychology deals with rotation more it presupposes rotation. (i.e. when facing another human they are rotated, so your mental rule of thumb is rotation).
Steelman said…
SL said: "People sometimes assume all questions can be answered by science. They would assume that the mirror puzzle must have a scientific solution. But it turns out that the mirror puzzle is a puzzle that science cannot solve. It seems that, sometimes, only philosophy will do."

I'm only a neophyte when it comes to philosophy and science, and I do not "assume all questions can be answered by science," but the explanation of what is happening in the Mirror Puzzle seems to me more scientific than philosophical: the affect of reflected electromagnetic waves on the cognitive behavior of a flightless land creature which evolved in a gravitational field (i.e., vertical axis of rotation assumption). It's mostly about physics and biology (philosophy of science and philosophy of mind figure in as well, I suppose). Your similar Door Puzzle literally adds rocket science.

SL: "It is a puzzle that is solved just by thinking."

True, compared to the expense of scientific research, these two thought experiments are a bit of "no money fun," but I don't think we would have these particular puzzles, and their solutions, had that "money" not been spent by scientists who came before us. If we had been discussing the Mirror Puzzle at the feet of Aristotle, for example, the answer might have included something about perfect solids and the ether. In other words, without science to inform us of matters of fact, philosophical inquiry alone can easily lead us in the wrong direction.
Stephen Law said…
What I had in mind when I said it was not a puzzle science can answer is - I included all the relevant scientific facts when I set the puzzle up, and they didn't answer it.

The answer is produced by reflecting on the concepts involved (top, bottom, left and right) and what we take for granted when applying them.

So it was a sort of conceptual clarification that was required. Not more scientific theory. And conceptual clarification is, I take it, one of the core activities of philosophy.

I do take the point that this is an atypical philosophical puzzle in that it does have a clear-ish solution (though there are papers published which suggest it actually goes much deeper than we have supposed - including a classic paper by Lycan).
In fairness, I think you set up the puzzle in a slightly misleading manner. It wasn't clear, to me at least, that this was purely about our perception of object orientation. Superficially, it seemed like a straightforward question about how a mirror works, which clearly caught a few others out as well, in so much that physics alone is sufficient to explain this phenomenon. Or maybe you did set it up out correctly, and we're just victims of scientific conditioning. That's probably a legitimate rebuttal right there.

Here's a question though: it's taken for granted that the visual cortex 'corrects' the inverted image projected onto the retina before sending it out to the higher areas of the cortex etc. Is such a correction really needed? Can we even ascribe spatial dimensions to what amounts to little more than a complex synchronised firing of neurones? I think this relates to what Pinker (I think it was him, or maybe he was quoting somebody else) termed the "the big question", which for now sets it beyond the realm of empirical science, but might be more suitable for a philosopher to ponder.
Anonymous said…
Yes, people take direction for granted. If exposed to it enough, people take any kind of information for granted.

Like clothes: you've been wearing them for so long, I bet you don't even feel it. Or like habits: you can walk without thinking about it.

Once information is taken for granted, or well-known, by everyone, it becomes 'common sense,' even if people don't know the reason for the information.

And of course, 'common sense' can be completely out of wack. (Seriously, a flat Earth in the center of the Universe?)

Everyone's seen a mirror, then everyone takes for granted mirrors reverse images vertically.

But of course, not everyone's seen a CONCAVE mirror. There's where 'common sense' fails. In a concave mirror, you can see yourself upside-down, with left and right in their proper place.

People who can let go of common sense can be philosophers.

P.S: In addition to Rev. Dr. Incitatus, our brain has this habit of trying to 'correct' or 'make sense' of things. (That's why we have philosophers, religion, and science) Of course, how we 'correct' something is based on previous knowledge. We all know (some) mirrors reflect left as right. We also know when someone puts out his/her left hand out in front of us, it looks like it's on the right. We also know to be in front of someone, you have to ROTATE VERTICALLY 180 DEGREES.

Most of us would then string all this information and come up with a conclusion that's wrong yet it becomes common sense ANYWAY: The 'most of us' would infer that mirrors ROTATE my image.

People who are not 'most of us' would give this matter more thought and research before surmising a conclusion.

Inferring without giving stuff enough thought is a dangerous thing to do.
"our brain has this habit of trying to 'correct' or 'make sense' of things. (That's why we have philosophers, religion, and science) Of course, how we 'correct' something is based on previous knowledge."

Cargo cults being a fine example of this.
Anonymous said…

When I read this puzzle, it left me confused and pondering for long periods of times, even at school or during meals.

The question Stephen Law raised "Why do mirrors reflect left as right instead of up as down?" is deceptional. A trick question.

Up stays up.
Left actually stays left too.

There are 3 dimensions in this world: left-right, up-down, and front-back.

When you face a mirror directly, the dimensions of left-right and up-down stay the same when reflected because they are parellel to the mirror.

Front-back, however, isn't.

The dimension of front-back is perpendicular to the mirror, reversing everything to back-front in the mirror.

I wish I could make it clearer with a thought experiment. But bottom line, left-right isn't reversed, front-back is.

"So WHY does my mirror image raise his left hand when I raise my right?"

Our perception of left-right is dependent on front-back. By the way, front-back is also dependent on up-down. Why? That's the way humans 'common sensified' direction.

Foolish humans. >:)
Unknown said…
The perpendicular mirror reflects, point to point, end of story. The reflection you see isn't real, so when you raise your left hand you're seeing the reflection of your left hand rise, it is not the image-you's right hand. If you are wearing a ring on your left hand but not your right, which hand is being raised? The ring hand. The terms 'left hand' 'right hand' are being misused.

A completely spherical being wouldn't have this problem.

The clock example is misrepresented too. It does have the same apparent reflection problem, in that its 3 is now where its 9 should be.

This is not a philosophical puzzle. It's not even a science puzzle. It's not a puzzle! Philosophy is not required, though thinking is, and that seems to be surprisingly absent. It appears that the real problem is that with only one line of symmetry many people find it difficult to know their arse from their elbow.
Anonymous said…
Quote: "People sometimes assume all questions can be answered by science. They would assume that the mirror puzzle must have a scientific solution. But it turns out that the mirror puzzle is a puzzle that science cannot solve. It seems that, sometimes, only philosophy will do."

Stephen, correct me if I'm wrong, but you seem to argue that deductive reasoning is entirely the purview of philosophy and that inductive reasoning and empirical observation are entirely the purview of science. This cannot be farther from the truth.

Yes, science rests upon the foundation of empirical observation, but these empirical observations are typically codified into concepts and a precise language that allow for direct manipulation of terms using deductive reasoning. What is mathematics but precisely the application of deductive reasoning? What you are essentially arguing in your piece is simply the application and exposition of logical arguments - how is that different from science?

Lastly, neither I nor the scientists that I have come across assume that science can solve all problems. It simply looks at all observable phenomena. Science cannot answer metaphysical questions, it can clarify but not answer many epistemological issues, and it is not going to provide you with any normative ethical systems. Philosophy still has its place.
Paul P. Mealing said…
I have explained this phenomenon at the following blog:

Please take the time to read it, because mirrors actually reverse everything (not nothing), but not how you expect them to. And it's a scientific explanation.

I like what you do.

Best Regards, Paul.
Stephen Law said…
Hi Paul

Thanks for the link. I think your solution is essentially the same, it's just a matter of how we describe what the mirror does - e.g. reverses nothing ( which is how I put it) or reverses back to front (which is how you put it). I suspect that "reverses nothing" isn't entirely problem free, but is probably preferable to "reverses back to front" as the puzzle arises even for objects that lack depth. However, maybe by "back to front" you mean, look from rear as normally look from front? But then that's not right either - a sheet of paper from rear looks different to how it normally looks from front, because you cannot see the writing on the front (which is why you then start talking about transparent sheets of paper). I think my way of describing situation is simpler, if not perfect. Ultimately, my solution doesn't require we describe the mirror as reversing anything. We can just draw the diagram of what happens optically, and then explain why we say it reverses in one way not the other in just the way I do.
Paul P. Mealing said…
Hi Stephen,

Thanks for your response.

One of my points of contention is that this is not a philosophical question but a scientific one, and as one of your contributors, The Barefoot Bum, points out, it does have 'an actual solution'.

Another of your contributors, Nutcasenightmare, in his 'BRAINSURGE' comment, then give us that solution quite succinctly and accurately. This is a physics problem, pure and simple.

Thanks, Paul.
Stephen Law said…
Hi Paul

But providing someone with all the info about what happens to light etc does not solve the puzzle.

So the solution is not scientific in that sense. That was the point I was making.

The solution requires thinking about what is taken for granted by describing something as "reversed left right but not top bottom". It is more of a conceptual/meaning solution, I'd suggest, that involves unpacking what we *mean* by describing something as "reversed". We are doing what Simon Blackburn calls "conceptual engineering".
Paul P. Mealing said…
Thanks Stephen for the interaction.

I will create a link from my blog to yours (regarding this topic), assuming that's okay with you.

Best regards, Paul.
Stephen Law said…
Sure, Paul. Thanks for contributing. We don't agree, but hey, that's what makes this interesting!
Michael Young said…
"So yes, it is true to say mirrors reverse left to right, but only if we choose a vertical axis of rotation. Choose a horizontal axis and they then reverse top to bottom."

I am probably getting fruitlessly sidetracked, but what could it mean to "choose" an axis here? It rather seems that my experience when looking at my mirror-image is necessary, and not any kind of matter of choice at all. Is there something I can do to see my reflection differently?

It is undoubtedly true that, in claiming that mirrors reverse left-right, we are assuming that the vertical axis is the axis in reference to which the judgment is being made. But this is just to explicate the content of the original judgment, and not to explain the state of the world in virtue of which the judgment is appropriate. And, again, I am probably borrowing more trouble than I need, but I would like to think that there is something about the real state of my mirror-image which grounds my judgment of left-right reversal, and my judgment that the vertical axis is *the* axis of concern.

Sorry if that is as clear as mud. All that to say -- mirrors still puzzle me.
Geert A. said…
I hope this is a simple answer to the question:

Put on a white t-shirt and position yourself facing north. Write in front of your t-shirt north, and on the back south. On your left side, write west, on your right side write east. On top of the t-shirt write up, at the bottom write down.

Place a mirror in front of you. You'll see that your mirror image (m.i.) still has a correct east, west, up and down marker. However, your m.i. faces south but m.i.'s t-shirt says north.

Place the mirror left or right of you. You'll see that m.i.'s t-shirt has a correct north, south, up and down marker. However, your m.i. t-shirt's west is in the east.

Place the mirror above or below yourself. You'll see that m.i.'s t-shirt has a correct north, south, west and east marker. Only you're seeing yourself upside down.

In all cases, the mirror only mirrors one axis. And, in all cases, when you lift your right hand, your m.i.'s left hand will be risen.

How is THAT possible? simple: we defined left and right relative to ourselves: standing upright, facing north we defined 'left' as the arm in the west. But turn yourself over any axis by 180° and your left arm will point to the east. What a mirror does is actually not TURN, but INVERT one axis (and it can be upside down, so the philosophical puzzle was flawed to start with), which has the same effect.

So, the answer is: up and down are relative to gravity, so up and down are only inverted for horizontal mirrors. Left and right are relative to our position, so are inverted always by a mirror. Any letters on our t-shirt were always written in mirror writ for the same

What does it learn me? That we, humans, have it hard to see beyond our own definitions once we consider them 'natural'.
MikeO said…
Hello Stephen,

It may be that I already posted this, but on the wrong page, so please pardon the repetition. I wish to offer some assistance to this mirror question. Although you do seem to have the essentials of a correct solution, my contribution will may be in cleaning up some semantics and adding a small additional insight.

The mirror reversal puzzle is not a matter of the science of light rays, optics, and the Physics behind reflection. It’s a people thing. I’d say it can best be solved by a science of human activities, a science that deals with how people interact with complicated or subtle things. The idea of “reversedness” in images perceived by humans is FAR more subtle than the idea of a photon trajectory reversing direction.

When people want to compare two nearly identical objects for some subtle difference there are two common strategies they can use. These two strategies are often useful, but they are oddly contradictory.


In one strategy, the two objects are lined up to face in the same direction before they are compared. For instance, if two nearly identical pens are to be compared, no one I know of would ever hold one pen horizontally, the other vertically, and then proceed to compare them. People commonly hold them facing in the same direction for such a task.

When a person uses this strategy in the mirror situation, as you noted, they like to imagine themselves rotating about a vertical axis for a comparison with their image, while facing in the same direction as their previous image was pointing. This also requires them to mentally freeze their image as it was when they faced the mirror. When all this is acomplished, the Left/Right reversal becomes obvious.


The second common human strategy for dealing with complicated situations, is to freeze EVERYTHING, and look at the situation “as is” in order to perform an analysis of the subtle differences between two objects.

In the mirror setup, performing this “as is” strategy means NOT rotating anything at all before doing the comparison, and the Left/Right reversal fails to show up. Instead, a Front/Back reversal is apparent in this “as is” comparison.


Of the two strategies, the second is the simpler. The first is almost too complicated when done mentally, and it’s often too much to document in any way. Yet, it can happen in a flash of mental imagery, only to fade as soon as words are brought in to capture it.

Often a person, deep in the throws of the mirror riddle, will drift from one strategy to the other subconsciously. This is often described as “magical” by those who delight in that sort of thing, while others will literally complain of the headache it causes them.

When each strategy is carefully thought through, ONE AT A TIME, clarity results.

And yes, if some gymnast were to apply the first strategy by performing a hand stand in order to face in the same direction as the earlier image, then Up and Down are seen to be reversed. But who is prone to do this difficult action? And not only difficult, but risking injury and even seven years of bad luck if the mirror is broken?

So, it’s not the mirror that does any reversing of perceived images, it’s people who do that by their selection of strategies. Mirrors reverse the direction of light rays, but people decide how they are going to compare image to object. The three strategies outlined above give rise to all three spatial dimension being "reversed."

I have a discussion forum website set up devoted to this mirror puzzle for those who want to see more of the details. Please come and visit:


Stephen Law said…
Thanks MikeO - I think you are right (we'll we are). Checked the website - it's good.
Paul P. Mealing said…
Hi Mike,

I'm sorry, but we still disagree.

"So, it’s not the mirror that does any reversing of perceived images"

The mirror does reverse images - it reverses them back to front.

Regards, Paul.
MikeO said…
Hi Stephen,

Thanks for visiting my humble web abode. And thanks for the opportunity to discuss this odd subject here.


Hi Paul,

Fancy meeting you here. I’m surprised you disagree again, after I re-wrote my piece with your objection in mind. Maybe you can reconsider after I point this out.

You wrote here: “The mirror does reverse images - it reverses them back to front.”

I think I agreed with that, from the perspective of the science of optics and the laws of physics. But I also stressed that this perspective is a world far removed from human activities, and where the mirror riddle really resides.

Physics always (and rightly so) strips out the human element. When that is done, and an artificial definition is made of what an image is, then the Physics of mirror images is as you say, and no Left/Right reversal comes up, only back to front.

But this analysis, and this science, helps no one UNDERSTAND the mirror riddle. A listener to the Physics “explanation” walks away still wondering why he still feels a L/R reversal, even though it’s just been proved to him that none exists... in the world of Physics and the science of bouncing light rays.

This is why I stress that the answer to the mirror riddle must be found in a science of human activities. In THAT world, when the first strategy I outlined in my post above is employed (as it commonly is), then a L/R reversal is very easily discovered to occur.

The practitioner of this science of human activities can rightly say that (within his science) a mirror DOES reverse L/R when humans employ strategy #1.

Now, Paul, I know you agree that there are two distinct worlds in which to discuss this mirror riddle, because you documented them on your website regarding an article by Dorothy Rowe a few years ago. There you write:

“Human behavior will never be distilled into a set of laws, even remotely like physics, or even biology.”

And you also wrote:

“So, at the end of the day, they deal with different issues, different problems.”

So, at the end of this day, I’d say that:

(1) Physics says there is no L/R reversal of mirror images.

(2) A science of human activities says that humans can correctly perceive a mirror reversing Left and Right.
Paul P. Mealing said…
Hi Mike,

"A science of human activities says that humans can correctly perceive a mirror reversing Left and Right."

Only it's incorrect and that's the point. There is a right and a wrong answer to this and you don't delineate them.

We agree on the psychology of how people perceive mirror reflection as L/R reversal, but you don't say that it's incorrect and that back to front reversal is the correct perception. It's a really important distinction because one is right and one is wrong.

Regards, Paul.
MikeO said…
But Paul, for someone who asks me the mirror riddle, and who does sincerely perceive a L/R reversal, telling them what you say is right will not help them.

You can prove it him with optics that there is no L/R reversal, but he will still feel it.

What you are stating is true within the world of Physics, but in the world of the sincere perceiver I mentioned, this truth is perplexing.

For thousands of years people have been employing strategy #1 as I posted above, and perceiving a L/R reversal. Physics has been only in existence for about 400 and some years. We owe it to the non-physicist to help them understand what came first. We don’t do this by saying their age-old, innate way of doing things is wrong.

I love the Physics and what is right in that field. But when someone asks me the mirror paradox, the only way I can solve it in good conscience is by showing them where the L/R reversal rightly comes from (strategy #1), and then why it rightly goes away (strategy #2 and Physics).

It’s a figure of speech, and a valid one, to say that a mirror reverses L/R when people employ strategy #1, which they DO, and ALL the time, almost. It’s speaking the language of the people.

The way physicists answer the mirror riddle (by denying the L/R reversal’s reality) reminds me of the way priests would say to a sincere questioner about some incomprehensible dogma “It’s a mystery. You have to take it on faith.” Such an answer in religion does no service to the sincere questioner, and it serves the priest only. It makes him a mysterious keeper of the secrets.

A physicist is one who loves imparting understanding, not in being admired as all knowing. Explaining the universe to the unknowing means speaking in their language, and speaking to their situation. That is the approach I take in the mirror riddle.

AFTER a sincere questioner “gets it” and sees where the L/R reversal comes from, and how strategy #2 might be a better approach, they can then abandon the perception. In order to see the right physics they have to see the L/R reversal in all its glory, and then they can drop it.

Does a mirror reverse L/R literally? No. But is anything gained by speaking ONLY literally to people? Not in the mirror puzzle issue.
Paul P. Mealing said…
Hi Mike,

'The way physicists answer the mirror riddle (by denying the L/R reversal’s reality) reminds me of the way priests would say to a sincere questioner about some incomprehensible dogma “It’s a mystery. You have to take it on faith.” Such an answer in religion does no service to the sincere questioner, and it serves the priest only. It makes him a mysterious keeper of the secrets.'

This is a really bad analogy - I'm not asking anyone to take anything on 'faith'. If people want an explanation, you tell them the 'truth'. My explanation is for non-physicists and non-scientists - I thought that would be obvious. I hardly discuss optics at all, except for one very succinct and self-explanatory statement: 'a plane mirror reverses everything in the dimension that's perpendicular to the plane'. The rest of my explanation is in terms of perceptions, just like yours.

The fundamental problem I have with your explanation is that you talk about the 2 perceptions: L/R reversal and B/F reversal as if they are equally valid when they're not. And also you make the specific statement that there is no reversal done by the mirror, only the observer ("it’s not the mirror that does any reversing of perceived images") which is simply wrong. The whole point of providing an explanation is to explain what's really happening and why they perceive an illusion.

"Does a mirror reverse L/R literally? No. But is anything gained by speaking ONLY literally to people? Not in the mirror puzzle issue."

If you can't explain to people what 'literally' happens then you don't have an explanation. In this statment you tell a half truth. There is no L/R reversal, but you don't say that there is a B/F reversal, which is the explanation, pure and simple.

Regards, Paul.
Paul P. Mealing said…
Hi Mike, again.

Our disagreement may seem trivial but it’s not.

We agree on the psychological explanation of why people perceive a mirror reflection as L/R reversed.

The only problem I have with your explanation is that you don’t tell people that the left to right perception is WRONG and the front to back perception is RIGHT. The explanation is so dead simple it certainly doesn’t require an esoteric knowledge of physical optics.

We mostly agree, but we disagree on what is RIGHT and what is WRONG, and if you don’t include that then you are short-changing your audience.

In particular, you mislead people into believing that mirrors reverse nothing, and that it’s all in the mind, which it isn’t.

I only harp on this point because it goes to the crux of the ‘mirror paradox’. If you don’t explain this then you have explained nothing. People who believe that mirrors reverse nothing don’t understand it and they haven’t found the solution, though they may think they have. It’s like believing you have found the solution to a mathematical puzzle, for example, when in fact, you haven’t. We’ve all been there.

Regards, Paul.
MikeO said…
Hi Paul,

Let me begin by apologizing if my priest allusion was too strong an approach. I only said it "reminded” me of such, and did not use the word analogy, but it may have still been an unnecessarily strong use of words.

It was mostly the lack of service to the questioner, and the exalting of the answerer that stimulated my memory. It only weakly reminded me of my past, not strongly.

When a non-physicist hears the standard Physics answer to the mirror riddle, and even understands the proof that L/R is not reversed, they often walk away puzzled and in a little awe at the one who gave them such a mysterious answer.

They know they felt a L/R reversal in the past, and soon enough that subconscious drift I mentioned toward strategy #1 occurs and they feel it again. They often think the physicist sees something beyond them (a tiny bit like a priest), when actually the myopia belongs to the physicist who can’t see and speak in the common language.


Now I’ll try to handle some of your recent statements one by one. In your February 7 post you wrote:

“The fundamental problem I have with your explanation is that you talk about the 2 perceptions: L/R reversal and B/F reversal as if they are equally valid when they're not.”

They are not equally valid in the world of Physics, but in the world of common human activities they are. The two strategies I mentioned are both heavily used, even by physicists. The two reversals are pretty equally valid to those people who perceive them, which is very sizable segment of the population.


You wrote: “And also you make the specific statement that there is no reversal done by the mirror, only the observer (‘it’s not the mirror that does any reversing of perceived images’) which is simply wrong.

In the world of Physics it’s the z component of photon trajectories that is reversed, but that is all. In the world of Physics the idea of an image is a rather artificial construct, and the idea of a perceived image is non-existent. Physics is just not nearly that powerful to include human perceptions.

What I mean when I say “it’s not the mirror that does any reversing of perceived images” is IN THE WORLD OF HUMAN ACTIVITIES (not the world of Physics) the REAL action is not performed by the relatively passive mirror (It only reverses photon z velocities) it is performed by the human employing the comparison strategy. When different things get reversed, which can only happen in the world of human activities, it’s because of a differing action by said human, not by the mirror.

You see there are two worlds to consider here. Non-residents of the world of Physics who are ready, willing, and able to look into the world of Physics can hear your explanation. The others are not served by it. I try to speak their language.


You wrote: “If you can't explain to people what 'literally' happens then you don't have an explanation.”

I’ll agree that in that situation you don’t have a “world of Physics” explanation, but not everyone wants that. Not only that, but image perceptions and the mirror paradox don’t even HAPPEN in that world of Physics. The only thing the Physics can explain is the triviality of the photon trajectories.


In your February 8 post you wrote: “The only problem I have with your explanation is that you don’t tell people that the left to right perception is WRONG and the front to back perception is RIGHT.”

Do you tell people who use the word “sunrise” that they are wrong?

In the world of Physics they are, but what good is correcting them? Those who understand the heliocentric model can happily use the word “sunrise” knowing all along that it’s not correct in the Physics, but just fine in everyday life.

The sun doesn’t rise in the sky, and mirrors don't reverse L/R, but only in the strictest, and less universally communicative “Physics world” sense. When I live in the world of regular people I can enjoy both sunrises and sunsets.


Paul P. Mealing said…
Hi Mike,

I feel this argument is becoming a little ridiculous.

One explains an illusion by revealing the truth. The sunrise/sunset is a perfect example. If the entire population of the planet believed that the sun literally rises and goes around the Earth, that doesn’t make it correct – and we know otherwise – should we not enlighten people with the truth? And the exact same principle applies to the mirror paradox.

You don’t think people can comprehend the truth, but I disagree and my post demonstrates the contrary.

The following statement effectively promotes ignorance:

”They are not equally valid in the world of Physics, but in the world of common human activities they are. The two strategies I mentioned are both heavily used, even by physicists. The two reversals are pretty equally valid to those people who perceive them, which is very sizable segment of the population.”

If a ‘sizable segment of the population’ holds a belief that is WRONG then that is alright in your view, and we shouldn’t attempt to enlighten them because they won’t understand it anyway (your point of view). This also applies to your sunrise example. An explanation that fosters an illusion is not an explanation at all. An explanation that explains an illusion by revealing the truth – that is an explanation.

When you say that what is real and what is illusion are ‘pretty equally valid’, then you are propagating a falsehood, and that means you’re in no position to expound on the mirror-image reversal puzzle.

Mike, we don’t even agree on what constitutes an ‘explanation’ or ‘solution’. For you, it can contain falsehoods and misperceptions, but for me, it must contain truths and revelations. That’s a pretty fundamental difference.

Regards, Paul.
MikeO said…

I'm trying to point out that there are very distinct and different worlds to consider. What is correct or important in one may not be in another. Definitions of words differ from one world to another. They speak different languages.

In your chosen world you and I are in complete agreement.

I'm happy to show non-physicists the absolute non-reversal of L/R in the objective world of Physics, using that world’s definition of the word "reverse." But I try to do so only to the extent they choose to go there for a visit. The word “objective” means stripped of human residue; only objects remaining. They often do not want to go there.

They are usually quite happy to have me show them the justification of their use of the word “reverse” in their world, in relation to their perception of L/R. For them to hear you tell them it’s incorrect to use “reverse” this way in your world is inconsequential to them, but it could be annoying. Telling them that they are incorrect in using the word “sunrise” would likely estrange you from them. In their world they want to speak their language, not yours.

Mike said…
Please consider this:

He was not studying medicine. He had himself, in reply to a question, confirmed Stamford's opinion upon that point. Neither did he appear to have pursued any course of reading which might fit him for a degree, in science or any other recognized portal which would give him an entrance into the learned world. Yet his zeal for certain studies was remarkable, and within eccentric limits his knowledge was so extraordinarily ample and minute that his observations have fairly astounded me. Surely no man would work so hard or attain such precise information unless he had some definite end in view. Desultory readers are seldom remarkable for the exactness of their learning. No man burdens his mind with small matters unless he has some very good reason for doing so.
His ignorance was as remarkable as his knowledge. Of contemporary literature, philosophy and politics he appeared to know next to nothing. Upon my quoting Thomas Carlyle, he inquired in the naivest way who he might be and what he had done. My surprise reached a climax, however, when I found incidentally that he was ignorant of the Copernican Theory and of the composition of the Solar System. That any civilized human being in this nineteenth century should not be aware that the earth travelled round the sun appeared to me to be such an extraordinary fact that I could hardly realize it.
"You appear to be astonished," he said, smiling at my expression of surprise. "Now that I do know it I shall do my best to forget it."
"To forget it!"
"You see," he explained, I consider that a man's brain originally is like a little empty attic, and you have to stock it with such furniture as you choose. A fool takes in all the lumber of every sort that he comes across, so that the knowledge which might be useful to him gets crowded out, or at best is jumbled up with a lot of other things, so that he has a difficulty in laying his hands upon it. Now the skillful workman is very careful indeed as to what he takes into his brain-attic. He will have nothing but the tools which may help him in doing his work, but of these he has a large assortment, and all in the most perfect order. It is a mistake to think that that little room has elastic walls and can distend to any extent. Depend upon it there comes a time when for every addition of knowledge you forget something that you knew before. It is of the highest importance, therefore, not to have useless facts elbowing out the useful ones."
"But the Solar System!" I protested.
"What the deuce is it to me?" he interrupted impatiently: "you say that we go round the sun. If we went round the moon it would not make a pennyworth of difference to me or to my work."
I was on the point of asking him what that work might be, but something in his manner showed me that the question would be an unwelcome one. I pondered over our short conversation however, and endeavoured to draw my deductions from it. He said that he would acquire no knowledge which did not bear upon his object. Therefore all the knowledge which he possessed was such as would be useful to him. I enumerated in my own mind all the various points upon which he had shown me that he was exceptionally well informed. I even took a pencil and jotted them down. I could not help smiling at the document when I had completed it.

A Study in Scarlet
Sir Arthur Conan Doyle
Thanks to University of Virginia Library
Paul P. Mealing said…
Hi Mike,

I actually explain the mirror-puzzle in plain language in my post, with no reference to esoteric optical physics, and people actually understand it - that's all that needs to be said on the topic of language and exposition. If you don't want to tell people the truth, that's your call, but don't delude yourself, or them, that you're actually explaining anything.

Your little extract from Doyle only demonstrates that some people prefer ignorance to knowledge, and such people will get no succour or support from me. I agree with the Dalai Lama that 'ignorance is one of the 3 poisons of the mind.'

Regards, Paul.
Paul P. Mealing said…
If I can elaborate on my last comment: I’ve spent my entire life trying to understand things, and solving puzzles and mysteries is a part of that. As I said on another blog, recently, real knowledge comes from knowing how much you don’t know. Even Confucius and Socrates made that point, as well as Wittgenstein, albeit more indirectly.

If you want people to maintain an illusion as ‘valid’ then there is absolutely no point in explaining it to them. In other words, why bother? And I believe that this is exactly what you are saying, whereas, for me, explaining a mystery or a puzzle is the whole point.

You are saying (by way of your literary extract) that it is okay for people to not know the ‘truth’ behind sunrises and sunsets, which is fine. And, obviously, from your perspective, the same applies to the mirror paradox. So, why even discuss it? It’s a waste of words.

Regards, Paul.
MikeO said…
Oh Paul,

Maybe you can take a cue from Dr. Watson and just be amused by my approach.

... AND we can celebrate that we agree on the Physics.
Paul P. Mealing said…
I take your point.

Enjoy reading Louisa Gilder.

Regards, Paul.
Yule said…
The reasoning about the mirror doesn't really make sense. You can't just choose a horizontal axis. You must choose a vertical axis because the image you see when you look in a mirror only fits to a rotation around a vertical axis. If you were to rotate around a horizontal axis, you would be standing on your head. When you look in the mirror while standing straight up, do you see yourself standing on your head? No. Therefore the image in the mirror is incompatible with a rotation around a horizontal axis.

The mirror does not reverse left and right, it reverses front and back. But we simply interpret it as a rotation around a vertical axis because the brain treats our reflection as if it is simply another human facing us.

You can, however, use reasoning somewhat similar to the reasoning you presented for why mirrors flip text left to right but not top to bottom. When we read text in a mirror, we must flip the paper before we can actually view the text in the mirror. The reason that left and right seem to be flipped is because we tend to rotate the paper around a vertical axis. If we rotate it around a horizontal axis, the left and right will stay the same, but the top and bottom will seem flipped. In actuality, however, in both cases the mirror is directly showing exactly what's in front of it at each point in space.

Remember, this works with text because you must physically rotate the paper before viewing it in the mirror, and you can choose whether to physically rotate it around a vertical or horizontal axis. In the case of a human, there is no physical rotation, but simply a perceived one, which is always around a vertical axis.
Paul P. Mealing said…
Yule, you've got it exactly right.

Regards, Paul.
Stephen Law said…
"You must choose a vertical axis because the image you see when you look in a mirror only fits to a rotation around a vertical axis."

No, you are free to choose either axis but the vertical is much more natural for two reasons - human vertical symmetry and the fact we normally move about by walking.

Notice that you would not "fit" into your mirror self if you had an arm missing (and so lacked vertical symmetry).
Stephen Law said…
PS but you are of course right that a mirror reverses front back.
Paul P. Mealing said…
You make a good point, Stephen.

In fact, if you did anything to asymmetricise (new word) your body, it would demonstrate that the left is reflected on the left and the right is reflected on the right. The same if someone is standing behind your right shoulder, they will appear on the right side of you in the mirror.

The other thing is that if you hold a handheld mirror near your face and have a distinctive mark under one eye (either one) it will always appear on the same side with every reflection. If mirrors reversed left to right then the images would alternate.

On the other hand, if you hold something between the 2 mirrors you will see the back and front of it in alternate images.

Yule also explains why writing appears back to front (left to right), which is one of the things that often confuses people.

Regards, Paul.
Hanging question lasted for years.
Robert Newton said…
Hi Stephen,
I've quickly read your explanation for the "mirror puzzle".
it's an explanation that I have seen several times.
I can easily PROVE that it's wrong.
Reply if you want details.
Paul P. Mealing said…
Hi Robert,

This is probably the only post that's not on my blog that I keep track of (I hope Stephen doesn't mind). The explanation is in the last half dozen comments that were posted in January last year, if you care to read them.

Mirrors reverse along the axis that's perpendicular to the plane of the mirror - in other words, mirrors reverse back to front - it's that simple.

Regards, Paul.
Robert Newton said…
Hi Paul,
I agree that reversal perpendicular to the mirror surface is the basic physics, but there's more to it than that, in my opinion.
Incidentally, I am confused because I thought I was going to discuss this with Stephen Law.
Perhaps you are working together. Anyway, what I am talking about is the hypothesis that our perception of left-right reversal is based on imagined rotations.
I would like to discuss that with him (or you). Please reply if you want me to give you my "disproof".
From a quick look at your stuff on the "Mirror Paradox"
you are not convinced about the psychology of this problem, so my ideas may be not of much interest to you. Still, I would like to point out the error in Stephen's explanation.
It's a mistake that even Richard Feynman made in one of his explanations.
Paul P. Mealing said…
Hi Robert,

My experience from previous excursions on Stephen's blog is that he's happy to let other people discuss issues that he's raised.

Yes, I know it's about perceived rotations; I thought I covered that. In fact, I discuss it at length.

If Richard Feynman made a mistake regarding this, I certainly would be interested.

Regards, Paul.
Robert Newton said…
Hi Paul,
I just spent half an hour writing my reply and then my computer went blank and I lost it all.
I may try again later this week.
Anyway, what I wanted to say is in the book that you mentioned, by Richard Gregory.
So, you should know it already really.
Robert Newton said…
Hello Paul,
I apologise for not reading your "Mirror Paradox" properly at first, but I was concentrating on Stephen Law's "Mirror puzzle-solution?".
In fact your approach is very similar to mine. It certainly makes things simpler if you treat writing as a three dimensional object instead of an idealised two dimensional object.
I'm having computer problems, so I will send my ideas in 2 or 3 consecutive messages.
Robert Newton said…
Hi again Paul,
Stephen's explanations based on imagined rotations about various axes are very unconvincing to me.
Consider the standard example of somebody looking at his/her mirror image or that of another person.
My next post will show how this approach cannot possibly be an adequate explanation.
Robert Newton said…
Hi Paul,
Simply set up a situation where an observer views another person's image, but is unaware of the mirror. I will skip the details of setting up this thought experiment.
When the person being observed moves a hand, the obsever sees the image move its other hand.
That's it, no rotations! This is a very persuasive argument against "imaginary rotations" with these sorts of images.
Robert Newton said…
Hi Paul,
So why do we so often perceive left-right reversals in plane mirror images?
It must be something to do with psychology and I will just give my (simplified) explanation for what it's worth.
Suppose front-back is reversed in a particular image, but top-bottom remains unchanged. That automatically re-defines
left-right, which is based on the other "dimensions".
We often seem unaware of a front-back change as a reversal, but we easily notice a right-left change.
Notice that the left-right change isn't an illusion, in one sense.
It follows auromatically from the real physical change.
That's all for now.
Robert Newton said…
Hi Paul,
I nearly got through without a "typo". Sorry about
"auromatically". It should be "automatically", of course.
Paul P. Mealing said…
Hi Robert,

Richard Gregory wrote something in The Oxford Companion of the Mind, published in 1987, and never mentions Richard Feynman.

I've read most of Feynman's books, and whilst he gives an excellent exposition on the quantum mechanics of mirror reflection, he doesn't talk about 'reversals' at all - not in the one record I have of him discussing the subject.

Regards, Paul.
Robert Newton said…
Hello again Paul,
I had completed my comments, but obviously I'm now replying to your latest comments.
My mention of Feynman was just incidental. However, what I meant was the video on YouTube. Just go there and enter "Feynman mirror" in the search box. At the end of the video, he talks about how we imagine going behind the mirror, to explain the perception of left-right reversal.
Of course, my main point was what Gregory wrote about the "disguised" mirror experiment. I don't agree with everything he wrote about this problem, but I think that experiment is a simple demolition of Stephen Law's "solution".
Paul P. Mealing said…
Hi Robert,

I guess you mean this.

Someone, who follows my blog, once suggested using compass points to explain this, just as Feynman does. This was in response to a sophist, I was arguing with at the time, who kept asking me to define what I meant by left and right.

Regards, Paul.
Robert Newton said…
Hi Paul,
Yes. That video is, of course, based on the adjacent original video showing Feynman as he talks about the mirror problem.
I think it was actually Martin Gardner who first came up with the "going behind the mirror" idea, as the explanation.
As regards defining left and right, that's really difficult only if you have to communicate with an "alien" with no common reference points.
Of course, Feynman wrote about that too, as you will know.
Paul P. Mealing said…
Sorry, I've been busy and distracted.
Yes, I read that account - I think it was in QED - possibly the same book where he gives an excellent exposition on the quantum interpretation of mirror reflection.

Regards, Paul.
Robert Newton said…
Hello Paul,
I don't visit this blog normally, but I was just checking because of my recent posts.
Anyway, just to say that I came across that Feynman stuff about left and right in the "Feynman Lectures".
It was in Volume One, I think.
Robert Newton said…
Hi again Paul,
I'm pretty sure now that it was in the last chapter of
Volume One.
That's chapter number 52.

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