true mirror
June 11, 2017 11:51 AM   Subscribe

Can someone please explain to me the differences between a regular mirror, "true mirror", and a photograph?

Can someone please explain to me the differences between a regular mirror, true mirror, and a photograph? Specifically, does a photo have the same effect as a "true mirror", and how does all this relate to the brain? Please, I am trying to understand it and just can't seem to figure it out. Is a photograph functioning as a "true mirror"?
posted by bananaskin to Science & Nature (15 answers total) 5 users marked this as a favorite
Is a photograph functioning as a "true mirror"?

In that a photograph doesn't reverse the image the way a normal flat mirror does? Yes, I suppose so. There's a comic in this "how-to" article that compares the three.
posted by supercres at 12:09 PM on June 11 [1 favorite]

This article on making a true mirror setup has some nice examples that may help: .
posted by nalyd at 12:10 PM on June 11 [1 favorite]

If you and your twin were facing each other and both raised your left hands, you would get a flipped version of what you see in a mirror.

Regular mirror: you raise your left hand, but the reflection, from its point of view, raises its right. The mirror is preserving absolute left and right from your point of view. What's on your left is reflected back to your left. Your left hand raises and so does the hand that is to your left in the reflection.

True mirror and photograph: preserve the subject's left and right rather than the observer's.
posted by zippy at 1:13 PM on June 11 [1 favorite]

An ordinary flat mirror presents the viewer with an image that's reversed front-to-back with respect to the plane of the mirror. So if you're looking straight into a mirror, stuff that's a long way behind you in real life will appear to be a long way ahead of you in the depths of the mirrored image.

When you're looking at a reflection of your own face in a flat mirror straight ahead of you, what you see peering back at you appears to be another person facing toward you. Your brain's visual processing system is not built to deal with mirrors, so the conceptual model it builds for what you're seeing there is the same one it uses for when you actually meet another person face to face.

If another person is standing next to you, then moves so as to face you, they almost always do that by turning 180° around a vertical axis and almost never do it by standing on their head. That means that their left hand side ends up on your right, and vice versa; and this is what your visual processing system tells you that the person you see when you look at your own reflection has also done.

It's the difference between what you see in a reflected image and this implicit and assumed 180° in-real-life turn that makes the mirror seem to swap left and right. The mirror itself does not swap left and right, only front and back.

If you take a sheet of paper with writing on it, and hold it up to the mirror, what you will see is mirror writing and it will also usually appear to have been swapped left-to-right. But it's not the mirror that does that swap: it's you, as you turn the paper to face the mirror. Again, when we turn a piece of paper around to face somebody else we almost always do that by rotating it around a vertical axis, swapping left and right; we do that because the natural assumption is that the person we're showing the text to will not appreciate seeing it upside down.

If you have a bright enough light between the mirror and the paper, or you use transparent film instead of paper, you can look directly at the back of the sheet and see what's written on the side now facing the mirror: and what you will see will be the very same mirror-writing you see in the mirror. All the mirror is doing is swapping that paper front-to-back, so the side that's further from you in real life is closer to you in the mirrored image.

The "true mirror" construction, where you look into the corner of a pair of flat mirrors set at 90° to each other with the joint run vertically, really does swap left and right as well as front and back. What you're seeing in a "true mirror" is actually a reflection of a reflection, and each of those performs a 180° swap to form the image.

Any 180° swap, regardless of direction - left for right, up for down, front for back, doesn't matter - of any 3D scene yields an image with the opposite chirality ("handedness"). That means that the second reflection you get from the "true mirror" restores the chirality that the first mirror flipped, and the image you see has a left hand where you expect its left hand to be and a right hand where you expect its right hand to be and the writing on the sheet it's holding up is properly readable.

If you turn the "true mirror" so that the corner joint now runs horizontally instead of vertically, you will see that the mirror is now swapping up/down as well as back/front, rather than left/right plus back/front the way it does when the joint runs vertically. The chirality of what you see in there is still correct, but now the reflection is upside down.

Now let's look at what a camera does.

A focussed camera lens is essentially just a fancy pinhole with better light-gathering properties. So the easiest way to think about what a camera is actually doing is to consider the paths that light rays take in order to form an image on the back wall of a pinhole camera or camera obscura.

Any light ray entering the camera from somewhere to the left of the pinhole is going to go straight through the pinhole and strike the back of the camera somewhere on the pinhole's right. A ray from the right of the pinhole will light up a spot on the back of the camera somewhere on the pinhole's left. Similarly, rays from above the pinhole will illuminate parts of the back wall below the pinhole, and those from below it will end up on the back wall above it. In fact the image formed on the back wall of the camera will have been swapped in two directions: left for right and up for down.

That's a pair of 180° swaps, which means that the image on the back wall of the camera will preserve the chirality of the scene in front of the camera.

And when you take the plate out of the camera and develop it, you're naturally going to rotate it until it's the right way up in order to look at it. Rotations also preserve chirality, so the image captured by the camera is not going to look mirrored.

If that image is on slide film, and you load the slide into a projector to throw it up on a display screen, you have to load the film into the projector in such a way that the side facing the light source shows the image you want to see projected - but you also have to turn it upside down. The projector lens does the same left for right, up for down pair of swaps that the camera pinhole does, and the upside-down slide ends up displayed the right way up on the screen.

If you load the slide into the projector with the image facing away from the light source, the screen image will have the wrong chirality: it will either be left for right or up for down swapped, depending on the rotation of the slide.

Ever seen an overhead projector, commonly used for presentations before PowerPoint ruined everything? Those have a flat mirror built into the projection optics. The lens in the projection head does the same left/right and up/down swappage as the one in an ordinary slide projector, and the mirror adds an additional front/back swap: so in order for the projected image to have the same chirality as the original, the original transparency has to get loaded onto the projector with the image side facing away from the light source. Which is handy, because that means you can write on it while projecting it.

So, short answer: no, the "true mirror" doesn't have exactly the same effect as a camera with a lens, in that the camera lens swaps both left/right and up/down while the "true mirror" swaps both left/right and front/back; but the fact that each of these constructions performs two 180° swaps means that both yield images with the same chirality as the original scene.
posted by flabdablet at 1:26 PM on June 11 [28 favorites]

Another thing that occurred to me after writing that answer last night is that the image reflected in a mirror is also not the same kind of image as the image captured by a camera.

The image captured by a camera is a two-dimensional projection of the 3D scene in front of the lens onto the flat plane of the film. It contains no explicit depth information at all. Distances to objects in the photographed scene can only be inferred from the way they occlude other objects, or appear bigger or smaller than other similar objects, or from focus cues.

The image reflected in a mirror, on the other hand, is a complete 3D replication of the reflected scene; it's as if the entirety of what's in front of the mirror has been flipped front-to-back and then viewed through a window where the mirror is.

The fact that it's so easy for us not to notice the difference between these two kinds of image is probably because the very first step in our visual perception mechanism involves a camera-like projection of the 3D scene in front of our eyes onto the 2D surface of our retinas. We're so completely accustomed to doing the image processing required to extract 3D measurements from our pair of retinal projections that doing the same kind of processing when we look at a flat photo comes very naturally.
posted by flabdablet at 10:13 PM on June 11 [1 favorite]

Your answer is impressively complete, flabdablet. Perhaps the only other thing worth mentioning is that our own eyes are also inverting images (much like a pinhole camera) but this is somehow 'fixed' by the brain in post-processing. So there's yet another chirality-preserving flip happening.

Also from the physics angle, it might be worth mentioning that the mirror world has different physics than our world. That is, you could tell if you were in the mirror world or not, by performing a physics experiment.
posted by vacapinta at 5:34 AM on June 12 [1 favorite]

Perhaps the only other thing worth mentioning is that our own eyes are also inverting images (much like a pinhole camera) but this is somehow 'fixed' by the brain in post-processing.

This is often remarked upon, but I don't think it's actually all that remarkable compared to the sheer amount of processing required to reconstruct a conceptual world of moving 3D objects and their relationships from of a pair of 2D retinal images. It's not at all clear that an explicit 2D inversion step would even be a necessary part of that processing.

If there were in fact a little homunculus inside my skull whose job it was to look at the images projected on my retinas and be amazed by the fact that they appear to be upside down with respect to the external world they're projected from, that would be remarkable. But as far as I know, I'm the only one in here and I don't make a practice of looking at my own retinas. I'm just happy that the wiring all seems to be mostly in working order; I don't particularly care about which way up the sensors are mounted.
posted by flabdablet at 6:03 AM on June 12 [1 favorite]

you could tell if you were in the mirror world or not, by performing a physics experiment

...except that you couldn't, because the only way to be in the mirror world would be to be of the mirror world, which would mean that you'd simply not experience the mirror world's reversed chirality as reversed. It would just be your normal.

Your experimental results would still show broken symmetry in weak interactions, but if you were comparing notes about that with a non-mirror-world experimental collaborator, both of you would swear up and down that it was you who was seeing the left-handed components of particles and the right-handed components of antiparticles participating in those weak interactions.

Possibly related: it's my considered opinion that electrical engineering is the mirror world of mathematics, and that the electrical engineer's imaginary unit j is actually not the same as the mathematician's imaginary unit i, but that in fact j = -i. Experiments designed to test this opinion have unfortunately been inconclusive to date.
posted by flabdablet at 6:12 AM on June 12

Wow! I am grateful for the depth and breath of responses… All of your responses have really picked my mind… And to be honest I'm still not sure I can grasp it...don't know why it's very hard for me. This is so elusive and intriguing to me to the point where I just can't stop thinking about it and I don't understand why I can't get it.... hmmmm
posted by bananaskin at 10:53 PM on June 12

Also it hit me by these comments, that even our own visual images that we "reconstruct "in our brains are not accurate actually either, as the images are TRANSLATED AND INTERPRETED. Fascinating. So can we ever really know for sure that what we are looking at is actually there and accurate???? Any thoughts on that?
posted by bananaskin at 10:59 PM on June 12

can we ever really know for sure that what we are looking at is actually there and accurate????

If we could, every stage magician in the world would be out of a job.

Also this.

It seems our visual processing subsystem is at least as buggy and peppered with exploitable security holes as any comparably complex engineered IT system.
posted by flabdablet at 7:40 AM on June 13

to be honest I'm still not sure I can grasp it

If you can find a way to put into words the aspect(s) you're having difficulty with, I'm sure that will help. If nothing else, it would give me a good excuse to pontificate at further length :-)
posted by flabdablet at 7:42 AM on June 13

Flabdablet, Thanks for pontificating. Honestly, I don't know why I can't grasp it or what it is about it I can't "get". I have 2 masters degrees, yet this eludes me. I guess I just can't get why this concept is so intriguing to the brain, and why the "true" image looks so weird to the owner's brain, why it looks so foreign and not like "ourself", why there is so much discomfort associated with looking at our self as the "true" image vs the mirror image.

It kind of reminds me of the story I heard on another NPR radio show the other day (can't remember the name) where the woman had her corpus callosum severed (which enables the 2 sides of the brain to communicate) and the resulting problems with the 2 sides of the brain unable to communicate with each other. I wonder if there is something like that going on here, or is it simply an issue of the emotions we attach to seeing our image in a certain manner and thinking "that's me" as we've seen many times in a mirror, but that in fact is "not" me in reality and we see/feel the incontinuity when we see a true representation.

i don't know. Any thoughts welcome.
posted by bananaskin at 1:44 PM on June 17

I guess I just can't get why this concept is so intriguing to the brain, and why the "true" image looks so weird to the owner's brain, why it looks so foreign and not like "ourself", why there is so much discomfort associated with looking at our self as the "true" image vs the mirror image.

That one, I think, is actually fairly easy. Seems to me that it comes down to a simple lack of familiarity.

We only ever get to see our own faces by using some kind of tool. The tools we use for that, in descending order of frequency, are flat mirror, photograph, "true mirror"; the first of these is far and away the most commonly used, and the last is something we'll generally only use to check out the effect rather than as a matter of course.

That means that our internal models of what our own faces look like are overwhelmingly based on what we see when we look in ordinary flat mirrors.

Human faces are only loosely symmetrical. So when we look at our own faces using a tool that presents us with a view having the opposite chirality of the view we would normally see, it just looks subtly wrong. The mole is not so much on the other side as on the wrong side. The hair is parted on the wrong side. The slightly droopier eye is on the wrong side. It just doesn't look like me. It looks like somebody impersonating me.

This is bad enough when it occurs in a photograph, but we're kind of used to photographs not being particularly good representations of the faces we see in real life and there's at least some tendency to compensate for that. Even so, most people do not like looking at their own photographs.

When we're using a "true" mirror, though, it gets really bad - because the image in the mirror, unlike the 2D projection presented by the photograph, looks super realistic: it contains the exact same amount of 3D-deriving information we'd get from looking through a window. That throws every tiny difference between what we see in the "true" mirror and our memory of what we "really" look like according to the usual flat reflection into sharp relief, causing an effect closely related to the uncanny valley. This thing that moves when I move and talks when I talk but doesn't look like me is quite strongly disconcerting.

Looking at a reflection with the wrong chirality yields, I think, some tiny inkling of what it would feel like to live with one of the various body dysmorphic disorders.
posted by flabdablet at 1:37 AM on June 18

Thanks. yeah, this makes sense. maybe that's all it really boils down to afterall.
posted by bananaskin at 2:00 PM on June 18

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