Why do mirrors flip left and right but not up and down? 

Mirrors don't flip left and right at all. When you look in a mirror, your left side is still on your left, and your right side is still on your right.

Strangely enough the thing I found most interesting (and spent the most time thinking about) was the animation you used when you were talking about the 'blobs' of professor farnsworth at around 5:50. You demonstrated reflection of a two dimensional object in a one-dimensional mirror which you showed using a three dimensional rotation around the distinguished axis. This highlights what I consider the fundamental problem to be when dealing with mirrors: people are too used to dealing with rotations. To start with: If we imagine that we were in a truly two dimensional space, 3D transformation wouldn't be possible, so we would instead have to pull the blob through itself over to the other side of the axis in order to transform the points to the correct place. (i.e. there is no single rotation or translation in two dimensions that we can use to map all the points correctly to their destinations) If instead we imagine a 2D object in a 3D space, and colour the front and back faces of the 2D object distinctly (say, blue and orange). When the object is reflected in the mirror, the colours will match up - if you stand on one side of the object, you will see the orange face of the object and the orange face also in the mirror, and vice versa for the blue side. If you were to then rotate the object around the distinguised axis onto its reflection the colours would no longer match (uh-oh) - if instead you use the 'pull it through itself' transformation, the colour parity is maintained. Imagine all 3D objects as lots of slices of 2D objects side-by-side, and all 2D mirrors as lots of lines side-by-side and you see that reflecting in 3D is exactly the same as in 2D (except replicated lots of times). (i.e. you have to pull it through itself instead of rotating it or you lose the 'colour parity'). Basically, a reflection is not a rotation, but people are used to handling rotations because it's easy to physically transform an object into a rotation of itself, but it is vastly more difficult to physically transform something into its own reflection. Apologies, this is long and possibly not articulated as well as I would have liked, but expressing reflections simply is hard without just repeating what other people have said.

note to self: never ask a mathematician to explain anything in the real world.

I don't normally like to praise but the level of professionality and fluidity in your videos is unprecedented. You present everything so simply without clutter or the minute imperfections most are unconscious to that what might otherwise be a confusing gimmick taught by most teachers instead replaces how I may have pictured the function in the first place. Bravo.

Nothing flips left or right or up or down when looked at in a mirror. Say you are wearing a tee-shirt with words on it. When you look down at your tee-shirt it is the right way around. When you look at it in the mirror they are backwards. I think of it this way. The only thing that flips is dimension perpendicular to the mirror. The words on your shirt are NOT flipping left and right. They are just moving through the mirror. Picture the letters on your tee-shirt magically floating out in front of you. You would see them flipped, but they are not flipped at all. You would just be seeing them from behind. The thing that has changed is your perspective.

I'm more confused after seeing this.

I came across your channel today, and when I looked at the titles, I went to this video first because I've seen the clip of Richard Feynman's explanation. I am overjoyed to see you referenced it straight away. I am a math ignoramus and struggled in high school with trigonometry. Some of this stuff is over my head, but your VISUAL explanations help me understand more than I did before, and your enthusiasm for the subject. Thanks for these videos.

Thank you for this very interesting and insightful lecture. I do think that one point that bears mentioning is that much "fuzziness" and confusion results from failure to make a distinction between an object and the nature of the embedding of that object in space. For example, the same person standing up normally versus standing on his head look very different, but those images are just 2 embeddings of the same object in R^3. When we compare what we see in front of a mirror to what we see in the mirror, we have to specify whether we are comparing the object to the virtual object we see depicted in the mirror or the images (imbeddings) of those objects. In order for 2 objects to be the same, we must be able to manipulate the images (imbeddings) so that they coincide. In our universe that means we can use rotations and translations. The image in a mirror is a reflection about the plane of the mirror of what is in front of the mirror, that is, the mirror reverses what we see in the dimension perpendicular to the plane of the mirror. The interesting point, which is not necessarily immediately evident, is that reflection about a plane differs from reflection about any other plane, by rotations and translations. So, on the one hand, if you are talking about images, it makes sense to say that a mirror reverses forward and back but not left and right or up and down. However, if you are talking about a specific object and the object depicted by its image in a mirror, it does not make sense to ask whether the object has left/right reversed versus up/down, etc., since there are only 2 versions of the object, the original and what you see depicted in a mirror. A person with left/right reversed is the same as a person with up/down reversed, since you can rotate them and move them around to make them coincide. Objects with some symmetry, such as people, are easier to compare with their "mirror-image" version by first lining up the objects in our minds with all the dimensions that lack symmetry, which then maximizes their similarity. Thus it is more natural to think of a person as having left and right reversed as compared to up and down.

To everybody who thinks "Mirrors don't exchange left and right, they don't exchange up and down but they do exchange front and back" is the best answer to this question, I suggest you try it on someone you know and then ask them to use this insight to explain why when you hold a piece of writing in front of a bathroom mirror left and right appear to be swapped but not up and down. I doubt you'll ever get a coherent answer. But just to mix things up a bit more consider all the different relative positions of original, mirror image and mirror (both 2d and 3d) that I consider in this video and try to use your favourite insight to have it all make sense to your victim (or yourself). Good luck :) I am not saying that the insight is not important in this context. All I am saying is that by itself it is not very useful as an explanation that people can use in a straightforward way to deal with all the different possible scenarios that can and should be considered in this context.

The way I explained mirror image to my kids is that we reference up/down relative to our *environment*, but left/right as relative to *ourselves*. As a result, when we view another person face on, we mentally rotate left and right for that person -- we "know" that their left arm is, as it were, on the opposite side of their body from our viewing perspective. This process is so ingrained by experience that when the brain sees a reflection it still automatically (and erroneously) does this rotation of left and right. This error initially goes unnoticed because of the left/right symmetry of the body. However, as soon as you (say) raise your left arm this all breaks down -- the arm that raises in the reflection is the "wrong" arm because we mentally tagged the left arm in the reflection as "right" when your brain did the erroneous rotation. So it's not the mirror that has swapped left/right, but your brain, which mistook a reflection for a rotation. When I explained it to my kids I had them hold a compass in front of them, and made them note that east/west didn't change in the reflection, only left/right.

depends on the shape of the mirror - concave curve flips on all axes - so they do flip up and down, too

Your orientation in 3D space can be represented by a 3x3 matrix. 1 0 0 0 1 0 0 0 1 A rotation by 90 degrees about the X, Y, or Z is equivalent to swapping two rows of the matrix and negating one of them, e.g., 0 0 -1 0 1 0 1 0 0 The mirror reverses front and back, which is equivalent to negating one row of the matrix. 1 0 0 0 1 0 0 0 -1 Because 90 degree axis-aligned rotations always involve 2 row operations (swaps + negations), and this matrix is different from the original by 1 operation, we can never recover the original by rotations. It has a the wrong parity for that. It is now a left-handed matrix instead of a right-handed one. However, by rotating the mirrored object, you can get the matrix -1 0 0 0 1 0 0 0 1, which is the original object with left and right flipped, or 1 0 0 0 -1 0 0 0 1, which is the original with top and bottom flipped. Thus, the mirror flipping front and back is equivalent to it flipping left and right, modulo rotation. That is, flipping an object left-to-right is the same as flipping it front-to-back and then rotating it. So, when Mathologer stands sideways to the mirror, the mirror shows a mirror-Mathologer, flipped front-to-back. But then the Mathologer turns to face the mirror, as does mirror-Mathologer, and that rotation turns mirror-Mathologer into the left-right flip of the Mathologer.

If mirrors were "flipping" the image, you would be able to read your shirt correctly. It's not flipping anything, it's just reflecting what's in front of it.

My simple 3D explanation is: When we see ourselves in the mirror we 'try to put ourselves in the position of our mirrored self'. We instinctively imagine doing that by turing 180 %, since that is how we usually move about. This movement keeps the up-down direction but flips the left-right. We could however just as well have imagined flipping forward onto our head. This would have kept the left-right direction BUT flipped the up-down. Since our bodies are left-right symmetric, this seems very wrong for us, but an up-down symmetric creature would have preferred this way! Summary, when imagining putting ourselves in the position of the mirrored self, we only think of rotating and movement (which is the only possible ways for us to move). However, a mirror operation includes an inversion along an axis, and since that is impossible to do using rotation and movement we choose the rotation that to us seems to give the most similar end result, which means keeping our head up and feet down!

The blob in turning into the prof. was the single greatest thing I have seen all day.

My explanation: A mirror doesn't flip, they form a simetric image. In the case of a 2D world, the mirror would be a simmetry axis. In the case of a 3D world (ours) the mirror would be a simmetry plane.

I always find it hard to understand how this can be a question which seems to continually need answering. The answer is "they don't". In the mirror your head is at the top, your feet are at the bottom, just like yours. Not reversed! Your right hand is on the right and your left hand is on the left (waggle your fingers to check) just like yours. Also not reversed! What else is there to say? I suppose the confusion comes from imagining a person is standing in front of you, whose right hand would be to your left because they are facing the opposite direction to you, i.e., they are turned relatively in the vertical axis through 180°. But it's a reflection in a mirror, not a person standing in front of you!

Your favorite Futurama character. I wonder why?

The mirror shows a virtual image. You see what you'd see if you stood where your virtual image stands. To move to that position, you'd have to turn round, not stand on your head. Same for the lake, but a different move. This intrigued me for a long time before I figured it out. I'm glad to know I'm not alone! Peace.

Of all your videos - this one I've been able to follow the longest. Several minutes before a full scramble. Thanks for always making great videos!

Great video, as usual! Another thing fascinated me about mirrors when I was a child was why when you look at two mirrors jointed at right angle your eyes stick to the juncture when you look at yourself, no matter where you move or at what angle you look. The explanation is actually very simple. but for a child with no education on geometry, it was a great discovery! :-) ...and it actually must work the same for every angle, not just right ones... but I haven't experience of anything different than that. and the angled mirrors don't flip the image, too! (or, actually, flip it twice)

Anybody leaving a stupid comment remember this It give's people a reflection of your personality

When I was a kid I was walking around the house with a mirror in my hands facing up and imaging myself walking on the celling....fun that was!

"Good news, everyone!"

The answer is stupidly easy. Mirrors *don't* flip left to right. They flip *front to back*. Proof: Get a piece of paper. Write on it. Hold it up to the mirror so its back is towards you so you can't see what your wrote. Behold, in the mirror, the front is towards you and you can read what you wrote. It flips back to front. Get an overhead transparency or some clear plastic. Write on it. Hold it up to the mirror. Behold! It DOESN'T flip left to right. What's on the left on your side is still on the left in the mirror. _Note: I made this comment before watching the video. Same answer from this guy. Good job, Mathologer._

I looked into the spoon like you suggested and discovered, there is no spoon!

The first really good explanation I have ever seen on this problem.

This question came to my mind about 20 years sago. I realized that mirror flips only back and front and that we confuse it with left and right because we project our left-right only symmetrical body into the world behind the mirror and wrongly match them to the mirrored body by turning it 180 degrees around vertical axes and fit left side of it into right side of the mirrored one and vice versa only because those are our only relatively symmetrical sides. We decide what is left , right, front or back only by the position of our body. We refer to gravity for up and down. If we would walk into the world behind mirror just straight forward, without turning around and adopting the point of reference of the front-back flipped body and confusing it to left-right because of symmetry, then the only flipped dimension would be front-back.

Great videos, but I find the surprise noise a bit unecessary

There is no spoon. Great video as always. Keep up the good work.

That mountain reflected in a lake is enlightening. It restores the symmetry by showing when the mirror plane is horizontal there is a vertical but not horizontal image flip, And when the mirror plane is vertical there's a horizontal but not vertical image flip.

The point where your image flips, when you look into the spoon, is the focal point. Once you increase the distance beyond that point, the features of the upper side of your face will be reflected in the lower part of the mirror (when you think of the path the light travels). The same counts for left and right, or any other axis you can think of.

Physics Girl from PBS Digital Studios had a great explanation of this a few months back.

The most confusing "explanation" I came up with many years ago is that our eyes are placed horizontally not vertically

To understand distorsion for the various reflective objects shown at the end of the video, you have to remember that a light ray bounce back to your eyes (with a few lost of power, but negligible) symmetrically to the normal of that surface. So when you look down inside a spoon, the light reflected actually comes from the top of the object because of the concave shape. Looking outside will makes you look "bigger" on the outside because of the convex shape. It's the same principle as the fisheye lens used in photography. Mr Escher did a really good work by drawing himself looking at a reflective ball. With "complex" objects, in 3D animations, you can actually use a 3D reflective map to simulate this effect without too much calculation power, our brain is not fast or smart enougth to recompose the real image from a too much distorted reflection .

This is one of those confounding things that seem obvious and easy to understand, yet are difficult to explain. This my best attempt: When light hits a mirror, as we all know, it gets bounced right back. When you look in a mirror, your left side is being bounced back to you on the left side because it IS on the left side, and likewise your right side is bouncing back to you on the right side, your eyes are bounding back at eye level, and your shirt collar appears down at shirt collar level. BUT- you are facing the mirror, yet your mirror image is facing BACK at you, in the OPPOSITE direction that you are facing.

LMFAO THE BLOB IS FARNSWORTH

I always thought they flip neither horizontal nor vertical, but front/back. "into" or "out of" the mirror

The concave side of the spoon gives you an upside-down image because the light rays cross before reaching your eye. The fact that they cross means that the concave mirror flips all three directions instead of just front to back, and because this is an odd number of flips it still looks reversed. The cylindrical mirror also has rays crossing, but only horizontally, thus it flips left to right and front to back. Two flips make a non-reversed image. If you held the cylindrical mirror turned 90 degrees you would have an image that was upside down but not reversed.

Intreguing I've never even questioned it in 40 odd years,, why is Intreguing me more so,, thanks for the flip side 😉❤️👍

Great video! Keep up the good work!!

It's flipping an Image or object on a vertical or horizontal axis.

I like your use of the mirror lake as an example of flipping on a horizontal, rather than vertical, axis. Another interesting thing to do with the bathroom mirror is to wear a shirt with lettering. Of course, looking in the mirror, it is flipped horizontally: top is top, but right is left. Now, while still wearing it, look down at your shirt directly (not through the mirror) You will see it flipped VERTICALLY relative to the mirror! Top is bottom, and right is left!

A comprehensive answer is very easy to find/understand. It flips front to back (as you would expect as that is perpendicular to the mirror). You combine that with a mental rotation in your head. You can combine a rotation and a mirror to produce any other mirror. Just like you put the CAT picture up, the text doesn't flip left to right, you are just looking at the back of it. Another good visualisation is a simple, handed glove. Take a right glove, then point it at a mirror. The object appears to be a left handed glove. To realise this, you can invert the glove front to back, which you can do by turning it inside out.

Haha , when i saw the transparent back I suddenly felt silly for thinking the mirror was "flipping" image.

I think it's simpler to explain the left-to-right but not up-to-down as a biased flip in the image. If you stand in the front of the mirror you'll see your reflection made from front to back(if you are facing north the reflection will face south), but to compare you'll have to look side-by-side, so the image will have to be turned and how the turn is made is what makes this difference. If you turn it in the vertical axis, you'll see that left and right are reversed, but up and down are not and if you turn it in the horizontal axis up and down will be reversed, but right and left won't. The bias may exist because it's acceptable to see our image reflected left-to-right, but if we turn it up-to-down the head will point down and the ground will be up, which is strange. So it's natural to prefer the turn in the vertical axis, but actually it's an arbitrary decision.

I vote this the clearest explanation I have yet heard. There is always an apparent axis of rotation, and we select it by how we compare the two images. I would like to add one more factor, that up and down are relative to the gravitational field, whereas left and right are relative to our orientation. This equating of different kinds of phenomena seems to me to be a contributing factor towards our confusion.

Excelente vídeo, muchas gracias por el excelente trabajo.

Mirrors don't "flip" anything. They reflect photons. A more accurate question would be "why does this confound human perception?"

Just curious, what is the significance of the definite integral on your t-shirt?

This is a great explanation, and I honestly never realized that there was a supposed problem until I heard people talking about it. I'm not a mathematician by any means, I guess I just didn't overthink it

Ahh I always wondered why mirrors seemed to flip top/bottom and not left/right, it's because I keep doing backflips to view the mirror. Thanks for the explanation! And now I know the proper way to view a mirror too.

in front of me: *this explanation* Me: I just asked how much for the mirror

“Go left. No, the other left!” What do you mean? There's only one left! “There are at least two lefts: yours, and mine.” Ugh.

Pointing out the axis is what really made it click for me, especially with the visual - probably the easiest way to think of it is, the axis is between yourself and the mirror. Looking from straight above, it makes perfect sense, or even looking 90 degrees straight-on at someone facing a mirror. Both of these angles clearly show the axis between the object and reflected image

At first I was tripping, but then I realize angle of incidence/reflection stuff makes it so obvious. Oh and like u mentioned the English is what makes it confusing

It seems you could have explained this a lot easier by using the directions of the light waves. Light refects off of your body or anything) in all different directions. Parts of the spectrum is absorbed and what bounces off is the variations in color and shades we see. The only thing you see is the light waves that enter your pupils which is a small fraction of the total. Joe will see only the waves that enter his eyes and Moe only sees different ones, but you still look about the same. Mirrors refect most all light rays. Think of a ball bouncing off the floor toss it down at a 30 deg. angle from perpindicular, it will bounce or reflect at a 30 deg angle from perpindicular but both the reflected direction and angle will be of opposite sign from the incident ones. Draw lines or arrows to your pupil to represent the incident and reflected light rays. As the angle changes, things can stretch (perspective) or flip a different way due to the angle. Y are not seeng the same light waves, but different ones with a different incident angle.

Now explain why I can't ever trim the back of my head without butchering it...

Pretty hard to explain this intuitively, but here goes I guess: Notice how in 7:25 As the mirror moves, the angle of both the mirror and reflection are amplified? And, the rotation the reflection experiences is always twice of the the mirror axis' rotation. So by rotating the axis around pi/4, the reflection experiences a pi/2 rotation. The gradient of the reflection's change is therefore always twice the mirror axis' change. As to why that is, well, to make it less technical, the distance between the end closest to the object shifts. The bottom left corner stays roughly the same distance from the mirror axis but the bottom right corner experiences an increase in distance from the mirror axis. Rather than view the object as a singular, it might help to plant some co-ordinates on the four corners of the objects and observe what happens when you rotate the mirror axis - At some point one of the points would get really close, to which minimal variance is observed while the points furthest from the point experience the most change. I'm not too much of a science person, but the scientific explanation should be something like the angle of incidence = angle of reflection, so the angle of incidence light rays from the object has when it hits your eyes is always going to be smaller than the angle of reflection light from the reflection hits your eyes at. The distance the light travels vs its speed is insignificant, but that distance still accounts for the angle which it reflects off of the object / enters your eyes.

I already knew why, but I'm excited to watch what you have to say about it. Plus, by coincidence I'm out with a friend to whom I have tried to explain it before, and we are about to watch it together. Let's see if it matches my expectations. I've been waiting for a new video for a long time!

Whenever I see the question given in the title of this video, I paraphrase it as "Why don't we have eyes on our feet as well?"

Mirrors don't ever flip images in the x or y axis direction. They flip images in the z axis direction (straight into/out of the mirror surface).

I thought about this question once and asked some people and none of us could really wrap our heads around why mirrors do this or SEEM to do this. Seems like this video doesn’t quite spell it out but gave enough hints that I could figure it out. Here’s my explanation or way of thinking about it.... It’s all psychological confusion based on these factors: -Our body’s left/right symmetry -The fact that the words “left” and “right” are always subjective to the person using them. -The fact that we are almost always oriented with head upwards, and look in mirrors in this orientation -Our written language (specifically it’s orientation along a horizontal line, i.e., a left/ right axis. So to explain a bit more. The apparent left right flip that a mirror performs only happens with anthropomorphic figures (people-shaped things) and with words. Other objects and images do not cause as much confusion. Let’s take ourselves looking in the mirror as the first example. Both our head and our reflection’s head are upwards-therefore it does not seem that the mirror flips us top to bottom, but our right hand seems to be our reflection’s left hand, so it seems it has flipped us left to right. BUT it only seems this way because 1) We mentally flipped ourselves to be standing in our reflection’s shoes and then imagine which hand we are waving around. So the mirror did not flip us, we mentally flipped ourselves. 2) Left and right are subjective to a human’s bodily orientation and have no objective meaning. This is the reason if you are facing someone (I.e, facing opposite directions and you tell them to pick up the ball on the right side, they will ask, “my right side or your right side?” So in this respect the video is a bit disingenuous in the beginning when he shows the “left” and “right” hands with different colored circles. That was a visual effect added to the video, whereas if you actually hold a red and yellow circle in your hands, and look in a mirror the same colors will directly correspond (no flipping). Unlike left and right, East and West have a more objective meaning, so if you hold a compass rose upright in a mirror with the East and West arrows oriented to the magnetic East and West, the arrows will be pointing In the correct direction both on the real object and in the reflected image. The other thing that makes it seem like mirrors flip things left and right is written words...because we are all familiar with seeing words on our shirt appear backwards in the reflection in the mirror. This has to do with the fact that our written language has a specific left/right (and top/down) orientation, and the words are always adjusted to be properly oriented to the body of the person reading them: if the words are sideways or upside down, we turn the book until they are oriented to our vantage point. The word on our shirt seems backwards to us because we are wearing it backwards. We wears shirts so people facing us can read them, not ourselves. If we took off our shirt and held it up in front of us with the front still facing forward, the word is backwards to us (we just don’t see it as such because we can’t see through the back of the shirt). The video demonstrated this well with the word on the clear surface. Again if we visualize a different scenario without a forwards/backwards bias (another subjective idea) it becomes much more clear that the mirror is not flipping anything. To us, arrows don’t have a specific proper orientation like words do, so it doesn’t make sense to ask if an arrow is forwards or backwards like with words. Try this: visualize, (or actually) cut an arrow out of a piece of cardboard. Then hold it up in front of you while facing a mirror. Now, ask yourself, which way the arrow is pointing: up, down, “left” or “right” it is pointing the same way both in physical reality, and in the reflected image. (Just don’t ask the dude or lady in the mirror which way their arrow is pointing, and it won’t be confusing). Problem solved! I hope that makes things more clear for some. But what about the image of the mountain flipping upside down in the lake? That is a different situation. Everything I described here and the main focus of this video only holds true when the plane of the mirror and the plane of the object being reflected are parallel. (that's why this is easier to discuss and imagine with 2D images, since 3D objects don't always have an obvious planar aspect to them. Words do since they are generally printed on 2D planes, and our body can be thought of as slightly planer in so far as we have a clear front and back with narrower sides. As the video and other commenters pointed out, mirrors only flip images in a front /back orientation. So if a mountain, person, word, or arrow is oriented perpendicular to the plane of the mirror (pointing at the mirror), then the image actually does flip in a truer sense, but that’s a slightly different topic. That's another way this video is slightly misleading in the beginning, because when he has himself and his mirror image they are both in the same plane facing the same direction, so the only way that this could be a mirror image from a real mirror is if he was standing with his shoulder toward the mirror, in which case the text on his shirt and his left right hands ACTUALLY are flipped left to right. Haha. Kind of muddies the waters a bit. If you want to flip it top to bottom, put the mirror on the ceiling above his head. It's all about how you orient the plane of the mirror to the plane of the body and words. So I think I understand the mystery of mirror reflection geometry, so now the real question I want answered is, if you chant the name Bloody Mary a hundred times into a candlelit mirror with a group of people, will you see her? I’m too scared to try.

the observer is a point which defined the dimensions of up, down, left, right, forward, and backward prior to engaging in inductive and deductive reasoning while choosing to only observe light traveling toward the observer with the primary focus along a single line and with secondary focus radiating outward from the line of sight. the mirror is a two dimensional object outside of and apart from the observer which manipulates light travelling along other lines of sight not originally directed at the observer. therefore, all observations of the alternate lines of sight are relative to the decision by the observer to define up, down, left, right, forward, and backward prior to engaging in observation.

when u do a head stand why does everything look upside down?

Because we put the mirrors up side down!

The mirror's flip along the axis normal to its plane (green arrow) explains the apparent left-right exchange on your image when looking into the mirror. It is because the way that we identify left and right on a person is relative to their front/back direction. When you reverse front/back, as the mirror does, then it also reverses the left/right sense that we assign to the image. Another way to visualize this: Pretend the mirror image is just a 3D contour surface, rather than a solid 3D object. Then take the mirror image and as though it were a cast plastic sheet, punch the center through so the relief goes in the other direction. That is, the nose for example will be pointing away from you instead of towards you, when you are done. Now which hand do you call the right hand in this axially-reversed image? It has reversed from what it was before, because that left/right assignment depends on which way you see the front/back axis running. In the other case, with the vertically reversed mountain landscape seen on the lake's surface, this is simply explained again by the fact that the mirror reverses the axis normal to its plane. The mirror is horizontal, so it reverses the vertical direction.

In our frame of reference, up and down are absolute. Left and right are relative to the observer. Your mirror image is also facing the opposite direction that you are.

9:34 haha, he said doodoo

Angle of light = angle of reflection.

Really nice video. I have a trapezoidal prism that is very interesting. When you look through it with the base at the bottom (and parallel to the horizontal plane), the image is right side up. If you rotate the prism 90 degrees, the image rotates 180 degrees. When the prism is rotated another 90 degrees (it is now up side down) the image is again right side up.

At the end of this vid, rather than a cylindrical mirror, which distorts by an amount that depends on its curvature and your distance from it, why not use a right-angle mirror? - two flat mirrors attached at a right angle. The image in that, amounts to a rotation around the line of intersection of the two flats, by 180º. So if you place it with the intersection line vertical, it rotates your image 180º around a vertical axis. If you place it with the intersection line in some other direction, then that will become the axis of the 180º rotation. This is part of a general property of any double-reflection; that it is equivalent to a rotation about the intersection line of the two flats, through twice the angle between the flats. (The sense of that equivalent rotation, depends on which mirror gets the first reflection, except for the 90º mirror-angle case, because the sense of a 180º rotation doesn't matter.) This in turn, can be used to show that any composition of axial rotations in 3D, is another axial rotation! Cute, eh?!

It’s not flipped it is an exact image of what’s in front of it!

Good news everyone!

This conundrum is multi-layered and deeper than it seems. It takes time and effort to understand it better. There are aspects of the problem that were barely touched upon in this video, if at all, both on mental and mathematical side. But it was a pretty good explanation. One important thing is that mirror reflection (in relation to 2D plane = reversing 1D) and point reflection (in relation to 0D = reversing 3D) are homologous in 3D, in the sense that they both inverse orientation. Thus the position of the plane of reflection is sort of irrelevant. Second crucial thing is that we are not evolutionarily adapted to see mirror images and so we has no option but to see a reflection of a familiar thing as it was a rotation. Which is false, but goes unnoticed due to the nearly perfect plane symmetry of (the surface of) human/animal body.

The way I figured about the Mountain Image and a Bathroom Mirror is it depends on the orientation of the mirror placement . If the mirror, (or lake), is laying down in front of the object you are seeing the light of the object coming from behind the mirror as it is reflected off the mirror )or the lake) which the results in flipping it top to bottom. Where as in the case of standing in front of the mirror it is reflected back to you showing the reverse image as you describe with the cat demonstration.

My difficulty from this question was the startling implication that it brought up: Why does the "universe" choose to flip along the vertical axis and not the horizontal? Is it just that we humans only notice flips in that axis but not the other? No, that is not the answer! In fact, we humans are very smart indeed and we are very capable of detecting flips no matter which axis is chosen thank you very much. From our perspective, it actually IS flipped horizontally but not vertically. But I now hear you ask: "Shouldn't it flip on either both or neither axes? Who decided which axis to flip? Was it God? Was it the universe (which you might ask if you're an atheist). The answer to both of these is an emphatic no! It was you that decided to flip on the vertical axis (silly you), and I'll now explain how you did that: Imagine that there is a mirror behind you and your friend (let's call him Rodger) in front of you. Rodger says that he likes the image on your shirt (your shirt has a picture of a T-Rex with laser beams attached to it's head). You say "darn it, I wish I could see how it looks on me." Rodger says, "there is a mirror behind you and you should take a look." At this point you think "I really want to see this EXACTLY the way that Rodger sees it." You turn around normally (along the vertical axis) but Rodger (who can look past you at the mirror) says "No, this is wrong, the T-Rex is facing right now, but he was facing left when you were looking at me." So you turn back to Rodger and start thinking. You decide to do a handstand (rotating along the horizontal axis that is parallel to the mirror) and look back at the mirror that way. "The T-Rex is facing left!" shouts Rodger, "We've succeeded in... oh wait, it's upside down now." This means that the T-Rex has now been flipped in the horizontal axis. I hope you can see now that it is impossible to ever see the EXACT image that Rodger saw by using a mirror. In order to look at the mirror (which will show you looking in the direction that Rodger originally saw you), you need to chose an axis to flip around. Which ever axis you choose, the image (from Rodgers perspective) will also be flipped. This means that it is not the universe that is doing this, it is you. It should be noted that when you did the handstand, you would have a 180 degree rotation to what Rodger saw, thus, you would still see the flip along the vertical axis. However, this is just because you happen to be upside-down at the time. In problems like this, you need to take the perspective of an impartial third-person (Rodger). So the real solution here is that it has to be flipped one way (It just so happens that which ever axis we choose to flip around, our head is also oriented accordingly, such that we humans, will only ever see the image flipped along the vertical. Hope this helped!

Anybody recognize the (very famous) cat in the logo?

by the way, i love this piece, specifically for the questioning of the very terms we reason about the reality with. this is truly challenging in every aspect. still there is room to explain the nature of the bias: why do we imagine this "left-right flip".

Looked away for a second and you were upside down so I flipped my phone over, immediately kicked myself

10:19 Sorry. I cannot take as self evident that you are a 3D object.

11:17 Aww, chibi Farnsworth is the cutest!

A mirror matches you perfectly. The line running from each point of your body to its reflection is perpendicular to the mirror. It's the eyes of someone looking at you that are flipping left to right relative to your eyes because they have done 180 degree turn in the horizontal plane. They don't do 180 degree turn in the vertical plane except in a Spider-man, position, although one example of a vertical eye flip is playing a guitar and looking down at the fret board. The bass E string should be at the "bottom" of what you see but if you watch yourself play in a mirror it will be at the top. This is why guitar tablature is written "upside down" compared to what string is closest to the ground when playing a guitar.

Just started the video - got my pen ready, no paper ready, complete with squares - so I can confirm that all said boxes are ticked in relation to how I feel your answers and investigations come across as to why, and why not a mirror can flip your reflection one way, yet not in the other. *tap* *tap* *tap* *whirls pen in the air towards the paper* *PLAY*

I don't really get the problem people are having with this...

I think the whole question of "why do mirrors flip an image" came from non-physics people trying to think scientifically. LOL As you scan the mirror, your eyes are simply receiving photons that have been reflected at a distinct angle that happens to hit your eyes. As you scan side to side, and up-down, you are changing this angle from which these photons arrive. These photons are just a tiny points of light. Points are dimensionless, they have no up, down, left, or right. How can you flip a point? When you observe any particular point on the mirror image, you are merely viewing the path at which those photons traveled to hit your eye after reflecting off the mirror plane. It's all perspective. The perspective of viewing the mountain reflecting "up and down" on the lake is not the same perspective as you looking at yourself in the mirror. But you can still imagine the light rays from the real mountain top traveling down to the lake at a certain angle and then bouncing up to your eye at that exact same angle. When you understand a little bit of the physics of how optics works, you become aware of something even more profound: your eyes only detect those photons that reflected off the mirror plane in the exact point and angle that will hit your eye. Many many more photons whizzed by your eyes completely undetected. And in fact, someone standing next to you looking at the same image is actually viewing completely different photons reflected at a slightly different angle, than the photons you are seeing.

I spotted Professor Farnsworth as the blob. Very happy you confirmed, as I wondered if I had the energy to go look at pictures to compare, before you did. :)

When I saw the thumbnail of the video, but before I watched it, I tried to figure the problem out, and came up with something like the transparent cat explanation. I used a non isosceles right triangle with the shorter sides vertical and horizontal. I, in my mind, stood in front of a mirror and held the triangle up in front of me. I see the triangle, and its image in the mirror, not flipped in any way. Of course, that's not normally how we'd think of looking at the triangle and then at its image in the mirror. So, I placed myself on the edge of a turntable, with the triangle at the center of the turntable, and rotate around 180 degrees. If the axis of rotation is vertical, then I see the triangle flipped left-right from my original vantage. If the axis of rotation is left-right, then the flip is vertical. Et cetera, for all axes of rotation that bring me to the other side of the triangle. Hence, it's a matter of my choice of how to come around to see the other side of the triangle. The reflection of the mountain is a different thing. In the above, I'm looking at the mirror perpendicularly, and thus I'm seeing the triangle in the mirror as though seen from behind. With the mountain, the mirror has been placed horizontally (the surface of the lake), and I'm looking at it nearly edgewise. Thus, I've rotated from seeing the mirror perpendicularly (the lake from above, if sufficiently reflective) by a left-right axis of rotation to seeing it nearly from the side. Again, it's the axis by which I've rotated from perpendicular to the mirror that determines the flip. To see the mountain's image looking perpendicular to the mirror, I'd have to have the mountain between me and the mirror, with the mirror perpendicular to me. (Or, the mountain behind me, but then I couldn't see both it and the reflection, so I'll choose the mountain to be between me and the mirror.) And so again, like the triangle, I'd be seeing the mountain from behind in the perpendicular mirror. Well, I'd actually be seeing the back side of the mountain, so I'd really need the mountain to be partly transparent, so that all of the mountain except the mirror side is transparent, and just the mirror side surface is opaque, with the colors that it has seen from the mirror side. Thus, seeing oneself in the mirror is like seeing oneself from behind, in this curious part transparent way. And in this way, seeing the flip as a flip from back to front makes a bit of sense, maybe.

i found an answer to the question!!! why do mirrors "flip" left-right? because GRAVITY!

The 3-chord into is the the same as the intro to Kate Bush's 'Babushka'. Mmmm. Kate Bush.

I'd say what happens is that by flipping one axis (front-back only), the mirror effectively changes the "handedness" of the axis system, and that's what affects us, because no matter how much we try to rotate the image in our heads we can never overlap it with the real thing.

I think that in the case of the "forward-backward" explanation that: 1) a flip of a 3d object on an axis plus a rotation is equal to a flip of the same 3d object on another axis that depends on both the first axis and the rotation. 2) when we compare the texts on the shirts that are aligned with the horizontal axis of the mirror, we mentally rotate the 3d body to be able to look at both texts on the t shirt at the same time. So we could say based on 1 and 2 that the "forward -backwards" flipping equals a left - right flipping plus a rotation of 180 degrees on the vertical axis.

There is nothing flip in the mirror. It's just a stamp of the things in the real world.

Does this actually need an explanation? Why in heavens name would the mirror flip the image up and down as well? Overthinking this a little I think.

What makes this mirror problem fundamentally difficult to relate to is that when we roll our heads left and right, our brains account for this and "roll back". Pick up an object and compare what happens when you turn your head and keep the object still, versus what happens when you keep your head still and turn the object. When you turn your head everything remains the same, but when you turn the object it rotates as you'd expect it to, even though geometry says that there shouldn't be any difference between the two. It makes me wonder what it's like to be an astronaut.

Haven't watched the video, but a mirror image really inverts you on the plane of the mirror. Your up is up in the mirror, your left is left in the mirror, and your down is down in the mirror.

wonderful graphic work on this one

Moving the mirror around the word CAT was a good demonstration of why the mountain is flipped top to bottom while a vertical mirror flips left to right. You can basically see the axis rotating around.

OK, before watching this, here's my own view. What a (plane) mirror actually does, is to reverse front-back, as determined by the plane of the mirror. Then, in our attempt to reconcile the image with the reality, we subconsciously imagine how the image can be returned to coincide with the real scene. This could geometrically be done by choosing any line contained in the mirror-plane as an axis, rotate 180º about that axis, then reflect in a plane that's perpendicular to the mirror-plane and passes through that axis. But owing to our own body's bilateral symmetry, and our deep consciousness of that fact, we automatically choose a vertical line as that axis. It is then that final, mental reflection that we perceive as the action of the mirror - a left-right reversal. Fred

It doesn't flip the image left/right (x-axis). However, you could say that the flip is taking place on the z-axis, because the image flips in depth of the 3rd dimension ("inside out") to a mirrored copy!