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

[@seymourwang1788]

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.

[@Mathologer]

Thank you for the compliment :)

[@jsmunroe]

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.

[@SgtSupaman]

+Jordan Munroe You are right, it is about perspective. I do want to correct one thing about your statement, though. When you look down at your t-shirt, the words are not the right way around. Your mind perceives it as being right, because you know how it should be to look right to other people, but when you look down at it, it is upside down. Just thinking one should be literal when talking about perspective.

[@jsmunroe]

+SgtSupaman I was aware of that. The words would be upside down. I didn't want to confuse the scenario. That fact was superfluous to my explanation.

[@SgtSupaman]

I just think it is interesting to note, because from your perspective, the mirror does indeed flip the words vertically as well as horizontally.

[@jsmunroe]

Interesting point.

[@thinkdunson]

when talking about a 2D image, yes you can say you're just seeing them from behind, but with a 3D object, it doesn't work. when i look at you from behind, i don't see your face reversed, i see the back of your head. so the mirror IS reversing the image. the best explanation, for me, is that the image will appear flipped on an axis perpendicular to the angle of incidence between the viewer and the object being reflected.

[@CJdude22]

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.

[@generalthl8078]

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.

[@Mathologer]

+generalthl Pretty much agree with everything you said here. My main aim in this video was to come up with an explanation that fits in with how most people tend to think about things and I ended up reducing everything down to the consideration of 2d objects which really makes things a lot easier. As I said there are lots of possible ways of explaining all this. What I've chosen for this video is just one (but one that I hope you won't find anywhere else this complete). Also, not sure whether you know this already, but a reflection of an n-dimensional object through an (n-1)-dimensional hyperplane can always be represented as a rotation in (n+1)-dimensional space. So a 2d reflection through a line (1d) can be represented by a rotation in 3-dimensional space (what I do a lot in this video) and a reflection of a 3-dimensional object in a 2-dimensional mirror can be represented by a rotation in 4-dimensional space (I talk about a bit in the videos on Klein bottles and Rubik's cubes :)

[@generalthl8078]

+Mathologer "a reflection of an n-dimensional object through an (n-1)-dimensional hyperplane can always be represented as a rotation in (n+1)-dimensional space." - I was actually wondering about this when I was writing the comment, so thanks for clearing that up for me! :D Thanks for the video, it really got me thinking.

[@Mathologer]

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.

[@thomsonandfrench4974]

All I can think of is that left and right >should< be flipped if you exchange front and back. The reason for this is that when someone turns to face you he/she rotates his/her body 180 degrees, and so the details rotate around him/her and ends up on the opposite side.

[@senshi01]

If I think of it digitally. Let's say I'm on paint and mirror an image. All the program si doing is inverting left and right. However, the only thing that cause me to think mirrors swap front and back is that I am opposing the mirror. So, if I take a picture of me pointing to the camera, mirroring it digitally will flip left and right, but if I put it in 3d the original image in front of its mirror, it will flip front and back.

[@senshi01]

in other words, if mirrors would "flip front and back", standing in front of a mirror, if you point at the mirror, you would see your back pointing in the same direction as you.

[@senshi01]

But, if you create a 3d human pointing in a direction, and inverse the z direction, it will make a mirror image too!!!

[@APromisePast]

It's actually quite simple to explain- you explained it yourself with the CAT example. The text "appears backward" because, from YOUR perspective (Not the mirror's!) It already IS backwards. Take off the shirt, don't turn it around, and hold it up to a light so you can see the text through the shirt, and it's backwards! The issue is that humans aren't used to SEEING THEMSELVES. They see a shirt on the rack, see the text, and ROTATE THE SHIRT to put it on facing the other direction! The text appears backwards because, you have already rotated it- but the fact that you already know what the shirt says and have already seen it forward earlier tricks you into thinking that you should be seeing it from the other way around.

[@cwldoc4958]

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.

[@mkevilempire]

I was going to comment "it's a trick question", but I think you summed it up much shorter than I could.. 🙃 Seriously though, this comment explains the problem maybe even better than the actual video, thanks.

[@timhill9039]

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.

[@Otacatapetl]

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.

[@Stratelier]

But it appears on the mirror version's "right side" because "right" is defined as 90 degrees clockwise from whatever direction the subject is facing. Since your mirror image is facing the opposite direction you are, its right is on your left, the same as it would be looking at any other person facing you.

[@GODemon13]

Exactly. Also, in so much as one might say it "flips", it will do it in any direction that you hold it. So this video is doubly wrong.

[@GODemon13]

This comment was to Otacataspetl, not Hugh Jones.

[@GODemon13]

@Hugh Jones How come when you stand facing somebody, their left is your right and their right is your left, but your top is not their bottom and vice versa? It has NOTHING to do with mirrors.

[@GODemon13]

On the other hand, a concave mirror does flip the image upside down. Such as a spoon.

[@Psycandy]

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

[@jandroid33]

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!

[@Mathologer]

+jandroid33 Yes, nothing wrong with this explanation. However, in my books it's not a complete explanation as it is too people centered whereas all of this also has to work for 3-d and 2-d blobs and different relative positions of mirror, original and reflection :)

[@jandroid33]

Mathologer Well of course the explanation is people centered. We are people right? :-) I think the thing you miss in your explanation is highlighting that the mirror operation can not be achieved by rotation and translation. At around 8:30 you talk about "put it next to the mirror image", the "put" for us humans means use rotation/translation because we can not perform an axis reversal of objects. So our explanations have to be people centered, because we are using operations that are achievable by people in the real world.

[@locutusdborg126]

How would an animal see its reflection? And what about an inanimate detector? That would remove the human neural bias.

[@jandroid33]

You are still using your brain to visualize the animal or the inanimate detector when you talk about it? I'm just trying to answer why this problem seems hard for us. The answer to why we think this is a bit complicated question is of course dependent on our selves, our inexperience of the mirroring operation. :-)

[@Stumdra]

Mirroring back to front can be understood as a compositon of a rotation of 180° along the z-axis composed with a mirroring left to right. Written in a (pseudo) formula it would be: M_y = R_180°;z ∘ M_x with a reflection M and a rotation R. Here the composition of a reflection through a plane and a rotation is just a reflection through another plane. Just like jandroid33 explained, the rotation is made automatically in our head and all there is seemingly left is the reflection left to right. Mirroring back to front could also be achieved by rotating 180° along the x-axis and then flipping up and down: M_y = R_180°;x ∘ M_z . So if we somehow could bring our brains to think the right way to 'adjust' image and mirror image is to rotate ourselves along the x-axis (right always staying right instead of up always staying up) we would perceive it as flipping up and down.

[@WarmongerGandhi]

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.

[@david21686]

"Your orientation in 3D space can be represented by a 3x3 matrix." "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.," I don't understand this at all. Please explain.

[@kevycatminecraftmore7721]

I know some about matrices, but... WHAT ON EARTH IS THE MESS OF NUMBERS?!?!?!?!?!?!?!?!?!?

[@danielfogli1760]

This! ;-) (thanks)

[@elyelyely]

I understood, but I feel the Matrices are unnecessary

[@nomadbakunin]

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!

[@WhompingWalrus]

I feel ya bro. Took me a couple watches, but we got there lol.

[@benbuckley2216]

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

[@attilakiss3786]

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

[@finnjacobsen684]

I'm more confused after seeing this.

[@johnnysparks44]

i can't let That fool confuse me.. it's too easy... The guy can't fix Fukushima so... might as well let His ass Explore simple shit.... Math must cause Delusional Behavior... concave being the same as convex in His Math.... How can He Produce Vector... without some Dot. two lines and no curve He can Reproduce with Irrational Numbers HA ha hahahahaaaaa… i can make an arch from a circle in a Heart Beat with a compass... in any Form and for any function. Geometry actually works well... it's a language issue in application of dichotomy... words are considered equations of Numbers... i guess... might as well just use colloquial Gibberish. why Hide Those Equations in Numbers anyway... mixing Latin and Greek is kinda confusing for normal People... even quarks are defined by Vector... or polarity... Smart Gravity i mean... it can be confusing just listening to them... what Unified Theory? right. They started Nuclear reactions and can't even stop one... That ain't Genius material. Moron is closer. Wonder what makes him think we need a Mirror Defined... it is Pretty Basic stuff... if we go Extinct we don't even Need Mirrors right not... maybe HE DOESN'T KNOW

[@keepingupwiththejoneses746]

sparks don't need youtube either, but here you are. You aren't as worried about the problem as you'd like to sound. Stop trolling the comments. If you don't care, walk away.

[@nonchip]

tl;dr: because you're looking straight at your bathroom mirror, it doesn't actually flip you, you're just standing the other way around when compared to a camera facing you. but when the angle changes (like with the lake) you have to take into account the way reflection works -> things further away from the mirror (such as the mountain peak) appear even further (at the bottom)

[@coreycox2345]

I am precisely as confused as I was before watching. It is a good question, though, Finn Jacobsen. I was hoping to find the answer.

[@johnnysparks44]

i Think Everybody's Crazy but Me... could it even Be a Possibility? H ah ahha h sss can we at least agree on Reciprocity

[@vblake530530]

Your favorite Futurama character. I wonder why?

[@psionic0]

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)

[@davidstokes8147]

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!

[@ruben307]

exactly the difference of a reflection looking at you and a person standing in front of you is that the axis is flipped. Which hides the real work of the mirror by only noticing that change.

[@mijnkampvuur]

Nicely explained!

[@cr1216]

I find this more plausible than the video itself...

[@dbz288]

Ruben So does that mean that the way we see ourselves in the mirror is the same way people see us? So the mirror is true? Or the camera? Cause when I take a selife of myself, my face looks backwards and it flips but the MIRROW isn't backwards and I like the way I look in the mirror. So does that mean that my face isn't backwards or flipped when looking at myself in the mirror? :)

[@dbz288]

David Stokes So does that mean that the way we see ourselves in the mirror is the same way people see us? So the mirror is true? Or the camera? Cause when I take a selife of myself, my face looks backwards and it flips but the MIRROW isn't backwards and I like the way I look in the mirror. So does that mean that my face isn't backwards or flipped when looking at myself in the mirror? :)

[@paulg444]

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

[@freedom4life123]

maths ARE the real world

[@freedom4life123]

@vince pie 3,6,9 Tesla

[@johnnysparks44]

so what color is our sky... it can't be Blue... right on... all were looking at is Reflections.

[@user-hy7cq9vi4h]

@@johnnysparks44 lmao

[@khajiithadwares2263]

Never understood why Math-people always want to overcomplicate things, create questions instead of give answers. Maths supposed to be generalistic and abstract, not convoluted. At the end of the day, even the numbers themselves are interpretable, the same way any language is. 5 inch =/= 5 feet =/= 5 meters. Gimme 5. Faif wha? Five.

[@neilterry1726]

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.

[@Amateur0Visionary]

As used in most of this video, "to flip" and "to reflect" are generally synonymous.

[@totheknee]

It flips the z-axis whether you want to admit it or not.

[@williambarnes5023]

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._

[@irrelevant_noob]

William Barnes ... umm... "the front is towards you and you can read what you wrote" -- not unless you can read right-to-left and recognize the flipped graphemes of what you wrote on that paper...

[@irrelevant_noob]

Also, the "Hold it up to the mirror so its back is towards you" part is ambiguous. Because if i flip it along its LONGER side to turn it towards the mirror, then it will still appear flipped, but not left-to-right... :-B

[@jursamaj]

​@@irrelevant_noob You've answered your own question: whether you flip the paper vertically, horizontally, or at any other angle, it is *you* flipping the paper, not the mirror.

[@irrelevant_noob]

jursamaj then can you please teach me how to follow William's instruction of "Hold it up to the mirror so its back is towards you" without flipping the paper? -.-

[@jursamaj]

@@irrelevant_noob You can't, that's kind of the point. Any way you flip it to present it to the mirror, the reflection will be flipped *that* way because *you* flipped it that way. Either way, it wasn't the *mirror* that flipped it.

[@Catlord98765]

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

[@domi_2164]

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!

[@mewan1708]

Shit I did that too bruv

[@allahspreadshate6486]

I did that too. Haven't thought about it in years... Thanks for the reminder. :D

[@LiborTinka]

Thanks for confirming I was not a weirdo :D Did just that...

[@ulysses4536]

Yeah, and I also found out that doors were very poorly designed for someone walking the ceiling.

[@SKyrim190]

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

[@codediporpal]

+Luiz Sarchis Haha try it with headphones. The previous video gave me a few good scares lol.

[@Mathologer]

+codediporpal I actually tried to be a bit gentler on the ears with the Prof. Farnsworth jingle :)

[@gerstensaft2936]

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

[@Mathologer]

+Gerstensaft There is no spoon? What happened to it? :)

[@stefanpanescu5683]

I see what you did there. :D #Matrix

[@tazanteflight8670]

@10:10 I dont know if you realize this, but the green arrow is the "normal" of the mirror. This gets flipped. The end. No mystery. Left stays on the left, top stays on the top. Whats the mystery? If you walk into the mirror, your left arm is going to hit the image of the left arm. What else would you expect !!!? The left to hit the image of the right ?!?!?!?!

[@aaronmicalowe]

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

[@s.a.morris8625]

...lol....pretty cool how concave, convex, flat, and wavy surfaces reflect differently...

[@Mindraker1]

> there is no spoon! Damn, beat me to it.

[@appenginenode]

How did you look into said spoon if said spoon is a no. This is incredible - may I suggest a video on said subject to enlighten and entertain the amateur mathologers in the world. I, for one, would have my pen and paper ready to tick some boxes of said representational results.

[@wjckc79]

@@appenginenode The spoon is no more real than anything else in the video. The video is just 1's, 0's and Boolean algebra. Hence the spoon you see is not the real spoon.

[@wjckc79]

@@appenginenode Also, it was a Matrix reference.

[@agiar2000]

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!

[@Sam_on_YouTube]

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

[@Mathologer]

+Sam Yes, I liked that one too, but found it got a bit confusing after stating the main message :)

[@harishramar]

😂😂

[@FirebrandFA]

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.

[@Mathologer]

+Orlando Semperfire Exactly right :)

[@zedwms]

"Good news, everyone!"

[@princeharris2660]

LOLOL

[@Wescola]

Bring back the blood.

[@johnnysparks44]

@@Wescola Ha ha h ah a Really.... i like to Eat what i Kill ok. no rules apply to me... other than Mine... i don't Have but one... Do unto others.... you want Blood ok... Bring it... Then Deal with yo own Desire... you want Blood oK… Deal with it.

[@gprime204]

“You’re reading this in the sound of my voice”

[@palamud]

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.

[@jhanks2012]

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

[@Mathologer]

+jhanks2012 I talk about the front to back business at the end of the video. You can definitely base a complete explanation on this insight but every time I have seen people attempt it they tie themselves into a knot because among other things the little problems that my friend Prof Farnsworth highlights at the end of the video :)

[@jhanks2012]

+Mathologer forgive me for commenting b4 completing ur video :) it's always made sense to me this way. similarly to a rear-view mirror things on left are still on your left, etc yet the direction is reversed , thereby a car making a left turn looks in your mirror as one would look making a right turn in your direct view.

[@deserdoo]

me too

[@chrispi314]

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 .

[@Mathologer]

+Chris Pi Exactly, right. Specifically, if we consider this soup ladle mirror as part of a sphere (ideally) then what you see depends on the distance of your eye's reflection in the mirror (greater, equal, or less than the radius of the sphere/taking the concave view as positive and the convex as negative :)

[@alexsantee]

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.

[@alexsantee]

I'm not really sure about this case, but here is my try. For the concave mirror those images should be analysed separatedly because they are formed differently(if you are between the vertex and the focus the image is formed from extending the light rays and if you are away from the focus it's formed from the rays really intersecting). In the first case the explanation is pretty much the same as the plane mirror In the second the image is reflected twice, both front-to-back and up-to-down, so it is equal to the original object, but a rotated version. The up-to-down reflection, however, is biased and depends on the position of the object: If it's placed vertically there will be a up-to-down reflection and if it's placed horizontally, there will be a left-to-right reflection.

[@SacredGeometryWeb]

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.

[@gregorymorse8423]

So by your logic mirrors stop working in weightlessness e.g. in space which is not true. So that explanation is lacking.

[@devandestudios128]

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

[@dude65535]

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.

[@hornbeakdarien]

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

[@1959Edsel]

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.

[@aidanhschofield]

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

[@good_one_raggy]

Makes no difference

[@pereraddison932]

theanaesthetist1 ... it would, if verticularly oriented eyeballs were opposedly set upside down, viewing sideways inside out from behind. Then, the brain would be perceiving reality as literally virtually false... ooooo... I'm good ... knot

[@pereraddison932]

Mitch Batten ... is ? ...

[@mikenumpty9366]

Simple explanation is where the image is mirrored as shown by the mountain and it's reflection in the lake. If the mirror was above his head or by his feet then the reflection will be flipped vertically

[@chrism546]

I actually agree with this. If you turn (only)your head 90 degrees then what was 'up and down' becomes your left and right. Also a mirror image doesn't change, from your perspective, if you rotate your head and the image together. Third if you rotate only the image 90 degrees, that changes what gets flipped in the mirror because something different in the image is on Your left and right. And it all has to do with our eyes being on the left and right sides of our faces. If our eyes were positioned one above the other then reflected images would appear flipped vertically.....For a real brain itch, rotate text 180 degrees and look at it in the mirror. The reflected text will be upside down but 'correctly' oriented left to right.

[@t.c.bramblett617]

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

[@TheRealTenTigers]

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

[@toogsintheteeth]

I agree. Just follow the straight lines photons follow. The only change is upon the contact with the mirror (reflection).

[@lavamatstudios]

I like this. Maybe our perception is just inherently, irresolvably confused, and the only thing we can do is try to explain _why_ this is. Like, what if there's a Kantian antinomy of flippery we're not aware of and we're just bumping into the limits of reason itself? This needs further investigation.

[@shambosaha9727]

Some random weirdo will now come and call you a nerd

[@shambosaha9727]

@꧁༒ⱤɨCʞƔ༒꧂ Thank you

[@sillysad3198]

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".

[@tonyhoable]

We don't "imagine" anything. We see the exact thing that we should see

[@mrping2603]

Great video! Keep up the good work!!

[@Mathologer]

+Michael Furtado Glad you like it, considering the simple question it is about this video was actually surprisingly hard to put together :)

[@2jonathandane]

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.

[@Nathanchooper]

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!

[@kittybeans8192]

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.

[@Dana5775]

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

[@A-Milkdromeda-Laniakea-Hominid]

Physics girl did a great demo by showing the mirror a left handed glove, then flipping it in the Z axis (turning it inside out) which then became a right handed glove! Perfect analogy.

[@BillM1960]

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.

[@BillM1960]

I should add the x component of the direction or velocity has the same sign, but the y component reverses sign.

[@Mathologer]

While all this is great, in my experience nothing like this work as an explanation for people who are actually confused by this questions. Also, most explanations that people actually are satisfied with really only explain a tiny speck of this mess :)

[@BillM1960]

Mathologer: The flip is in the direction of the mirror with respect to the waves (photons) that hit it from the object and are bounced back to your eye. The flip appears left and right, but is not. I get that when you raise your right had the image raises it's left and words read backward, but point at the mirror and it points back at you. That is the flip. You are turning the image inside out but only in one direction. Proving this is just drawing lines. Turn your shirt inside out and it will read backwards. Maybe you are right about convincing people, but it is just drawing lines. I like your videos, just trying to offer what seems to be a simpler explaination.

[@Mathologer]

Sure, no problem at all.

[@abstractapproach634]

mirror mathologer, best guest ever, need more of him. you do risk getting showed up though

[@ulilulable]

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?"

[@tejing2001]

I once heard this as "if mirrors reverse things left to right, when I lie down in front of one, why don't I see my feet?" I prefer the 3D answer (mirrors reverse front and back) combined with the following insight: our brains know that objects can't be "pulled through themselves" in the way that would be necessary to invert just 1 dimension, so we instinctively seek out the 3d rotation of the object that is the "closest match" to what we're seeing. Since many objects in our environment have left/right symmetry, that generally leaves a discrepancy in the left/right direction after the rotation. (but when I lie down in front of the mirror, now I have up/down symmetry, and I find a rotation to match that).

[@Pikopati]

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

[@chrisg3030]

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.

[@World_Theory]

“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.

[@pratherat]

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.

[@Lowraith]

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).

[@artofgameplaying]

Exactly! Mirror images are just images in plane symmetry.

[@Maxander2001]

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. :)

[@kenglover8443]

Angle of light = angle of reflection.

[@COZYTW]

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.

[@christophergood2314]

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

[@chado3000]

You shouldn't try to trim your head. Just get a bigger hat.

[@johnnysparks44]

i bout cut my Tattoo off my head last week bra... i know just what you Meme.... Ha h ha h ha aaaaaa … i'm not even gonna try to splane that shit ok. keep practicing... ya might make it to Carnegie Hall.

[@wesofx8148]

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.

[@CristianoGuerra23]

Because we put the mirrors up side down!

[@catkeys6911]

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.

[@Kihidokid]

LMFAO THE BLOB IS FARNSWORTH

[@hobosmith5431]

Oh yeah lmfao futurama

[@the_jimnasium]

+Anthony Ingram I thought it looked familiar hahaha

[@subsnovideoschallenge-go2op]

Checking comments to see who else noticed

[@hobosmith5431]

+10,000 subs no videos challenge! Your accounts gonna get deleted lmao

[@Mr.D.C.]

Well lol you find that out in the middle of the video

[@QuantumSpark]

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.

[@freedom4life123]

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

[@Sukerkin]

Because the way your brain has learned to interpret its visual inputs is with you being head-upwards. If you wore glasses which inverted the image then your brain would, over time, relearn to process the inputs and everything would look ‘normal’ again.

[@johnnysparks44]

Ha h ah h h h h h haaaa

[@graboy12345]

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.

[@Mathologer]

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

[@manfred4004]

+Mathologer the Cheshire cat?

[@Mathologer]

Yes, the Cheshire cat :)

[@outputcoupler7819]

It's the difference between 22/7 and pi, from a famous proof that 22/7 is an overestimate of pi (because the value of that expression is positive).

[@thomasruiz9083]

The original illustration of the first edition :)

[@healer180]

think i solved homer's (Simpson) theorem. the question you left at the end of the video was is there any triangle that fit the theorem: sqrt(a)+sqrt(b)=sqrt(c) so i will give you an answer : a triangle on a sphere where the angle opposed to c is larger then 180. take the image you had on the video, if c went from the one point to the .other through the back then c could be much larger the a+b then it's just a matter of find a combination that is exactly equal legit answer?

[@paulgee4336]

I have never watched ANY of these that actually made clear sense.

[@Sinom.]

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

[@Mathologer]

+sinomsinom Google the question (when I did the search engine came up with 70,600,000 results :)

[@sebastianschon3141]

Same here, couldn't believe some people actually ask themselfs this question - beside from a mathematical or philosophical standpoint maybe, but from a logical standpoint, asking why it doesnt flip vertically is just stupid. It doesnt even have anything to do with mirrors, look at a stamp (preferrably with words / no simmetric image) for 20 seconds and everyone should realize what stupid question they just asked lol

[@sebastianschon3141]

It doesn't flip in any direction actually. It would be kinda weird logically to flip anyting. your right hand is still on the right side of the image. I get that it appears to be flipping but actually no single point is modified in any way even closely related to a flipping procedure. A mirror is basically no different from "a shadow with painting".

[@aepokkvulpex]

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

[@Mathologer]

+Devin Delaney Bit tricky because there is no distinguished axis when you look straight onto the mirror. As I say in the video, in this special case it is us who supply the orientation of the axis :)

[@nrganabaglia1838]

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

[@KaiHenningsen]

I think for the 3d case, the important insight is flipping a 3d object along an axis (across one plane) is not something you can do with almost any real tangible 3d object, because it isn't a rotation. We can do rotations just fine, but not flips. The closest you could come is if you have some object made of soft material, with a hole (like many pieces of clothing, where this is actually a common occurrence), and you pull it through the hole, essentially flipping it inside out. Now if the two surfaces were exactly identical, then the resulting object would be a mirror image of the original object, and any writing would be reversed. So that is essentially what a mirror does, and it shows why you can't do this with most real-world objects you might put in front of a mirror - no rotation around any axis will give you that effect. But if you think of yourself as a hollow film around empty space and a hole in that film you could pull it through to invert inside out, and you put the result nose-to-nose, fingers-to-fingers with the original - that's exactly what you'd see in a mirror. And when you then look at how some point on the surface moved, you'd see that it did indeed invert front to back. But it's a flip, not a rotation, and especially not a shift (what you'd need to look at the back of your head). Now as for the last, cylindrical mirror - I can't see enough of you or your shirt to tell, but Farnsworth is still flipped in that image. Look closely in which hand he holds the tool. The one in front of the mirror uses his left hand, the one in the mirror uses his right. Now there's something really strange going on there - how can the mirror show us the side of the hand that is away from the mirror? That would need another mirror behind the camera. Conclusion: there is likely a little bit of dishonesty (a.k.a. creative editing or other trickery) going on here.

[@kerolox7929]

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

[@fortytwo6257]

+Jesus2ndCousin I was wondering that too, it equals roughly 0 though because 22/7 is an estimation for pi

[@nikolalozajic]

+Jesus2ndCousin It is a very nice result as you can see and it is sometimes used to "prove" that 22/7 exceeds pi. Isn't particularly useful, just has an amazing result.

[@jeffreyblack666]

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.

[@ablationer]

9:34 haha, he said doodoo

[@wecomeinpeace1989]

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.

[@deanlhouston]

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.

[@marianneoelund2940]

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.

[@sillysad3198]

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

[@betaneptune]

The short version: Make a thin rectangular piece of clear plastic that says CAT on it. Stand in front of a mirror and hold the plastic up in front of yourself so that it reads CAT, directly and in the mirror. Now rotate the plastic 180 deg. about a vertical axis. It will be left-right reversed both directly and in the mirror. Rotate it back so that it reads CAT both directly and in the mirror. Now rotate the plastic 180 deg., but about a horizontal axis. You will now see up and down reversed for both the sign and its mirror image. So it is the axis of rotation that determines what gets reversed. Because of gravity we normally rotate toward and away from mirrors along a vertical axis. Hence the very common left-right reversal. Our bilateral symmetry also contributes to the apparent left-right "bias". (As a quick aside, note that clockwise becomes counterclockwise and vice versa regardless of the axis of rotation.) What about the mountain and the lake? The lake is basically a mirror that you could imagine was at first an actual mirror in front of and facing the mountain. Now rotate the mirror 90 deg about its bottom edge toward yourself. You have now reversed up-down instead of left-right, because you've rotated it along a horizontal axis. If you had instead rotated the mirror 90 deg. along its left or right edge, you'd get left-right reversal, since the rotation is then along a vertical axis. It is the axis of rotation of the object or the mirror that determines the direction of reversal. And because of gravity's up/down bias, we usually rotate about a vertical axis, giving left-right reversal.

[@particleonazock2246]

I love how you casually introduce Professor Farnsworth!

Good news everyone!

[@sayamqazi]

Hey fansworth what are you doing here?

[@KnakuanaRka]

Basically, the central idea is that what a mirror image flips is not up-down or left-right, but _front-back,_ and the image gets flipped left-right when we try to make it face forward again. For example, imagine you’re wearing a watch on your left hand, and you look at yourself in a mirror. The arm you’re wearing the watch on faces to the left, and the same is true for the image; it also has the watch on the arm facing left, but it’s facing the opposite direction to you. If you mentally spin this image around so it faces the same way as you, you switch its front and back so they’re the same way as you, but at the same time, you switch its left and right; thus, the watch will be on its right arm. And if you’re wondering about text being inverted on a shirt or something in a mirror, think about it like this: imagine you’re holding the shirt in front of you so you can read the text on it. Then you put the shirt on so the text is on the front, and you can see it in the mirror. What do you have to do to the shirt’s orientation? You have to flip it over. If you took the shirt off without flipping it back over and, say, looked through it at a bright light so you could see through it, you would see the text as backwards. When someone looks at you while you’re wearing this shirt, they would be facing the opposite way to you, so the text would be flipped back over and thus readable to them. When you look at yourself in a mirror with the shirt, due to the aforementioned front-back switch, you can see the front without it being flipped back over, similar to if you looked through it at a bright light, so it appears backwards. I actually wrote that out before I watch, and I do like this explanation with the mirror image and how we are biased in placing the image and original (we place them so the reflection axis is left-right because that’s more natural), though I think I included that in my own. And our explanations of the 2D one are pretty similar, through yours generalizes better; I was thinking about reflection by an axis and trying to include it, but wasn’t sure.

[@Redhotsmasher]

11:17 Aww, chibi Farnsworth is the cutest!

[@PrincessJayseff]

wonderful graphic work on this one

[@bri3fcas3]

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

[@gabejohnston1556]

Commenting on the video title and not the video, obviously. Try again.

[@spiderduckpig]

Gabe Johnston Boomer

[@darkfire8008]

The answer to the puzzle of why the words on the shirt are "flipped" even though the mirror does not flip left or right, is because of the axis facing it. Each point that marks a corner or line of "Mr. Messy" will have it's same point at the exact same place along the mirror along the left/right axis. For example: Set the left/right axis to X, Up/Down axis to Y, and the distance axis to Z. Center distance between mirror and body is 0. Mirror reflection always creates a horizontal line along the Z axis. If the period for "Mr. Messy" on the body is at point (2,2,3), the mirror, when moving along the Z axis would cause the period to appear on (2,2,-3). This action does not create the flipping effect, but we would perceive it like that as we see the image starting at the mirror side, not the body side.

[@tonyennis3008]

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

[@Mathologer]

+Tony Ennis Did not do this on purpose, but definitely sounds like it :)

[@TimpBizkit]

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.

[@RN-uo2vo]

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.

[@grawl69]

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.

[@artemiosnicola523]

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!

[@Mathologer]

+Artemios Nicola Let me know whether this one worked for you and/or your friend :)

[@jeffreyblack666]

For the spoon, when looking at the back, the same explanation applies, it flips front to back (for each point on the surface), but because the surface isn't flat it will be distorted. When looking into the spoon, it will vary depending on how far. If you are close enough, you only get one reflection and thus the same explanation applies. When far enough away, you don't see a direct reflection of yourself in the "mirror". Instead, you see the mirror in the mirror. This results in you being mirrored twice before seeing yourself.

[@davidlocke7667]

Mirrors do not flip left and right. The easiest way to see this is to face a mirror and point one finger to your left. The reflection also points to your left. Mirrors do reverse chirality, meaning they will make a left hand look like a right hand. They do this by reversing in the direction perpendicular to the mirror. When you face the mirror wearing a T-shirt with the writing "Physics is Awesome" from left to right. The "P" in "Physics" will be farthest to your left in reality and in the reflection. The straight part of the "P" will also be on the left and the curved part on the right. What is different with your reflection is that the letter has been pushed through to the other side of the fabric of the shirt. Another way to see this is cut out the letter P from a piece of paper. Hold it in front of you as you face the mirror. The reflection has the same left-right orientation. People get confused on this subject, because they have been mislead to think left and right are flipped.

[@mahamahawi3243]

hanks for the explanation i agree with you that the image reverses the front and the back but my question is does it affect our physical image in other words is that others see us the same way when we see ourselves

[@DodderingOldMan]

This is one of those question where I thought, well, that's incredibly simple, then, wait, that's actually kind of tough, then, no wait, it's actually incredibly simple, but tough to explain well. Which you have done :)

[@Mathologer]

+Buffoon1980 Great, that's exactly how I fell about this question. Incredibly simple but very tricky to give a complete explanation :)

[@AugustSchunk]

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.

[@Mathologer]

Also have a look at these true mirrors :) www.amazon.com/True-Mirror-12-Inches-Black/dp/B0083PLA3K