Yup. Mirrors reflect front to back. It's the struggle between accepting as literal what you've always been told, and the data being reported by your own senses, mitigated by language and cliché.
Isn't it the photograph that is flipped? After all if I'm in front of a mirror my left hand appears to the left and the right hand appears to the right. But on a photograph it's the opposite.
Intuitively just consider the difference between the two:
What DO you see? In case of the mirror, you see what's BEHIND you, because the stuff in front of you is blocked by the mirror, no? And just to be clear, by "you" I mean your eyes, and in particular the direction your eyes are looking at.
Now in contrast a photograph never shows what's BEHIND the camera (now that would be kind of funky, don't you think?), but - just like your eyes - only captures what's in front of the lens.
I don't know how to "explain" intuition, but usually I imagine not myself but some kind of geometric shape in front of a mirror (say a square with the edges labelled).
If I try to visualize how light bounces, it is intuitive that in a mirror I'm seeing the light bouncing from mirror -> me in the proper way and in a photo, I'm looking at the shape directly with a camera (I'm where the mirror was).
The paradox exists because when you ask a person "why it flips horizontally but not vertically" most people can not respond. Usually they can not even begin discussing the premise of the question. Notice how even in your comment you did not really attack the premise, just gave a parallel explanation that skips talking about the premise. This does not really help, because as with most paradoxes, the issue is exactly with the premise. The linked video by Physics Girl does a great job at explaining the paradox away.
I've found that explanation to be pretty good, as a matter of fact. The paradox seems to arise because from a psychological effect of "projecting" the directions with respect to the image "looking" back at you. Once you get people to stay in their reference frame (left, right, top, bottom above) they see their mistake.
Take 2 flat mirrors, set them edge to edge at an angle of 90°, mirror side facing into the angle. Position the mirrors in front of you with the edge horizontal and both mirrors angled at 45° towards you, i.e. look into the inner corner made by the 2 mirrors. The image you see in that corner will be flipped vertically.
The same trick can be used to create a horizontal-flipping mirror, simply by positioning the mirrors so that the edge is oriented vertically. You can make one of these by sticking two pieces of mirror in an inside corner in a room somewhere.
grab a piece of paper with text on it. place it in your hands as if you were about to read it.
Now flip it so a mirror in front of you can see it. The text is right to left, isn't it?
Now notice that, in order to "show it to the mirror", you applied an horizontal rotation to the paper. Try placing the piece of paper as it was at the beginning, so it's readable to you again, and then "show it" again to the mirror, but this time flipping it with a vertical flip.
There you go, the text is left to right but upside down. Vertical flip!
You're probably thinking "yeah but the original is upside down too" to which I would reply, yes, and in the first case the original was also right to left from your position - you just coudn't see it because the paper is opaque. writing in a piece of glass , you can see it left to right in the mirror when it's left to right in real life.
A normal mirror already does flip things vertically just as much as it does horizontally, which is to say not at all.
This about your expectations of what a person (or thing) facing you looks like. Normally when someone turns to face you they'll spin around while staying in a head-upward orientation. That puts your right hand and their right hand on opposite sides because they've spun around, while your reflection's right hand stays on the same side as your own because the mirror doesn't flip anything.
If you instead expect the other person to turn to face you by doing a hand stand, then you can say "Why is my reflection's head on top?! It should be on the bottom! The mirror has flipped it vertically!"
Two mirrors at 90 degrees to each other should do it. Do you mean for it to flip both horizontally and vertically though? That would be more difficult. I'm not sure but maybe a type of prism.
Stand on a mirror. Your reflection will be flipped vertically along the y-axis. Your reflection will be upside down relative to you.
The flip happens perpendicular to the surface of the mirror. That's what trips everyone up. They think that a flip happens parallel to the mirror, but the flip happens into the mirror. Like flipping a glove inside out.
~~First, the Z axis is commonly used to represent height rather than width.~~
Second, the mirror is not flipping anything.
It's just reflecting things in a straight line. This is easily demonstrated by holding a sign with a transparent background in front of the mirror. The image you see on the back of the sign aligns with the one you see on the mirror.
A person in front of the sign is able to read the words properly because, relative to you (and the sign) they are flipped. Their right eye is in front of your left eye and vice-versa.
The mirror gives the impression of a flipped image precisely because it's not flipping anything!
Edit: It's already been pointed out twice to me that Z for height is not in any way a convention. I never thought it was, which is why I used the phrase "commonly used" instead. Turns out that doesn't seem to be the case either, regardless of my personal experience so this is an acknowledgement of that mistake.
Exactly. The image in a mirror is physically symmetrical to the direct image from objects in the real world, with the mirror itself as the plane of symmetry.
I find the front-to-back explanation to give a better intuition than the typical "but left and right are relative to your body", which only serves to explain the paradox of "left-right are reversed but up-down ar not", but not the fact that everything looks flipped.
Well, it flips front-to-back. But this side of the mirror, we can't physically do that, so it's not in our brain's list of expected possibilities. We can, however, rotate ourselves 180 degrees. And because we're bilaterally symmetrical, our brain finds it easy to interpret the front-to-back flip as a 180 degree rotation. But that leaves left-to-right weird, because what happened wasn't actually a 180 degree rotation.
The usage of the z-axis is absolutely correct in the article.
The author has essentially defined the x and the y axes. Useful physics (or math), as opposed to what appears to be an arbitrary common convention in whatever field you're familiar with, would suggest placing the z-axis in the direction that is co-perpendicular to the defined x and y axes.
That a z-axis represents height and not depth is the least physics thing I've ever heard. Frankly, I dont think that's a thing at all.
I've only ever known the Z axis to represent depth. Be it maths, physics or software development (web dev: "z-index", Direct3D, etc).
Also your second point is reiterating exactly what the video said. She repeatedly says "the mirror isn't flipping anything [along the horizontal axis], you are."
The physics of what she's discussing is correct, you've just been a bit rash to judge it.
> I've only ever known the Z axis to represent depth. Be it maths, physics or software development
A standard math textbook will usually show the x-axis pointing toward the reader, the y-axis pointing right, and the z-axis pointing up. Something like this:
z
|_
/ y
x
Similarly, if you're defining a cone or a spiral or what have you, you'll usually do it in terms of an r/θ/z coordinate system, where z is height. So the convention exists.
But obviously where the x and y axes are defined, the z axis will be perpendicular to the x-y plane.
Yes. Usually, the right-hand rule is followed. A positive rotation is from the positive x axis toward the positive y axis. If you curl the fingers of your right hand in that direction, then the thumb points along the positive z axis.
The way X,Y,Z axis are portrayed in the way that is most common in computer graphics. X is left-right, Y is up-down, Z is front-back. That's convenient because X,Y are your screen coordinates for 2D work, if required, Z is stored in a separate buffer, aptly called the Z-buffer.
Orientation of the base vectors can vary between tools, engines and APIs but the Z axis is almost always perpendicular to the screen, and having the Z axis perpendicular to the mirror follows this convention.
And a mirror certainly flips things. In a mirror image, parity is reversed, right hands become left hands, screws turn the other way. A person in front of you doesn't see you flipped, he sees you rotated 180 degrees around the up-down axis. You can achieve the same effect with two vertical mirrors at a right angle from each other. Because there are two mirrors, the image is flipped twice, and because of the way parity works, it is the same as not flipping.
One thing we can say is that flat mirrors both flip and rotate. The flip is always the same, there are only 2 parities and the only thing you can do is go from even to odd and odd to even. The rotation depends on the position and orientation of the mirror. If the mirror is vertical, the axis of rotation is vertical and therefore, it will flip left-right. If the mirror is horizontal the axis of rotation will be horizontal and it will flip up-down. Funhouse-style distorted mirrors also flip, like all mirrors, but will apply a complex, non-linear transformation instead of a simple rotation.
Don't beat yourself up about Z. The Z axis is both a convention and commonly used for height in many fields, such as civil engineering, vehicles, and geology. All areas where the horizontal ground is important. It's computer graphics with its vertical screens that mainly has Z for depth.
There does seem to be an underlying commonality to these conventions which might be that Z is normal to some important reference plane, the direction without homogeneity, or the most unique direction.
Their conclusion is inaccurate and may be disproven simply by leaning oneself over to a 90 degree angle, or greater, while leaving the mirror and the text source stationary.
"Mirror image is a tricky thing, but it's pretty clear when you look at words in a reflection, that mirrors flip things horizontally rather than vertically. Or, at least it seems that that's the case."
Majority of HN comments:
"A mirror doesn't flip anything"
The "At least it seems that's the case" clearly suggests that there isn't an actual flip. But ask a regular person whether a mirror flips that is what they will say. The article addresses both the common wisdom and the actual science.
Absolutely, this is a pretty solid explanation and HN (and similar places) always have the bizarre take on explaining of paradoxes to shout "It's not a paradox!" Paradoxes are about appearing, at first thought, to be impossible, not it being literally impossible. In this case, it's the two observations:
1) A mirror is rotationally symmetric so should treat left/right the same as up/down.
2) A piece of paper with writing held up to a mirror reads right-to-left instead of left-to-right. But it does not read bottom-to-top.
This asks for an explanation - one that the article gives. Why do so many here feel the need to say that since this has an explanation, it is not a paradox? Outside of fiction, every paradox has an explanation and, moreover, we're discussing an article that gives that explanation.
But: a mirror does flip something, it flips in-and-out. Mirror images are not the same.
The (perhaps overly) charitable take on "It's not a paradox!" responses is that it's something which didn't appear impossible or weird to that responder, and the article failed to make the case for why there's even something that needs an explanation.
I'm curious to know what percentage of commenters who know exactly how mirrors work can perform simple tasks like assembling a puzzle with the same speed only looking through a mirror.
I don't think that would prove anything at all, since knowing how something works doesn't mean you can use it in place of your usual behaviour. You also have to unlearn manipualting things in non-mirror space.
> Paradoxes are about appearing, at first thought, to be impossible, not it being literally impossible.
That's not true, or at least it's not the whole truth. Real paradoxes do exist: A barber shaves everyone who doesn't shave themselves, who shaves the barber?
So if true paradoxes do exist, it seems fair to call out alleged paradoxes for not truly being paradoxes.
If the barber doesn't shave himself, then he must shave himself because he shaves everyone who doesn't shave themselves. But he only shaves those that don't shave themselves, so he cannot shave himself....
There is only one barber and he's not bald or otherwise excluded from the 'everybody' in "he shaves everybody who doesn't shave themselves." It's not a lateral thinking problem, or a matter of thinking outside the box. The scenario described is simply impossible. Everybody, including the barber, is either shaved by the barber or [XOR] shaves themselves, which is impossible in the case of the barber.
From your wikipedia link:
The barber is the "one who shaves all those, and those only, who do not shave themselves". The question is, does the barber shave himself?
If the answer is "no", then he's shaved from another barber and the problem is solved. Nowhere is stated there's only one barber in the world.
Tattoo artists don't tatoo themselves but they're not living paradoxes. How is this different?
Again, I'm sorry for the obvious elephant in the room I keep missing.
EDIT: I see your answer to sumtechguy, I understand now it's more metaphorical than pratical. In my understanding, the paradox seems to arise when you try to put all your existing elements to fit one of 2 kind of boxes, which are clearly not enough.
Parent poster forgot a critical condition for it to be a paradox. As they stated it's not, a second barber could shave both themself and the first barber.
The paradoxical statement would be "A barber shaves all those, and only those, who do not shave themselves. Who shaves the barber?" Without the second condition (only those who don't shave themselves) it's non-paradoxical.
Replace 'A' with 'The' and it works. Tbh I assumed people were already familiar with the Barber Paradox and didn't word it defensively, but if you take 'a barber' as referring to a specific barber then it's a paradox.
Right, the mirror doesn't actually flip. It's just we think about turning around to try to "match" what we see.
And humans are more left-right symmetric than up-down symettric.
If we try to do a headstand to match the image in the mirror then it actually "mirrors" it top/down instead of left/right.
Another example: looking at writing in the mirror, we've actually turned it around to point at the mirror. If we flip it over to point it at the mirror instead then again it'll appear upside down in the mirror instead of left/right flipped.
Edit: I should have read the article, because indeed this is exactly what it explains.
I think people here just have an aversion to (some* ) cutesy explanations of things that just confuse things.
The article itself concludes with: "The reality is that the mirror isn't flipping things horizontally or vertically at all" and you wonder what mental model it thought it was explaining in the first place.
* We never tire of cutesy useless explanations of monads though.
I'd guess that more than just some commenting didn't look at the article. There's complaints in the comments that only make sense if you ignore that there's an article at all.
But despite Physics Girl's video embedded in there being much better than the text, I can't fault anyone for not watching it. There are many situations where you can read through something, but can't watch a video.
Tech people faced with a perception/biology/social issue in a nutshell. It matters that it feels weird, that's the whole point. "Flip" is a human word, it's not a mathematical definition.
It's likely that a lot of those commenters only read the title, and not even the beginning of the article. I'm not accusing anyone in particular†, I just think it's worth acknowledging in terms of understanding how HN functions.
Most HN commenters are wrong. A mirror DOES flip one coordinate; the coordinate that is orthogonal to the plane of the mirror. That's what makes it a mirror, and not a window.
Use east/west instead of left/right and you’ll see there’s no flipping.
Left and right are defined with respect to the person, and so they are different for the person and their image. East and west (or up and down) are defined with respect to environment, and they’re not flipped.
If you use east/west as constants, you will find that the mirror is flipping north and south.
No matter what convention you use to define relative positions between objects, the mirror is physically creating a symmetric image of those, switching distances from closest to farthest from the glass.
> And why, when you raise your right hand, does your mirror-self raise its left hand, but it still moves it up rather than down?
The words “up” and “down” are absolute, but the words “left” and “right” are relative to you. If we instead of “left” and “right” use the words “south arm” and “north arm”, then the mirror suddenly does not “flip” anything. This is a strong clue that the apparent paradox is conceptual, not real.
Hmmm. Just made me think that you probably couldn't explain that "paradox" to most 6yo who just about learned to tell left and right apart. In my experience they will consistently get left and right hands of others wrong when facing them, because they always treat those relative to themselves. So the mirror doesn't flip anything to them.
> Hmmm. Just made me think that you probably couldn't explain that "paradox" to most 6yo who just about learned to tell left and right apart.
A typical 6-year old can say what their left-hand is. But if you tell them to point to MY left hand, they will instead point to my right hand. It takes additional effort and training to teach young children how to see from other people's perspective.
This seems reasonable explanation on first glance, but on further thinking it seems to miss something. Assume 'down arm' as leg, and 'up arm' as head, relative to the person who has the arm just like left and right arm. Even then the mirror doesn't flip up and down arm, but only flips left and right.
agreed. As another commenter mentioned, what a mirror does is not flip left-right, but front-back. (notice front-back are still relative terms, so parent comment argument is moot)
Up and down are relative too, and not absolute. People in the Northern pole vs Southern pole will both point "down" toward the centre of the earth, in opposite (absolute) directions.
The concepts of North and South also fail dramatically when close to the poles.
The article is just simply wrong. The mirror "person" also raises the right hand. Its just our brain tricking us into thinking that if we would be in the position the mirrored person appears in (rotated 180 degree), that it would be our left hand but we cant be in a mirrored position ever.
Indeed, like we physically did with the piece of paper, we have mentally chosen to think of our image in the mirror as like ourself but turned horizontally (around the verticle axis) to face us - ending up flipped left-to-right.
If we instead think of our image as like ourselves but turned vertically (around the horizontal axis) - like you lept headfirst into the mirror and landed upright on your head - then you'll find that your left and right sides are the correct way round but the image is vertically flipped. It's very hard to think this way because (a) we're mostly symmetric horizontally, certainly a lot more than vertically, and (b) we very often interact with other people that have turned horizontally (around the verticle axis) to face us but very rarely interact with other people that have turned vertically to face us.
Another aspect that makes this hard mentally is that if you have any identifying non-symmetrical features, like birthmarks, then they appear horizontally flipped in the mirror compared to photographs. Again, it's the photograph that's turned incorrectly. This one is particularly hard to sell, because surely a photo with a ground at the top can't be the right way round? The answer is, for the purpose of matching your left and right, the "correct" way round is for the photo to face away from you. Makes logical sense, but very unintuitive.
You are tricked by what you see. You assume the other person is a person that looks like you but is rotated towards you, while in reality the other person would need to be a mirrored version of you.
Your brain doesn't see that it's mirrored because you are used to see "yourself" this way.
I'm not looking at my reflection. I'm looking at you and your reflection(or a very good clone). Depending on my orientation, I might not even be able to figure out which figure is the mirrored image.
> The words “up” and “down” are absolute, but the words “left” and “right” are relative to you.
I disagree. In this sort of conversation, "up" refers to the direction from your feet to your head, not away from the ground. If you do a handstand and hold your piece of paper up to the mirror then you'll still find it flipped left-to-right but not top-to-bottom if you turn it the instinctive way, and still find it flipped top-to-bottom but not left-to-right if you turn it vertically.
I am not joking. When you stand on the mirror the direction from your feet to your head is different than for the guy in the mirror. It shows that the mirror changes only one axe, orthogonal to its surface. It does not rotate anything nor change up/down or left/right. So when I look at the mirror en face only the direction of y axis is changed, x and z is not affected.
I agree, and that doesn't contradict what I said in my original comment. I think we are just getting tangled in semantics rather than fundamentally disagreeing on anything.
> In this sort of conversation, "up" refers to the direction from your feet to your head, not away from the ground.
I disagree. To me, "up" is opposite the direction of gravity. If I were doing a handstand on the ground and someone told me to look up, I'd look toward my feet.
Mirrors flip things inside out not left to right. You see your images face not the back of the head. This confuses left to right as you’re referring to port and starboard, assuming your image isn’t inside out.
Mirrors don't flip anything. They change direction of photons.
Trow a ball on a wall at an angle it bounces of at the same angle there is no flipping.
Write a word on a paper with fresh paint then press in on a wall then remove it. The word on the wall is exactly want you pressed on the wall it didn't flip the paint you did when you flipped the paper.
A light source moving away from you to a mirror is getting dimmer, but it’s reflection is getting brighter. That’s a measurable physical property that’s reversed. Similarly, a red or blue shifted object between the mirror has a reflection that’s revered in the other direction. However, when looking at an object behind you that doesn’t happen as the reflection shows the same side.
>A light source moving away from you to a mirror is getting dimmer, but it’s reflection is getting brighter.
The distance to the light source grows if you move it away toward the mirror it gets dimmer.
The the distance of the light in the reflection however gets shorter so it get brighter.
If the light is right next to you the distance is zero.
The reflected light however traveled 2 times the distance to the mirror (dimmer).
If you move the light to the mirror both "lights" are one mirror distance away so they have the same brightness (assuming a perfect mirror).
There is no "physical property reversed" at all. You could remove the mirror and measure the light intensity twice the distance away instead. Then move the light to the middle where the mirror was and obviously the sensor would measure and increase while you see a decrees in brightness.
This is going to seem really pedantic, but many properties of the photons are consistent with a path that reflects off of a mirror. However, it’s unclear if it actually takes that path.
You can't prove this at all. How do you know the photons don't pass through the mirror? What you are seeing are photons from the flipped alternate world on the other side of the mirror. Your reflection sees you and you see your reflection.
In a sense if you replace the mirror with a real reflected universe the same photons will hit your eyes and your perception of the reflection will be identical as if you are seeing an alternate world. That is what we perceive instinctually and we wouldn't be able to tell the difference. You literally cannot prove it, but that's besides the point.
When people refer to flipping in the reflection they are not referring to the physical phenomenon of reflection but they are referring to the interpreted equivalent meaning that if the reflection was replaced with an identical universe to our own how is this reflected universe transformed relative to ours? The answer is: Something flipped.
In this case what we are saying is that the z-axis flipped.
Every surface is a mirror just a bad one. If your "theory" would be correct every surface emits light form some alternative universe but only if light form your universe hits it.
I did and I pointed out why your theory is garbage.
I didn't comment the last part because as its simply wrong. Nothing is flipped at no axis at all. If what you see in the mirror would be another universe then it would have to me MIRRORED to look like we see things in a mirror. Every row of atoms right-angled towards the mirror would have to have the exact opposite order. Would the other universe be flipped? No it would not. The wrong assumption is that your universe and the one you see in the mirror is identical. But it would have to be mirrored it can not be identical and also not flipped. No matter how you would flip the other universe it would never look like what you see in a mirror.
Just use 2 identical but non-simple objects place them next to each other for example 2 coins.
No matter how you flip or rotate the coins it will never look like there is a mirror in between. You would need a mirrored coin for that.
The full post is saying that the interpretation of what you see is NO DIFFERENT from an alternate universe. I am not saying this is actually what's going on.
All reflections on all surfaces can be interpreted this way.
The point of the example is to say that the language people use to refer to reflections is to refer to this alternate higher level interpretation and is still valid. Only the most pedantic person will say "nothing" has flipped and call it just bouncing photons.
> If what you see in the mirror would be another universe then it would have to me MIRRORED to look like we see things in a mirror.
This is exactly what I'm saying nothing precludes the alternate universe to be MIRRORED. The alternate universe is a mirrored universe, Get it?
>The wrong assumption is that your universe and the one you see in the mirror is identical.
This is your assumption. I never said this. I said ALTERNATE universe. <--- read the word ALTERNATE. I'm assuming here that you might be delusional and seeing the word IDENTICAL instead of alternate.
>No matter how you would flip the other universe it would never look like what you see in a mirror.
Again if the atoms in this universe and flip them across the Z-axis the light bouncing off those atoms would produce exactly what you see in the mirror.
>Just use 2 identical but non-simple objects place them next to each other for example 2 coins. No matter how you flip or rotate the coins it will never look like there is a mirror in between. You would need a mirrored coin for that.
When I say a z-axis flip I mean inside out. Imagine holding a glove, then turning that glove inside out. That is a z-axis flip. Your coin analogy is completely off.
>I did and I pointed out why your theory is garbage.
I never even made a theory I just used the alternate universe thing as an example of the vernacular people use... people refer to the reflection as a real object and not as bounced photons and this interpretation is valid because it can't be proven otherwise. You just didn't get it. Hopefully you reread my post and realized that it is not my "theory" that's garbage but your brain.
'inverted' might be a slightly better descriptor than 'flipped', but still, my left hand is on the left in the mirror as well, but it's still the mirror person's right hand.
and your distinction of 'real' vs 'conceptual' relative to paradoxes doesn't make sense. a paradox is real because it's conceptual, as paradoxes are relative to humans (or more generally, earthly life).
>The words “up” and “down” are absolute, but the words “left” and “right” are relative to you. If we instead of “left” and “right” use the words “south arm” and “north arm”, then the mirror suddenly does not “flip” anything.
No dude. The mirror flips left and right Relative to you. The mirror ignores up and down relative to you. The paradox is real when thought of in these terms.
Truth be told the flip is neither left or right nor up and down. actually It is actually inside out on the z axis: towards you. Translational coordinates along the xy plane must be preserved and this is what causes the perceived left right flip.
The actuality is nothing was flipped along x or y, it was kept the same.
The mirror doesn't flip anything at all. As humans we normally keep our feet on the floor and turn around by rotating around the vertical axis, thus when we face another human they've normally rotated around the vertical axis relative to us.
We're just not used to seeing the fronts of humans who have not rotated relative to us, so the mirror appears to have flipped the image horizontally.
If we customarily rotated around a horizontal axis, i.e. every time you look "behind" you're upside down (note this won't actually work very well given that you'd normally want to rotate around the axis perpendicular to the surface of the Earth, but just for sake of argument...), then we might believe that the mirror has flipped things vertically. It still hasn't actually flipped anything, it's just that we are viewing the front of a person who has not rotated.
Exactly. And it is even easier to convince oneself that that's actually what is going on if instead of trying to explain why the mirror "flips" the image of a person, one try to explain why the mirror "flips" a written word.
Take a piece of paper, write a word onto it, and turn it towards the mirror. Now observe the word. Is it flipped left to right? If so, it's because when turning it towards the mirror _you_ turned it around the vertical axis. Do this again, this time rotating the paper around the horizontal axis and voilà, the word is now flipped upside down.
IIRC that's Feynman who have written somewhere that mirrors do not flip things right to left, nor top to bottom. They flip things front to back.
I once got into a bar fight trying to explain this.
I somehow got the idea that people who are used to write top-to-bottom might see it as flipping upside down. At the time I thought of Chinese letters being used that way, so while I was trying to tell about this to my friends a guy at the near table got really offended and went “you talking to me? You calling me chinese? Lets go outside!” It ended well :)
The mirror DOES flip one coordinate, the "hither" versus "yon" coordinate.
If you hold a paper of text up against the mirror, and it looks mirrored, then you can notice that the original text ALSO looks inverted to you, if the paper is translucent. Right is right. Up is up. However, "hither" becomes "yon."
Exactly like we would expect by looking at the math for reflection in a plane.
You mean like, why do the people who paint markings onto an ambulance have to do it reversed?
Yeah that's a good question. If I'm sitting in my car and looking at an ambulance in the rear-view mirror, it's not the mirror itself that reverses the lettering, and that's the key thing to understand.
The only thing the mirror is doing is reversing the Z-axis. So the question becomes, why does a Z-axis reversal cause me to perceive that the X-axis is getting reversed?
If I turn around to look at the ambulance, I just took my head through a 180 degree rotation around the Y-axis. Then (and only then) does the image get reversed on the X-axis.
If you could imagine being behind the ambulance, and it were made of some imaginary transparent material, you would still see the lettering as not reversed.
The key is to be precise when you use words to describe an optical phenomenon. A mirror reflects, and that's all it does.
There are really two "flips" that are often talked about with a mirror:
1. It flips things in the direction perpendicular to the mirror. If you're facing a normal wall-mounted mirror then that means it flips your "forward" into your "backwards". This is a real physical effect that no one would normally dispute.
2. It appears to flip things left to right, and most people (before mirror-flipping enlightment) would reasonably believe this. But it's a human psychological effect, not a real physical one.
This article is about the second point. You're talking about the first point. The placement of the mirror is a red herring: even with a ceiling mounted mirror, if you show a piece of paper to it by putting it above your head in the natural unenlightened way and look up, you'll find the text is still flipped left to right. In fact it maybe even emphasises the illusion because you can turn to face any direction (and without thinking you'll turn the piece of paper too of course) and still see the same effect!
(BTW I upvoted your comment because it's not the only comment to post this mix up - but it seems to be the first - so I think it deserves a bit of visibility for others thinking the same thing.)
The image in the mirror appears to have reversed chirality. Reversed chirality is simply that, it doesn't have a preferential direction of horizontal or vertical.
But our environment has a preferential direction in that we orient ourselves with respect to the Earth's surface, and the horizon is, well, horizontal. Our body is constructed with vertical bilateral symmetry which means our "halves" are horizontally oriented when in a normal standing or sitting position.
All of this causes us to perceive and define reversed chirality in terms of handedness, left or right. Things that we perceive with a left-to-right orientation appear as right-to-left if chirally reversed.
If we were spherical beings with limbs and eyes poking out at various angles from our bodies, living in microgravity on a space vessel, we would just perceive the reversed chirality in our mirrors as "enantiomorphic" and not assign a spurious L/R directionality to it.
The confusion ultimately comes from a nebulous understanding of "flip". This is what we mean when we say our mirror image is flipped: We imagine the mirror represents an extension of our normal 3D world and rotate our body around the z-axis until our head and legs line up. That's we interact with our 3d world: we translate and rotate objects.
However, this isn't the only way to "flip" (i.e. rotate back). It seems like the only way because it is the only way to rotate the mirror image onto something that aligns with the non-mirror reality. The head must align with the head and the legs must align with the legs, and there is only one rotation that makes it work.
But now imagine you had some sort of isle of man flag [1] type body. That is, your arms remain, but your feet and your head turn into an arm. For lack of better term, call your "head-arm" upper-handed and call you "leg-arm" lower-handed.
Now when you look at your freakish mirror image, there are TWO ways you can rotate your the mirror image to correspond in some way with your body. You can rotate as usual around the z-axis, but you can also rotate around the y-axis. In that case, your left and right arms are not flipped, but your upper-arm and lower-arm are flipped.
That is, the whole confusion occurs because humans are symmetric in one dimension and non-symmetric in another.
You're in a room with your friend. You look at a sign on his forehead saying "AOM". There's a mirror on the wall. You can see your friend in the mirror, the sign on his forehead is now saying "MOA". Nobody turned anything to the mirror, the whole scene is stationary. Why is it "MOA" instead of "VOW"?
Look in a mirror. Raise your right hand, THE HAND ON THE RIGHT GOES UP. There is no reversal, it's a myth.
When you stand facing a real person, THATS the reversal. If they raise their left hand, you see it on the right. Because THEY are reversed. They are facing the opposite direction.
Ever tried to read text in a mirror? Why is the word AMBULANCE flipped horizontally on ambulances and not vertically? Why is ƎƆ ИA⅃UᙠMA and not ∀WB∩Г∀ИCE or ƎƆ N∀˥∩𐐒W∀?
Write AMBULANCE on a piece of paper. Now turn the paper around so the word faces away from you. Hold it up to a light and you can see that the word is now flipped horizontally. Now face a mirror: the image is projected onto the mirror with no change, so you see the exact same thing you saw when it held it up the light.
IOW the mirror is inessential. We can ask the same question about just a transparent piece of paper.
That's because you flipped the paper horizontally not vertically. If you flipped it vertically it would be flipped verically. But you didn't flip the ambulance.
Um, because it's not flipped around. Seriously, look at any text in the mirror. The rightmost feature of the text will be the rightmost feature in the mirror, and the leftmost will be leftmost.
You would need to flip it horizontally to make it look "normal"
Stand facing a mirror. Hold an open book up so you can read it. Now turn it to face the mirror. The text is backward!
Wait. How did you turn the book? Right-to-left? Well, that's why its 'backward'. Try it again, but this time flip the book vertically to face the mirror. Now the test is not flipped right-to-left, but top-to-bottom.
It's nothing to do with 'physics'. Its just perception.
174 comments
[ 4.9 ms ] story [ 209 ms ] threadI never quite got why this was a paradox tbh.
What DO you see? In case of the mirror, you see what's BEHIND you, because the stuff in front of you is blocked by the mirror, no? And just to be clear, by "you" I mean your eyes, and in particular the direction your eyes are looking at.
Now in contrast a photograph never shows what's BEHIND the camera (now that would be kind of funky, don't you think?), but - just like your eyes - only captures what's in front of the lens.
And there's your difference.
The same trick can be used to create a horizontal-flipping mirror, simply by positioning the mirrors so that the edge is oriented vertically. You can make one of these by sticking two pieces of mirror in an inside corner in a room somewhere.
Now flip it so a mirror in front of you can see it. The text is right to left, isn't it?
Now notice that, in order to "show it to the mirror", you applied an horizontal rotation to the paper. Try placing the piece of paper as it was at the beginning, so it's readable to you again, and then "show it" again to the mirror, but this time flipping it with a vertical flip.
There you go, the text is left to right but upside down. Vertical flip!
You're probably thinking "yeah but the original is upside down too" to which I would reply, yes, and in the first case the original was also right to left from your position - you just coudn't see it because the paper is opaque. writing in a piece of glass , you can see it left to right in the mirror when it's left to right in real life.
This about your expectations of what a person (or thing) facing you looks like. Normally when someone turns to face you they'll spin around while staying in a head-upward orientation. That puts your right hand and their right hand on opposite sides because they've spun around, while your reflection's right hand stays on the same side as your own because the mirror doesn't flip anything.
If you instead expect the other person to turn to face you by doing a hand stand, then you can say "Why is my reflection's head on top?! It should be on the bottom! The mirror has flipped it vertically!"
The flip happens perpendicular to the surface of the mirror. That's what trips everyone up. They think that a flip happens parallel to the mirror, but the flip happens into the mirror. Like flipping a glove inside out.
~~First, the Z axis is commonly used to represent height rather than width.~~
Second, the mirror is not flipping anything.
It's just reflecting things in a straight line. This is easily demonstrated by holding a sign with a transparent background in front of the mirror. The image you see on the back of the sign aligns with the one you see on the mirror.
A person in front of the sign is able to read the words properly because, relative to you (and the sign) they are flipped. Their right eye is in front of your left eye and vice-versa.
The mirror gives the impression of a flipped image precisely because it's not flipping anything!
Edit: It's already been pointed out twice to me that Z for height is not in any way a convention. I never thought it was, which is why I used the phrase "commonly used" instead. Turns out that doesn't seem to be the case either, regardless of my personal experience so this is an acknowledgement of that mistake.
I find the front-to-back explanation to give a better intuition than the typical "but left and right are relative to your body", which only serves to explain the paradox of "left-right are reversed but up-down ar not", but not the fact that everything looks flipped.
The author has essentially defined the x and the y axes. Useful physics (or math), as opposed to what appears to be an arbitrary common convention in whatever field you're familiar with, would suggest placing the z-axis in the direction that is co-perpendicular to the defined x and y axes.
That a z-axis represents height and not depth is the least physics thing I've ever heard. Frankly, I dont think that's a thing at all.
Also your second point is reiterating exactly what the video said. She repeatedly says "the mirror isn't flipping anything [along the horizontal axis], you are."
The physics of what she's discussing is correct, you've just been a bit rash to judge it.
A standard math textbook will usually show the x-axis pointing toward the reader, the y-axis pointing right, and the z-axis pointing up. Something like this:
Similarly, if you're defining a cone or a spiral or what have you, you'll usually do it in terms of an r/θ/z coordinate system, where z is height. So the convention exists.But obviously where the x and y axes are defined, the z axis will be perpendicular to the x-y plane.
Orientation of the base vectors can vary between tools, engines and APIs but the Z axis is almost always perpendicular to the screen, and having the Z axis perpendicular to the mirror follows this convention.
And a mirror certainly flips things. In a mirror image, parity is reversed, right hands become left hands, screws turn the other way. A person in front of you doesn't see you flipped, he sees you rotated 180 degrees around the up-down axis. You can achieve the same effect with two vertical mirrors at a right angle from each other. Because there are two mirrors, the image is flipped twice, and because of the way parity works, it is the same as not flipping.
One thing we can say is that flat mirrors both flip and rotate. The flip is always the same, there are only 2 parities and the only thing you can do is go from even to odd and odd to even. The rotation depends on the position and orientation of the mirror. If the mirror is vertical, the axis of rotation is vertical and therefore, it will flip left-right. If the mirror is horizontal the axis of rotation will be horizontal and it will flip up-down. Funhouse-style distorted mirrors also flip, like all mirrors, but will apply a complex, non-linear transformation instead of a simple rotation.
There does seem to be an underlying commonality to these conventions which might be that Z is normal to some important reference plane, the direction without homogeneity, or the most unique direction.
Also, z axis is generally used as the height.
Meh. Onward.
"Mirror image is a tricky thing, but it's pretty clear when you look at words in a reflection, that mirrors flip things horizontally rather than vertically. Or, at least it seems that that's the case."
Majority of HN comments: "A mirror doesn't flip anything"
The "At least it seems that's the case" clearly suggests that there isn't an actual flip. But ask a regular person whether a mirror flips that is what they will say. The article addresses both the common wisdom and the actual science.
1) A mirror is rotationally symmetric so should treat left/right the same as up/down.
2) A piece of paper with writing held up to a mirror reads right-to-left instead of left-to-right. But it does not read bottom-to-top.
This asks for an explanation - one that the article gives. Why do so many here feel the need to say that since this has an explanation, it is not a paradox? Outside of fiction, every paradox has an explanation and, moreover, we're discussing an article that gives that explanation.
But: a mirror does flip something, it flips in-and-out. Mirror images are not the same.
Smarter Every Day actually has a video demonstrating a similar thing: https://www.youtube.com/watch?v=MFzDaBzBlL0
That's not true, or at least it's not the whole truth. Real paradoxes do exist: A barber shaves everyone who doesn't shave themselves, who shaves the barber?
So if true paradoxes do exist, it seems fair to call out alleged paradoxes for not truly being paradoxes.
I'm clearly missing something but how is that a paradox?
This statement is false.
https://en.wikipedia.org/wiki/Barber_paradox
See also: https://en.wikipedia.org/wiki/Russell%27s_paradox
If the answer is "no", then he's shaved from another barber and the problem is solved. Nowhere is stated there's only one barber in the world.
Tattoo artists don't tatoo themselves but they're not living paradoxes. How is this different?
Again, I'm sorry for the obvious elephant in the room I keep missing.
EDIT: I see your answer to sumtechguy, I understand now it's more metaphorical than pratical. In my understanding, the paradox seems to arise when you try to put all your existing elements to fit one of 2 kind of boxes, which are clearly not enough.
The paradoxical statement would be "A barber shaves all those, and only those, who do not shave themselves. Who shaves the barber?" Without the second condition (only those who don't shave themselves) it's non-paradoxical.
And humans are more left-right symmetric than up-down symettric.
If we try to do a headstand to match the image in the mirror then it actually "mirrors" it top/down instead of left/right.
Another example: looking at writing in the mirror, we've actually turned it around to point at the mirror. If we flip it over to point it at the mirror instead then again it'll appear upside down in the mirror instead of left/right flipped.
Edit: I should have read the article, because indeed this is exactly what it explains.
Isn't the point that it does? It flips front and back.
The article itself concludes with: "The reality is that the mirror isn't flipping things horizontally or vertically at all" and you wonder what mental model it thought it was explaining in the first place.
* We never tire of cutesy useless explanations of monads though.
But despite Physics Girl's video embedded in there being much better than the text, I can't fault anyone for not watching it. There are many situations where you can read through something, but can't watch a video.
However, nobody is requiring you to comment critically on something you haven't actually watched, heh.
I haven't seen anything about monads for going on maybe five years now. It seems that trend has come and gone.
Why not both? https://en.wikipedia.org/wiki/Flip_(mathematics)
† Except myself—I do it sometimes!
No matter what convention you use to define relative positions between objects, the mirror is physically creating a symmetric image of those, switching distances from closest to farthest from the glass.
The words “up” and “down” are absolute, but the words “left” and “right” are relative to you. If we instead of “left” and “right” use the words “south arm” and “north arm”, then the mirror suddenly does not “flip” anything. This is a strong clue that the apparent paradox is conceptual, not real.
A typical 6-year old can say what their left-hand is. But if you tell them to point to MY left hand, they will instead point to my right hand. It takes additional effort and training to teach young children how to see from other people's perspective.
The concepts of North and South also fail dramatically when close to the poles.
No they don't. They only fail when on the poles.
If we instead think of our image as like ourselves but turned vertically (around the horizontal axis) - like you lept headfirst into the mirror and landed upright on your head - then you'll find that your left and right sides are the correct way round but the image is vertically flipped. It's very hard to think this way because (a) we're mostly symmetric horizontally, certainly a lot more than vertically, and (b) we very often interact with other people that have turned horizontally (around the verticle axis) to face us but very rarely interact with other people that have turned vertically to face us.
Another aspect that makes this hard mentally is that if you have any identifying non-symmetrical features, like birthmarks, then they appear horizontally flipped in the mirror compared to photographs. Again, it's the photograph that's turned incorrectly. This one is particularly hard to sell, because surely a photo with a ground at the top can't be the right way round? The answer is, for the purpose of matching your left and right, the "correct" way round is for the photo to face away from you. Makes logical sense, but very unintuitive.
I see a two identical individuals raising their opposing hands in unison.
I disagree. In this sort of conversation, "up" refers to the direction from your feet to your head, not away from the ground. If you do a handstand and hold your piece of paper up to the mirror then you'll still find it flipped left-to-right but not top-to-bottom if you turn it the instinctive way, and still find it flipped top-to-bottom but not left-to-right if you turn it vertically.
I disagree. To me, "up" is opposite the direction of gravity. If I were doing a handstand on the ground and someone told me to look up, I'd look toward my feet.
A light source moving away from you to a mirror is getting dimmer, but it’s reflection is getting brighter. That’s a measurable physical property that’s reversed. Similarly, a red or blue shifted object between the mirror has a reflection that’s revered in the other direction. However, when looking at an object behind you that doesn’t happen as the reflection shows the same side.
The distance to the light source grows if you move it away toward the mirror it gets dimmer. The the distance of the light in the reflection however gets shorter so it get brighter.
If the light is right next to you the distance is zero. The reflected light however traveled 2 times the distance to the mirror (dimmer). If you move the light to the mirror both "lights" are one mirror distance away so they have the same brightness (assuming a perfect mirror). There is no "physical property reversed" at all. You could remove the mirror and measure the light intensity twice the distance away instead. Then move the light to the middle where the mirror was and obviously the sensor would measure and increase while you see a decrees in brightness.
In a sense if you replace the mirror with a real reflected universe the same photons will hit your eyes and your perception of the reflection will be identical as if you are seeing an alternate world. That is what we perceive instinctually and we wouldn't be able to tell the difference. You literally cannot prove it, but that's besides the point.
When people refer to flipping in the reflection they are not referring to the physical phenomenon of reflection but they are referring to the interpreted equivalent meaning that if the reflection was replaced with an identical universe to our own how is this reflected universe transformed relative to ours? The answer is: Something flipped.
In this case what we are saying is that the z-axis flipped.
I didn't comment the last part because as its simply wrong. Nothing is flipped at no axis at all. If what you see in the mirror would be another universe then it would have to me MIRRORED to look like we see things in a mirror. Every row of atoms right-angled towards the mirror would have to have the exact opposite order. Would the other universe be flipped? No it would not. The wrong assumption is that your universe and the one you see in the mirror is identical. But it would have to be mirrored it can not be identical and also not flipped. No matter how you would flip the other universe it would never look like what you see in a mirror.
Just use 2 identical but non-simple objects place them next to each other for example 2 coins. No matter how you flip or rotate the coins it will never look like there is a mirror in between. You would need a mirrored coin for that.
The full post is saying that the interpretation of what you see is NO DIFFERENT from an alternate universe. I am not saying this is actually what's going on.
All reflections on all surfaces can be interpreted this way.
The point of the example is to say that the language people use to refer to reflections is to refer to this alternate higher level interpretation and is still valid. Only the most pedantic person will say "nothing" has flipped and call it just bouncing photons.
> If what you see in the mirror would be another universe then it would have to me MIRRORED to look like we see things in a mirror.
This is exactly what I'm saying nothing precludes the alternate universe to be MIRRORED. The alternate universe is a mirrored universe, Get it?
>The wrong assumption is that your universe and the one you see in the mirror is identical.
This is your assumption. I never said this. I said ALTERNATE universe. <--- read the word ALTERNATE. I'm assuming here that you might be delusional and seeing the word IDENTICAL instead of alternate.
>No matter how you would flip the other universe it would never look like what you see in a mirror.
Again if the atoms in this universe and flip them across the Z-axis the light bouncing off those atoms would produce exactly what you see in the mirror.
>Just use 2 identical but non-simple objects place them next to each other for example 2 coins. No matter how you flip or rotate the coins it will never look like there is a mirror in between. You would need a mirrored coin for that.
When I say a z-axis flip I mean inside out. Imagine holding a glove, then turning that glove inside out. That is a z-axis flip. Your coin analogy is completely off.
>I did and I pointed out why your theory is garbage.
I never even made a theory I just used the alternate universe thing as an example of the vernacular people use... people refer to the reflection as a real object and not as bounced photons and this interpretation is valid because it can't be proven otherwise. You just didn't get it. Hopefully you reread my post and realized that it is not my "theory" that's garbage but your brain.
and your distinction of 'real' vs 'conceptual' relative to paradoxes doesn't make sense. a paradox is real because it's conceptual, as paradoxes are relative to humans (or more generally, earthly life).
No dude. The mirror flips left and right Relative to you. The mirror ignores up and down relative to you. The paradox is real when thought of in these terms.
Truth be told the flip is neither left or right nor up and down. actually It is actually inside out on the z axis: towards you. Translational coordinates along the xy plane must be preserved and this is what causes the perceived left right flip.
The actuality is nothing was flipped along x or y, it was kept the same.
That's what trips everyone up.
We're just not used to seeing the fronts of humans who have not rotated relative to us, so the mirror appears to have flipped the image horizontally.
If we customarily rotated around a horizontal axis, i.e. every time you look "behind" you're upside down (note this won't actually work very well given that you'd normally want to rotate around the axis perpendicular to the surface of the Earth, but just for sake of argument...), then we might believe that the mirror has flipped things vertically. It still hasn't actually flipped anything, it's just that we are viewing the front of a person who has not rotated.
You're still right of course.
A table football player looking at himself in the mirror would wonder why he was upside down.
Take a piece of paper, write a word onto it, and turn it towards the mirror. Now observe the word. Is it flipped left to right? If so, it's because when turning it towards the mirror _you_ turned it around the vertical axis. Do this again, this time rotating the paper around the horizontal axis and voilà, the word is now flipped upside down.
IIRC that's Feynman who have written somewhere that mirrors do not flip things right to left, nor top to bottom. They flip things front to back.
Yeah that's a good question. If I'm sitting in my car and looking at an ambulance in the rear-view mirror, it's not the mirror itself that reverses the lettering, and that's the key thing to understand.
The only thing the mirror is doing is reversing the Z-axis. So the question becomes, why does a Z-axis reversal cause me to perceive that the X-axis is getting reversed?
If I turn around to look at the ambulance, I just took my head through a 180 degree rotation around the Y-axis. Then (and only then) does the image get reversed on the X-axis.
If you could imagine being behind the ambulance, and it were made of some imaginary transparent material, you would still see the lettering as not reversed.
The key is to be precise when you use words to describe an optical phenomenon. A mirror reflects, and that's all it does.
1. It flips things in the direction perpendicular to the mirror. If you're facing a normal wall-mounted mirror then that means it flips your "forward" into your "backwards". This is a real physical effect that no one would normally dispute.
2. It appears to flip things left to right, and most people (before mirror-flipping enlightment) would reasonably believe this. But it's a human psychological effect, not a real physical one.
This article is about the second point. You're talking about the first point. The placement of the mirror is a red herring: even with a ceiling mounted mirror, if you show a piece of paper to it by putting it above your head in the natural unenlightened way and look up, you'll find the text is still flipped left to right. In fact it maybe even emphasises the illusion because you can turn to face any direction (and without thinking you'll turn the piece of paper too of course) and still see the same effect!
(BTW I upvoted your comment because it's not the only comment to post this mix up - but it seems to be the first - so I think it deserves a bit of visibility for others thinking the same thing.)
Sometimes I think we're nearing the end of human advancement because we've built up so much knowledge that we're forgetting as fast as we learn.
But our environment has a preferential direction in that we orient ourselves with respect to the Earth's surface, and the horizon is, well, horizontal. Our body is constructed with vertical bilateral symmetry which means our "halves" are horizontally oriented when in a normal standing or sitting position.
All of this causes us to perceive and define reversed chirality in terms of handedness, left or right. Things that we perceive with a left-to-right orientation appear as right-to-left if chirally reversed.
If we were spherical beings with limbs and eyes poking out at various angles from our bodies, living in microgravity on a space vessel, we would just perceive the reversed chirality in our mirrors as "enantiomorphic" and not assign a spurious L/R directionality to it.
However, this isn't the only way to "flip" (i.e. rotate back). It seems like the only way because it is the only way to rotate the mirror image onto something that aligns with the non-mirror reality. The head must align with the head and the legs must align with the legs, and there is only one rotation that makes it work.
But now imagine you had some sort of isle of man flag [1] type body. That is, your arms remain, but your feet and your head turn into an arm. For lack of better term, call your "head-arm" upper-handed and call you "leg-arm" lower-handed.
Now when you look at your freakish mirror image, there are TWO ways you can rotate your the mirror image to correspond in some way with your body. You can rotate as usual around the z-axis, but you can also rotate around the y-axis. In that case, your left and right arms are not flipped, but your upper-arm and lower-arm are flipped.
That is, the whole confusion occurs because humans are symmetric in one dimension and non-symmetric in another.
We are:
==Y==
X=O=X
==Z==
As opposed to
==Y==
X=O=X
==Y==
[1] https://en.wikipedia.org/wiki/Flag_of_the_Isle_of_Man
A mirror doesn’t flip left to right. It flips front to back. YOU flip left to right when you turn things to the mirror.
Look in a mirror. Raise your right hand, THE HAND ON THE RIGHT GOES UP. There is no reversal, it's a myth.
When you stand facing a real person, THATS the reversal. If they raise their left hand, you see it on the right. Because THEY are reversed. They are facing the opposite direction.
IOW the mirror is inessential. We can ask the same question about just a transparent piece of paper.
The leading A and the trailing E are in the same right to left position that they are in the real sign. There is no reversal.
You would need to flip it horizontally to make it look "normal"
Hhhmm, no. I can't even understand the supposed problem / paradox here?
Wait. How did you turn the book? Right-to-left? Well, that's why its 'backward'. Try it again, but this time flip the book vertically to face the mirror. Now the test is not flipped right-to-left, but top-to-bottom.
It's nothing to do with 'physics'. Its just perception.
The internet is fucking lazy anymore.