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

by birtanpublished on September 4, 2020

you hello everybody I'd like to talk about a little problem that has intrigued people ever since we discovered mirrors let's have a look at what I see when I look into the bathroom mirror in the morning

Scary okay when I point up mirror mythology points up when I point down mirror mythology points down when I raise my left hand mirror mythology raises his right hand when I raise my right hand mirror mythology raises his

Left hand strange also with writing the tops of these characters are on top pause here and for the mirror mythology and the bottoms are at the bottom here and also for a mirror mythology but this one here

Runs from left to right the other one runs phone right to left so what's going on here it appears that mirrors reflect left and right but not up and down and in this setup everything's sort of equal so if something gets flipped one way it

Should also be flipped the other way right now just to scramble your brain a little bit further have a look at this photo here of a mountain reflected in a mirror lake here up and down is being flipped but not left and right now if

You find all is intriguing very good company I've linked in a video here of one of my favorite scientists Richard Feynman talking about him being a tricked by this Richard phiman genius Nobel laureate really really famous

Theoretical physicist this is a very slippery eel to pin down because when it comes to words like flipping mirror reflection mirror images ordinary language is very fuzzy for example it doesn't distinguish between different

Phenomena when it comes to reflection or mirror images of 2d objects and 3d objects and that's also part of the reason why most of the explanations of this puzzle even the really really good ones kind of go off course a little bit

And maybe in the end confuse more than they explain so what I thought I'd do today is try to provide a there's many really clean explanation so there's one very important observation which lets a sidestep this

Work on fusion 2d 3d and that is whatever the explanation if it works it has to work for 2d things like writing here my t-shirt and if it works for 2d things it automatically works for 3d things why

Because I can replace any 3d things like myself with a photo which is a flat thing and show it to the mirror ok so a clean explanation of the puzzle should just talk about 2d things ok I've prepared a 2d thing cat written on a

Piece of paper now what exactly is the mirror image of a 2d thing like this well let's have a look look at this thing in the mirror there's the mirror image now to really pin this thing down let's press the piece of paper against

The mirror now the original and the mirror image are basically in the same spot so corresponding points are touching each other so if I were to make the piece of paper transparent except for the writing the back of this would

Actually be the mirror image right and I've actually arranged this so that this actually works so now things are transparent you can see this one object is one object its picture frame has the original and the mirror image on both

Sides so it's really the same thing in some ways and this provides us with a short answer to our puzzle which is this when we're saying the mirror exchanges left and right but not up and down what we're really doing is we are comparing

The original to the mirror image so we first look at the original and then to be able to look at the mirror image we make a flip to either show the thing to the mirror or here the physical object so the flip is done by us in some way so

There's a flip in there it's not the mirror the mirror reflects whatever is here on the right comes back straight here where I was on top comes back straight here whatever see a comes back straight here

The mirror doesn't exchange anything okay that's a short answer but there's a bit more to it so for example what what about this this mountain reflected in a lake

So what I want to do now is to compare the original to the mirror image in all possible ways and see what I can say in general okay and I've prepared a very special object to the object it's just a blob to take out any sort of bias that

We might have I'm not using a cat or something else recognizable okay let's have a look at the mirror image there it is but even this representation has a bit of a bias built in the way we kind of

Put these things next to Joe will become very important in a little while but for a moment let's just put this thing down in an arbitrary way okay now now we're comparing original to mirror image and if you just kind of looked at this for

The first time you may not even see that there's any similarity between those two things definitely no flipping happening but when we move things one on top of the other we get one of those strange rush

Of pictures with a nice symmetry axis here pull them back apart again and you'll see that the mirror image differs from the original by a flip across this distinguished axis there you go and that will always be the case no

Matter how we juxtapose original and mirror image there's always going to be this distinguished access so whenever we're comparing original and mirror image there's a distinguished axis across which we flip together from one

To the other it's always going to be there and that of course explains most of the puzzle but we still have to somehow explain why do we get a vertical axis and not some other axis but actually usually when you look at

Something by a mirror you see the thing and a mirror image at the same time and whenever you do this the s that this axis is going to be apparent so the bathroom mirror service a bit different from that because there you only see the

Mirror image so let's us have a look at the usual setup you look at something buy a mirror and you see the mirror image and the original where the excess is then depends on the relative position of the mirror and original so in this

Case you basically got the mountain and Mirror Lake set up the mirror axis is going to be down here and we actually can do the flipping here physically like so

when I changed the position of the mirror axis will change will always be the bottom part of this mirror frame here and we can do the flipping so there's the flipping happening and we

Move things a little bit further there's a flip like that happening now let's have a look at the special case bathroom mirror right bathroom mirror will only see the mirror image actually have to fess up here I've got a special guest

Again the blob was really not a blob it was Professor fancy was one of my favorite characters from Futurama I'm a huge Futurama fan so this is what Professor Farnsworth sees in the mirror in the morning okay now that's the only

Thing he sees now he makes a statement about left and right but not up and down how does the original come into the picture well he or we supply it we somehow put it in virtually in our minds so how do we put it in well if I give

You your original on a piece of paper so would you put it next to that one like that probably not the way you put it next to the mirror image is going to be like this there's a certain bias in which we put mirror image and original

Next to each other it's our bias it's what we do we provide the second image in a certain way and it's kind of natural I don't mean this guy here is basically like a person standing up in front of us with a

Natural up going up so when we put original next to that what we'll also put up up because that's how people stand in space so the explanation Falls is whenever you compare original to mirror image there's always going to be

A flip axis and for a special case of the bathroom mirror we arrange things in a certain way so we arrange for the missing picture to be compared to the original in a certain way and that then ensures that we get a vertical axis now

Often you find explanations of this puzzle culminating in the statements marathoned exchanged left and right they don't exchange up and down what they do do is exchange front and back that's a true statement but it's

Actually confusing in this context as I said before you only need really to talk about 2d images that's the essential bits as soon as you kind of drag in the 3d bits things get confusing so explanation for the puzzle is finished

Now what comes now as a footnote but left and right doesn't get flipped well that's reflected by these two arrows here going in the same direction up and down don't get flipped d'etre corresponds to these two red arrows go

In the name direction but what happens to the green arrow the green arrow that's kind of pointing towards the mirror the reflection is actually pointing in the opposite direction okay so in terms of 3d objects like myself a

3d mirror image is actually only inverted in the direction of the of the green arrow that's how I turn myself into my mirror image

You you also us being roughly self-similar across this mirror plane here probably contributes to the overall puzzlement

That we experienced at the very beginning now I'm really crazy about mirrors and it would be a lot of more things that I can say what I want to do is I would just leave you with a couple of fun things and for those have asked

My friend Professor Farnsworth to model so he is standing in front of a straight mirror now what I want you to do is I want you to get a spoon like this and then you look at it in various ways so for example if you look into the spoon

And something strange happens all of a sudden you see yourself standing on your head if you look at a spoon like this you will actually just see a normal mirror image a little bit distorted now for something really spooky just take

The spoon and put it really close to one of your eyes now you can try and explain those things in the comments looking forward to your answers also if you want something else crazy to experiment with you need a mirror like this I cut this

Out of a garbage bin and what a mirror like this does is it actually shows you like other people see you so not flipped so that this thing doesn't show your normal mirror image it shows you the way other people see you a little bit

Distorted with this one but basically that's what it is so all very nice effects hopefully you've enjoyed this and hopefully you'll be able to provide some explanations here that's it for today


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