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Math Professor Invents Non-Reversing Mirror

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Re: Math Professor Invents Non-Reversing Mirror

#61

Post by anonymous »

sliverstorm wrote: post #55
jpdoctor wrote: post #6

> When you look in a normal mirror, the image you see of yourself is in reverse. Funny thing: Mirrors don't reverse left and right. They reverse front and back. So this "non-reversing" mirror is actually mapping y to -y, x to -x (Where the mirror is in front of you in the z-direction. Curious. Edit: I believe tomerv below is correct: x is mapping to -x but y is kept the same.

I still don't intuitively understand how reversing front to back results in what we perceive as a left/right inversion.

The real headscratcher comes when you realise that all reversions are equivalent disregarding rotation. That is, reversing left/right is the same as reversing up/down and rotating around z.

You can actually get a up/down mirroring effect (intuitively speaking) by standing on a mirror and holding a piece of paper perpendicular to it. It will look up/down reversed, not left/right.

Re: Math Professor Invents Non-Reversing Mirror

#62

Post by saraid216 »

woah wrote: post #56
rada wrote: post #48

Earlier quoted context omitted.

Fifty Shades is pornography for women. IMHO that's the only reason everyone is clutching their pearls about the bad writing. Your typical male pornography storylines/cinematography are much, much worse - and yet they are typically spared the high-brow literary scrutiny.

Yep, must be the patriarchy oppressin' again. The reason that 50 Shades of Grey is subjected to highbrow literary scrutiny, is that it pretends to be highbrow literature. Male pornography usually makes no pretense, being more along the lines of logjammin' "ich bin here to fix your kable"

Not really. The reason 50 Shades gets its scrutiny is because it has enough exposure. There's some damn good male pornography (yes, it's literary; yes, I read it) out there, but it's not for sale at Barnes & Noble.

That's the patriarchy angle, if you actually want it.

Re: Math Professor Invents Non-Reversing Mirror

#63

Post by r00fus »

Jun8 wrote: post #14

And he's holding MTW's Gravitation tome in the photo! BTW: Why do so few people pose with their favorite books (or holding any book) in profile photos, this was common when people had their portrats painted in the past. Has it become a turn-off?

> And he's holding MTW's Gravitation tome in the photo!

I think it's because it's book with very large title font, which shows the mirror isn't reversing the text. It just also happens to be a favorite book of his (much better than if you saw "$AUTHOR_NAME" which is what you'd see for popular fiction, wouldn't you say?)

Re: Math Professor Invents Non-Reversing Mirror

#64

Post by QuixoticChris »

sliverstorm wrote: post #55
jpdoctor wrote: post #6

> When you look in a normal mirror, the image you see of yourself is in reverse. Funny thing: Mirrors don't reverse left and right. They reverse front and back. So this "non-reversing" mirror is actually mapping y to -y, x to -x (Where the mirror is in front of you in the z-direction. Curious. Edit: I believe tomerv below is correct: x is mapping to -x but y is kept the same.

I still don't intuitively understand how reversing front to back results in what we perceive as a left/right inversion.

Since left and right and up and down are both the same, it's essentially as though you're looking through the back of the object. Imagine if you made a sign clear and looked through the back. Even though no reversal has taken place, the text looks backward. This is why things appear reversed.

If you are confused about how left and right are not actually switched, I would say the easiest way is to think in absolute terms, not relative. That is, don't think about left and right, think about east and west. Face north and paint your east (right) hand red. Now when you look at a mirror (you're still facing north), your east hand is red, but the reflection's east hand (think in real world terms here) is also red. That's because the reflection's horizontal aspects have not been reversed.

Richard Feynman enjoys discussing this: http://www.youtube.com/watch?v=msN87y-iEx0&gl=CA

Re: Math Professor Invents Non-Reversing Mirror

#65

Post by rprospero »

sliverstorm wrote: post #55
jpdoctor wrote: post #6

> When you look in a normal mirror, the image you see of yourself is in reverse. Funny thing: Mirrors don't reverse left and right. They reverse front and back. So this "non-reversing" mirror is actually mapping y to -y, x to -x (Where the mirror is in front of you in the z-direction. Curious. Edit: I believe tomerv below is correct: x is mapping to -x but y is kept the same.

I still don't intuitively understand how reversing front to back results in what we perceive as a left/right inversion.

Print out a word in a very large font on a piece of paper. Now, hold the blank side up to a light and try to read the word - it will be backwards. This is because you're reading the paper back to front.

Our mind makes it a left to right inversion because we first try to think of it as a rotation. Look in the mirror while holding a hat in your left hand and a shoe in your right (the objects are arbitrary - substitute where necessary). Now, look in the mirror. The hat will be on YOUR left and the shoe will be on YOUR right. There's no left to right swap. The reason that I capitalized "YOUR" is that I don't want you considering whether it's on the left or right of your REFLECTION. That's where the left to right inversion mistake comes from - we think the shoe is on the reflection's left. Normally, when we're facing another person, that person has rotated 180 degrees to face us. That puts her left on our right and vice versus. We mentally assume that's the case with the reflection in the mirror - that the reflection's right hand is on our left. However, the reflection wasn't rotated 180 degrees to face us. It was flipped front to back. The reflection's left hand is on our left, just as you would expect from something that has not been flipped left to right.

Re: Math Professor Invents Non-Reversing Mirror

#67

Post by Retric »

anonymous wrote: post #61
sliverstorm wrote: post #55

Earlier quoted context omitted.

I still don't intuitively understand how reversing front to back results in what we perceive as a left/right inversion.

The real headscratcher comes when you realise that all reversions are equivalent disregarding rotation. That is, reversing left/right is the same as reversing up/down and rotating around z. You can actually get a up/down mirroring effect (intuitively speaking) by standing on a mirror and holding a piece of paper perpendicular to it. It will look up/down reversed, not left/right.

It's still left right reversed though, just try it with something printed on the paper.

Re: Math Professor Invents Non-Reversing Mirror

#68

Post by cma »

sliverstorm wrote: post #55
jpdoctor wrote: post #6

> When you look in a normal mirror, the image you see of yourself is in reverse. Funny thing: Mirrors don't reverse left and right. They reverse front and back. So this "non-reversing" mirror is actually mapping y to -y, x to -x (Where the mirror is in front of you in the z-direction. Curious. Edit: I believe tomerv below is correct: x is mapping to -x but y is kept the same.

I still don't intuitively understand how reversing front to back results in what we perceive as a left/right inversion.

Ambulances have the word Ambulance flipped backwards, not flipped upside down.

This intuitively seems to be a major break of symmetry, why would a mirror have a horizontal preference?

It isn't the mirror with the preference, but the vehicle. To understand why, consider an ambulance facing you head on with the word "AMBULANCE" printed on it and the paths it could take to show up in your rear-view. It could move along a lateral half-circle or a vertical one (or something in-between). If it went along a vertical half-circle it would end up upside-down and behind you; since it goes along a lateral one it also gets laterally-flipped, but because cars have left to right mirror symmetry , you don't notice (except for the words ambulance).

We have a huge bias evolutionary bias towards that type of lateral symmetry (e.g. in animals, other humans) and to things moving along a lateral plane while maintaining vertical orientation.

Re: Math Professor Invents Non-Reversing Mirror

#70

Post by Someone »

sliverstorm wrote: post #55
jpdoctor wrote: post #6

> When you look in a normal mirror, the image you see of yourself is in reverse. Funny thing: Mirrors don't reverse left and right. They reverse front and back. So this "non-reversing" mirror is actually mapping y to -y, x to -x (Where the mirror is in front of you in the z-direction. Curious. Edit: I believe tomerv below is correct: x is mapping to -x but y is kept the same.

I still don't intuitively understand how reversing front to back results in what we perceive as a left/right inversion.

I do not know whether this will help or confuse, but it is a different way to look at it:

Look into a mirror with your nose pointing North. Your left hand will point West, and your right hand will point East.

Your mirror image has a nose pointing South, a left hand pointing West (!) and a right hand pointing East (!)

You know it is his left hand pointing West because it moves when you move your left hand. Also, you may wear a ring or have distinctive features on one hand.

You know that left hand is pointing West because you can see the sun set in that direction.

So East and West stayed where they were. Also, up and down still are where they were; rain still falls on your head, not on your chin.

The directions that changed are North and South.

The effect of that is that, from the point of view of the mirror image, East and West seem to have switched sides. The mirror image is looking South, and yet, West is to its left and East to its right.

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