
Math Professor Invents Non-Reversing Mirror - ColinWright
http://www.techfragments.com/1774/inventions-non-reverse-mirror/
======
jpdoctor
> _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.

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

~~~
anonymous
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.

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

------
Jun8
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?

~~~
pretoriusB
Because most people don't read at all, or read BS (self-help books, how to
succeed, cheap thrillers, 50 shades of gray...)

~~~
jeremyarussell
Have you read fifty shades? I find that people like to bag on stuff they've
never actually experienced first hand.

~~~
jere
Embarrassingly, I listened to a youtube video where a woman read the book
aloud (I listened for about 30 pages). She ended up hitting herself in the
head about a dozen times because the writing is that awful.

~~~
rada
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.

~~~
woah
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"

~~~
saraid216
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.

------
jere
After knowing the Feynman puzzle, I think this is probably more correctly
described as a _reversing_ mirror.

If you look into a metal spoon, you'll see both X and Y reversed. So I'm
wondering if you could make this mirror simply by only curving the horizontal
part. That's kind of what it looks like in the photo. And if so, why didn't
someone think of this early? It's quite obvious.

~~~
eru
People thought of this before--just place two mirrors at a 90 degree angle.
The guy's innovation is to make it very smooth.

------
naner
I'm having a hard time visualizing this.

If I am standing directly in front of this mirror and slowly reach forward
with my right hand until I touch the mirror, will my hand be touching its
mirrored self?

~~~
adamman
I'm guessing that the only way you could touch the mirror image of your finger
is by doing so in the middle of the mirror. If you move the finger out toward
the shoulder, I'm betting your arm would stretch off the mirror away from your
body. I could be totally wrong though.

~~~
dllthomas
Look at the cover of the book that the trick mirror is resting on.

------
joshdick
For those interested in learning more about this, including the math behind
the mirror's curve, check out Prof. Hicks's website:
<http://www.math.drexel.edu/~ahicks/>

~~~
Someone
Relevant part (<http://www.math.drexel.edu/~ahicks/papers/physics-today.pdf>):

 _"As a second example, take the object plane and the image plane to once
again both be at x = 1 and define T(1, u, v) ≡ (1, −αu, αv). As with the flat
mirror of the previous example, the transformation scales the image plane, but
be- cause of the relative minus sign in the y and z coordinates, the solution
surface will not reverse an object as a conven- tional mirror does._

 _The relative minus sign also means, alas, that no exact solution surface
exists. I obtained an approximate solution surface confined to the rectangular
volume x = 34 ± 1 cm, y = z = 0 ± 3 cm, and constructed a prototype mirror.
With α = 160, the mirror’s field of view is wide enough that I could see
myself in the mirror when it was held at arm’s length, as shown in figure 1.
To achieve the appropriate ray paths, the mirror is saddle-shaped."_

So, this mirror only does its magic in a small volume; if you move your eye
closer to the mirror or sideways, or even when you look at it with two eyes,
the effect breaks.

From cursory reading, I even get the impression that this mirror is also
tailored to the positions and shapes of the objects being photographed.

But as I said: cursory reading. Corrections welcome.

------
phaet0n
Feynmann's great mirror story [1]. Try and solve the puzzle before watching
the whole clip.

[1] <http://www.youtube.com/watch?v=msN87y-iEx0>

------
drcube
How can he "invent" this? Hasn't it been known for years? It's the same
principle as two mirrors at right angles, only instead of a corner, there is a
gentle bend. I'm pretty sure I read about this in George Gamow's "One, Two,
Three... Infinity".

------
SethMurphy
This would be great for giving myself a haircut, but not so much for shaving.
Probably because it is more left to right than back to front. I also shave
more often and have built up my muscle memory more.

------
mistercow
>The precise manipulations change the directions light rays are reflected off
of the surface in a manner similar to changing the angles of millions of tiny
facets on a flattened disco ball, but decreasing the size of each facet until
a smooth surface is achieved.

Oh, so it's like a Fresnel lens, but it's a mirror instead of a lens. That's
pretty clever. You get the non-reversing property of a curved mirror, but it's
still flat.

Edit: Another way of thinking of it is that it's a normal map applied to a
real-world object.

------
salimmadjd
This is probably a small array of double mirror. If you look at the images you
see slight loss of light (a bit darker) on his none-reversing mirror. Which is
probably due to the gaps between the arrays behaving a bit like a scrim in
shooting sets.

I think the invention will have some uses. For anyone who has tried to do
anything that requires precision in front a mirror the reversing of the mirror
is disorienting. I could even imagine mechanics who use a mirror to see what
they are doing in tight spots be able to use it to coordinate their motion to
put the ranch on the right nut when they are using a mirror.

~~~
joshdick
No, it is not two mirrors. What Prof. Hicks made is a single mirror. The
linked article explicitly says this.

------
prawks
Completely disagree with the OP's idea of putting this in a rear-view mirror.
One benefit of a rear-view mirror is that things that are on the right side of
the mirror are to the right of you, and vice versa. This mirror would break
that, unless I'm misunderstanding it.

I'm interested in what applications this may have, if any really. I can see it
working as a vanity mirror quite well, as then you can truly see yourself as
other do. Aside from that?

~~~
shardling
The rear-view mirror mentioned by the article in passing is not a reversing
mirror -- it's just supposed to be another example of this guy's expertise at
fabricating mirrors, in this case to improve the field of view and to remove
blind spots.

------
raimondious
You can simulate one of these yourself by getting a wide flexible plastic
mirror (dimensions along the lines of 1:4) and bending it to be concave until
you look undistorted. Looking into this bent mirror, if you raise your right
hand, the hand on your left side in the reflection will move.

~~~
jlgreco
Perhaps even easier is to secure two flat rigid mirrors at a right angle,
like: /\

------
DanBC
He's looking for uses beyond art galleries. I'm reminded of "The Man Who
Mistook His Wife For A Hat" by Oliver Sachs.

([https://en.wikipedia.org/wiki/The_Man_Who_Mistook_His_Wife_f...](https://en.wikipedia.org/wiki/The_Man_Who_Mistook_His_Wife_for_a_Hat))

------
duaneb
Is this not just a reflective lens? I.e. a quadratic surface? If it is, I just
assumed people didn't use them because non-reversing mirrors are actually
rubbish. There's a reason cameras reverse the image in software but
transmit/store the non-reversed image.

------
leeoniya
was hoping for more technical details. maybe they're still going through the
patent application?

~~~
andrewcooke
according to the wikipedia article it's a surface of micro-mirrors that work
in pairs. so it's basically a pair of mirrors scaled down and repeated.

<http://en.wikipedia.org/wiki/Non-reversing_mirror>

not very exciting really.

~~~
joshdick
No, that is not what Prof. Hicks made. His mirror is a single curved piece.

Source: I am a former undergrad research assistant of his.

~~~
andrewcooke
huh. thanks. so that's the second type listed at wikipedia? or am i confused?
perhaps you or he could fix / clarify the wikipedia article? i guess i could
but it feels odd to do it third-hand...

~~~
joshdick
I wish I could give you a link to one of Prof. Hicks's published papers on the
topic, but I'm having trouble finding one that isn't behind a paywall. This
seems like a nice introduction:
<http://www.math.drexel.edu/~ahicks/papers/physics-today.pdf>

If you have access to journals through a university, you could take a look at
some of his papers yourself (His website is
<http://www.math.drexel.edu/~ahicks/>). They're easy enough for a sophomore to
recreate the results. (I know, because I did for an independent study with
Prof. Hicks.)

------
readme
I can't wait until these are on the market. I could save so much money on
haircuts. (Assuming the motor-confusion doesn't happen when using this mirror,
because the image is not reversed)

------
eps
A video of this mirror in action would've been very helpful.

------
Thrymr
Not exactly new: <http://www.truemirror.com>

~~~
joshdick
No, that link is for 2 mirrors.

What Prof. Hicks made is a single curved mirror. That is new. That is why his
results got published and he was awarded a patent for it.

If you had bothered to read the linked article, you'd already understand the
distinction.

~~~
jonhendry
The curved mirror exhibits distortion at the edges, which doesn't seem to be a
problem with the two-mirror approach.

Also the curved mirror doesn't present the image at full size, it appears
smaller.

------
DeCaMil
Breaking news.... HN abuzz with 2.5 year old story...

Hick's work was published via New Scientist
(<http://www.newscientist.com/gallery/dn16585-amazing-mirrors>) in February of
2009.

------
0x0
I'd love to see a movie demonstrating what this looks like!

~~~
ubercow13
Here's a pic [http://www.newscientist.com/gallery/dn16585-amazing-
mirrors/...](http://www.newscientist.com/gallery/dn16585-amazing-mirrors/1)

~~~
GIFtheory
That links also mentions that his amazing 45 deg. FOV side-view mirror is
banned in the US, because curved mirrors are illegal in the US. What the hell?
Doesn't congress have anything better to do than shoot us all in the foot,
repeatedly?

------
catshirt
a different implementation of the non-reversing mirror:
<http://www.truemirror.com/>

bonus points: you can buy this one!

------
lurkinggrue
I want one.

------
thejad
This is pretty great!

~~~
tesko8482
Want.

