Re: Fabulous Adventures In Coding (Eric Lippert)

Tech-Archive recommends: Repair Windows Errors & Optimize Windows Performance

From: Lasse Reichstein Nielsen (lrn_at_hotpop.com)
Date: 02/13/04 

Date: Fri, 13 Feb 2004 20:39:20 +0100

"Richard Cornford" <Richard@litotes.demon.co.uk> writes:

> If you are loosing sleep over it try this formulation: All perpendicular
> distances to the plane of the mirror are rendered negative in the
> reflection, their magnitude remains the same and there are no other
> transformations.

Hmm. The distance alone won't explain why writing on a paper also
looks "mirrored".

But the conceptual problem, as I prefer to think about it, is that you
*expect* the image to be reversed, when in fact it isn't.

If you hold up a piece of paper in front of you and look at it in a
mirror, you compare it to how you *would* look at it directly (even if
you haven't even looked yet).

To look at it directly, you would *rotate* it around the vertical axis
in order for it to face your eyes. That would swap left and right. You
*could* rotate it around other axes, but the vertical one is the one
you consider most natural (keeping upside up).

So, looking in the mirror, you see a non-rotated image, compare it to
the rotated image, and conclude that the *mirror* is the one doing it
wrong.

You could just as well rotate the paper around the horizontal axis in
order to see it directly. You would then be able to conclude that the
mirror had turned it upside down in comparison to "how it really
looks".

Or, to go at it in the other direction: Take a paper with some writing
on it, stand in front of a mirror with the paper in front of you,
still looking directly at the writing. Then rotate the paper around
the horizontal axis. What you see in the mirror is the writing, except
that top and bottom have been reversed. The letter to the left is still
the first of the writing, but it's top has become its bottom.

You are not surpriced, after all, you flipped the paper upside down
yourself.

The try again, but rotate around the horizontal axis. You now see the
writing in the traditional "mirrored" style, where left and right are
reveresed, but top and bottom are retained. You should not be
surpriced here either, after all, you flipped the paper left-to-right
yourself.

For bonus points: try flipping around a diagonal and try to decide
which direction is reversed. :)

Mirrors mirror quite obliviously to direction. Which way something is
"wrong" only depends on how you imagine you would reverse it to look
at it directly, and keeping the upside up is how we expect that to
happen (and experiments with beer mugs have enforced it).

/L 

-- 
Lasse Reichstein Nielsen  -  lrn@hotpop.com
 DHTML Death Colors: <URL:http://www.infimum.dk/HTML/rasterTriangleDOM.html>
  'Faith without judgement merely degrades the spirit divine.'

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