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From: throopw@rtp47.UUCP (Wayne Throop)
Newsgroups: net.physics
Subject: Re: Yet Another Flaky Paradox
Message-ID: <64@rtp47.UUCP>
Date: Sat, 8-Jun-85 13:28:39 EDT
Article-I.D.: rtp47.64
Posted: Sat Jun  8 13:28:39 1985
Date-Received: Thu, 13-Jun-85 22:47:09 EDT
References: <5377@tektronix.UUCP> <53@rtp47.UUCP> <206@kontron.UUCP>
Organization: Data General, RTP, NC
Lines: 65

[Hit "n" now, or forever hold your peices]
[or, what does a one-eyed person see in a mirror?]

> > > When you look in a mirror, the image you see is reversed left to right.
> > > -- Carl
> > However, ... flipping the image in the verticle axis rather than the
> > horizontal axis is a convention due to gravity bias[.] I find [this
> > explaination] unconvincing.  So here is a more convincing (to me)
> > explaination.
> > -- Wayne Throop
>
> I have it on good authority that if your eyes were above and below
> your nose, instead to the left and right, mirrors would indeed flip
> in the vertical direction instead of the horizontal. Something to do
> with incidence angles. Of course to get it to flip both ways, you
> would need four eyes.
> -- Steve McIntosh

Since mirrors don't reverse right-left even when eyes are arranged to
the left and right of the nose, I see no reason to conclude that if eyes
were arranged  vertically up-down would be reversed.  I don't know what
*you* see when you look in a mirror, but I see this situation (viewed
from above):

            "reality"      mirror       image

               left          |           left
                |            |            |
           back-+-front      |      front-+-back
                |            |            |
              right          |          right

If up-down were included, it would behave like right-left, and would not
be reversed.  If you had one eye or a dozen, things would still be the
same.  If your eyes were arranged vertically, horizontally, inside out,
upside down, things would still be the same.  If your eyes were
backwards, on stalks, or in bony pits, things would still be the same.

The illusion of left-right reversal is created by an odd convention.
The obvious transform to map "reality" onto "image" is reversal of
front-back.  Most folks, when looking in a mirror, think of the
transform "rotate 180 degrees on the up-down axis and reverse
left-right", which also works.  An equaly valid (and similarly
overcomplicated) transform is "rotate 180 degrees on the left-right axis
(ie, stand on your head) and reverse up-down".

Of the three given transforms, "reverse front-back" is the simplest,
the one involving rotation about the up-down axis is most conventional,
and the one involving rotation around the left-right axis is almost
never used (and of course there are a slew of other almost-never-used
transforms that will perform the perceived mapping).

The point of all this is that the arrangement of eyes along the up-down
axis wouldn't make the rotation about the left-right axis any more
appealing, since the preference for the up-down-axis-rotate transform is
rooted in the "gravity bias".  That is, because of gravity it is easy to
both do and think about rotation around an up-down axis, but hard to do
or to think about rotation around a left-right axis.

The whole point of this so-called "paradox" is that the initial
statement, "When you look in a mirror, the image you see is reversed
left to right", is in error.  My conclusion is that the above mentioned
"good authority" should be sent in for routine maintenance.  :-)
-- 
Wayne Throop at Data General, RTP, NC
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