Re: mirrors: front-to-back

["John S. Denker" <jsd@MONMOUTH.COM>]

At 04:56 PM 8/4/00 -0400, Michael Edmiston wrote:
> images observed in the mirror are ... reversed "front to back."

Exactly so!

> Note, a mirror does not reverse left/right directions as some respected
> textbooks claim... that is simply wrong.

Indeed!  This is a very widely held misconception.

Most people don't care about what a mirror is or what it does... but
if/when they start wondering about it, this misconception causes all sorts
of difficulties.

Here is a modest conjecture about how such a misconception could arise:

Suppose you are facing south.  You hear an interesting noise to the north.
You turn around to face it.  The normal way to turn around is to rotate
yourself around a vertical axis.  It would be highly abnormal to rotate
yourself around a horizontal axis, so that you wind up doing a handstand
--- although this would quite effectively leave you facing north.

Rotations about a vertical axis are, to a good approximation, a symmetry of
everyday terrestrial life.  Rotations about a horizontal axis are not.

So, if I hold a book to a mirror, it can be equally well described as
  a) being reversed front-to-back, or
  b) being rotated 180 degrees about a vertical axis _and_
     reversed left-to-right, or
  c) being rotated 180 degrees about a horizontal axis _and_
     reversed top-to-bottom.

According to this conjecture, people latch on to description (b) and fail
to notice the rotation, perhaps because rotations about a vertical axis are
such a common and unremarkable part of everyday life.