A Mirror to Physics

    "Although to penetrate into the intimate mysteries of 
     nature and thence to learn the true causes of phenomena 
     is not allowed to us, nevertheless it can happen that 
     a certain fictive hypothesis may suffice for explaining 
     many phenomena."
                                     Leonhard Euler, 1748

     Question: "What does that sign say?"
     Answer: "It doesn't say anything, you have to read it."
                                                Traditional


One of the most frequently asked questions in sci.physics is
why the image of an object appears reversed left-to-right rather 
than top-to-bottom when viewed in a mirror.  By implication, the 
"reversal" in question is relative to how the object appears when 
viewed directly.  The answer, as explained by every introductory 
text on optics, is simply that an image viewed through a mirror 
appears reversed about the axis around which the viewer rotated 
his field of sight in turning from the direct to the reflected 
image.  Since we ordinarily rotate our field of sight about a 
vertical axis, mirror images usually appear reversed left-to-right.  
(For a fuller explanation, see What Mirrors Do.)

Sometimes, however, we come across a completely different 
"explanation" of "what mirrors do", the idea being that mirrors 
actually reverse things "front-to-back", as illustrated by a 
drawing like this:

                             mirror     reflected
                 chair         |         chair
                               |
                 /|            |            |\
                 ||            |            ||
                 ||____        |        ____||
                 |____/|       |       |\____|
                 ||  | |       |       ||   ||
                 |   |         |        |    |
                               |

The most interesting thing about this "explanation" is that it's 
clearly based on a counter-factual premise.  The "chair" shown on 
the right side of this drawing does not exist.  What really exists
are reflected rays of light bearing a particular relationship to
the direct rays of light from the chair.  The corresponding images,
which are 2D projections of those families of light rays for a
particular observer, appear reversed about the axis of the observer's 
rotation.  Nevertheless, the counter-factual explanation based on 
the fictive hypothesis of an imaginary chair with imaginary 3D 
properties appeals strongly to many people.  It's actually given 
as "the answer" in the sci.physics FAQ written by Scott Chase based 
on an "explanation" given in one of Isaac Asimov's books.

This is a nice example of a "fictive hypothesis" that is quite
successful at explaining things - up to a point.  If we are
standing next to the real chair we can deduce how the reflected
image will appear from various points of view by *imagining* 
another chair in the fictitious "space" on the other side of the 
mirror, with the understanding that all "objects" in that "space" 
are reversed front-to-back, i.e. symmetrical with the real objects 
about the plane surface of the mirror.  Of course, there's a point 
at which this fictive hypothesis ceases to be useful.  For example, 
if we try to walk over to the reflected chair and sit down we 
quickly discover the limitations of conceptualizing reflected 
images as 3D objects.

The reason this counter-factual description seems so natural is that 
we are accustomed to dealing with our psychological constructions 
rather than with the primary sense perceptions on which those 
constructions are based.  We normally presume a fairly reliable 
isomorphism between our perceptions and the associated mental 
constructs, but mirrors are somewhat unusual in that they present 
us with sense perceptions that we intentionally construe in a 
counter-factual way.  A mirror is *designed* to simulate the sense 
impressions of things that really aren't "there".  Notice that 
mirrors are among the few objects on which we almost never focus 
our eyes.  We don't look AT mirrors, we look IN mirrors, with our 
focal lengths adjusted into the fictitious space on the "other 
side".

In addition to the natural tendancy to deal with our mental
constructs rather than our direct perceptions, the counter-factual 
explanation of what mirrors "do" is motivated partly by the 
traditional desire of physicists to separate the observer from 
the phenomenon.  The original question asks what mirrors "do", and 
we tend to think this should be definable without reference to 
what the observer does (e.g., rotating his field of sight).  
However, a question about the *appearance of images* can only 
be properly answered by considering not only what mirrors "do", 
but also what WE do when we look in mirrors.  If we remove the 
observer from consideration, we can no longer deal with images 
and appearances (which is what the question asks about), because 
an image implies a point of view and an orientation.  Without 
these concepts we can't really address the question at all.  For 
example, the Scott Chase FAQ article declines to even acknowledge 
the basic observation that prompts the question (reflected text
appearing backwards but not upside-down), and never addresses the 
correlation between the observer's axis of rotation and the 
resulting appearance of the reflected image.

Overall, mirrors provide an interesting reflection of physics in 
general and the sci.physics newsgroup in particular.  They nicely
illustrate two problematical features of our thought processes:
(1) the tension between our imaginary psychological models and our 
direct perceptions, and (2) our tendancy to separate the observer 
from the phenomenon.

For a related discussion, see Reflections on the Mirror Question.