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Path: utzoo!linus!bbncca!rrizzo
From: rrizzo@bbncca.ARPA (Ron Rizzo)
Newsgroups: net.philosophy
Subject: Re: Why do mirrors reverse left & right, not up & down?
Message-ID: <543@bbncca.ARPA>
Date: Thu, 2-Feb-84 13:08:07 EST
Article-I.D.: bbncca.543
Posted: Thu Feb  2 13:08:07 1984
Date-Received: Fri, 3-Feb-84 02:24:12 EST
References: <541@bbncca.ARPA>
Organization: Bolt, Beranek and Newman, Cambridge, Ma.
Lines: 76

THERE'S MORE TO MIRRORS THAN MEETS THE EYE

To further investigation of mirrors, I'll create fictitious persons
to make up for the lack of real ones posting to this mailing list &
submit the following imaginary dialogue:

PSEUDO-TAYLOR: What a crock.  OK, eliminate images of persons, or
even distinct objects.  Our vision contains an implicit model: the
visual field is a planar projection, or better, a projection onto
a surface whose curvature derives from the eye's structure.  As seen,
the drawing-room is a projection surface.  Now just apply the front-
to-back mapping to that.  That's all.

RIZZO: I appreciate your point.  I do that agree your "front-to-back
mapping" accounts for why points on the reflected object correspond 
to points in the image that appear to be on the "wrong side".  For-
mally restated, your "front-to-back mapping" is an automorphic (maps
an object onto itself) transformation involving a 180 degree rotation
about a top-to-bottom axis.  In effect, yours is a proposal to trans-
fer the explanatory burden from one distinction, left/right, to an-
other, front/back.
	But a problem arises.  Why is the axis of rotation a top-to-
bottom one?  Rotation through a left-to-right axis (or any other axis
coplanar with the top-to-bottom axis) is equally a "front-to-back
mapping".  In fact, the terms "front" & "back" don't contain the
extraneous notions "top" & "bottom" : which axis you use ought to be
irrelevant.  So the offered "mapping" can't be called "front-to-back"
since those terms can't carry all the explanatory burden.

PSEUDO-TAYLOR: Alright, so call it "mapping X".  You still know exact-
ly how it works.

RIZZO: But what is "X" ?  I'd like to know, because this "X" manages
to get mirrors to do something very strange: to posit a particular
axis that determines their behavior when it's hard to see from the
properties of glass, light, & 3-dimensional space why mirrors would
favor such an axis.  Why do mirrors use a vertical axis, & not, say,
a horizontal one?

(A brief pause in the conversation ensues. Then:)

PSEUDO-TAYLOR: They don't.  We do.

RIZZO: Intriguing!  Why do we?

PSEUDO-TAYLOR: Because our vision is binocular.  Binocularity creates
handedness.

RIZZO: Hmm.  Yet, close an eye.  You're monocular.  Your open eye still
comprehends "left" & "right".

PSEUDO-TAYLOR: No! your single open eye is binocular.  Binocularity is
not a matter of how many eyes you're using.  It refers to a model of 
HOW to see (how to visually interpret the world), which we LEARN as we
experience the world in our first years.  Having two eyes may be a pre-
condition for acquiring binocularity, but once it's achieved, even a
single eye sees "as two".

RIZZO: Now that's pretty impressive.  

(Another pause occurs.  Then continuing:)

RIZZO: Suppose our Alice has experienced a "change".  Her eyes now lie
on her face on a vertical, not a horizontal, axis (poor thing!).  With
her back to the fireplace, she surveys the drawing-room.  The green
chair is in the corner to her "bottom" (on her bottom eye's side of the
visual field, i.e. our left) and the mahogany writing-desk in the corner
to her "top".  Once again she clambers up onto the mantlepiece and gazes
into the looking-glass.  "Oh, dear!" she cries.  For in the glass the
mahogany writing-desk appears at the "bottom" (our left) and the green
chair at the "top".
	It's seems like we're dealing with an invariant (right/left)?
	Perhaps the above scene misconstrues binocularity.  If so, tell
me more about it, so I can correctly understand it.

Any real persons care to join this debate?