Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83; site bbncca.ARPA 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?