Lecture 15 – Mirrors and Twisted Space (10/18/04) pp 68-73

1. Mirrors

Why does a mirror reflect left-right but not up-down? The best picture of a person and her reflection that I could find!
(from http://www.throughthelenz.com/)

• First, let's get clear – think of your reflection geometrically, as a literal mirror image body; what you see in a mirror is exactly what you would see if such a duplicate were on the other side – the image that you see in the mirror gives the illusion of a mirror image person.
  

• Answer One: a reflection turns everything into its mirror image – a left hand is the mirror image of a right hand, but feet are not the mirror image of a head!
• But why does the image of my feet end up down, while that of my left hand end up on the right?
  

• Answer Two: the question presupposes a particular way to judge up-down and left-right relative to our bodies – pick a different way and a different transposition occurs! The mirror can be said to reflect whatever direction you like.
  
• But surely the judgement is not arbitrary – comparing by jumping over the mirror is crazy?!

• Answer Three: according to the fitting account, the rules we have adopted for judging the left and right sides of another person require us (mentally) to move ourselves into congruence with them – logically abitrary, but very convenient! And by that standard left-right is reflected.
• I see! Wow, the fitting account is great.
  

• The possibility of handedness depends not just on an object being an enantiomorph, but on the topology (= overall 'shape') of space:
• Counterparts with dimensions lower than the space they inhabit are never incongruent
• Even in a space of the same dimensions, counterparts may never be incongruent, if the space loops – like a cylinder – and also twists – like a Möbius loop. (These examples generalize to spaces of more than two dimensions).