2 - Hands, knees and absolute space

Summary

Counterparts and enantiomorphs

My left hand is profoundly like but also profoundly unlike my right hand. There are some trifling differences between them, of course, but let us forget these. Suppose my left hand is an exact mirror-image replica of my right. The idea of reflection deftly captures how very much alike they might be, while retaining their profound difference. We can make this difference graphic by reminding ourselves that we cannot fit left gloves on right hands. This makes the point that one hand can never occupy the same spatial region as the other fills exactly, though its reflection can. Two objects, so much alike yet so different, are called ‘incongruent counterparts’.

In my usage that phrase expresses a relation among objects, just as the word ‘twin’ does. Thus, no one is a twin unless there is (or was) someone to whom he is related in a certain way. Call this relation ‘being born in the same birth’. Then a man is (and has) a twin if and only if he is born in the same birth as another. Let us call the relation between a thing and its incongruent counterpart ‘being a reflected replica’. Then, again, a thing is an incongruent counterpart if and only if it has one. My right hand has my left hand, and the left hands of others, as its incongruent counterparts. If people were all one-armed and everyone's hand a congruent counterpart of every other, then my hand would not be (and would not have) an incongruent counterpart.