Topics Space

Question I'm thinking about relative position (left, right, up, down, ahead, behind). My general question is whether you think that these three oppositions (left/right, up/down, ahead/behind) have the same "status". For instance, for every point moving on a straight line, there is a meaningful and precise difference between ahead and behind, but not necessarily between left and right or up and down. Another example: for any (physical) object on the surface of a planet, the difference between up and down is clear, but not the remaining two oppositions. Another one: if it is settled, in a given 3D situation, what is left and right, then it is also necessarily settled what is ahead and behind, and what is up and down, but this does not (always) work the other ways around. What do you say? And do you think that the opposition between inside and outside has some relation to the other ones?

Accepted:
February 20, 2009

Comments

Offhand, it's not clear why we'd think there's a difference in status among these oppositions. Once we fix a point on a line as the "origin," it's still up to us which direction counts as ahead and behind. What's up where I am on earth is down from the point of view of folks across the center from me. And so on. Space is isotropic; any direction is as good as any other. (And just a side note: if we fix left and right, we haven't fixed up and down. Imagine holding your arms out and rotating 180 degrees around the axis they define. You'd flip up and down, and also ahead and behind.)

Still, there are some interesting points in the neighborhood. In our space, there's such a thing as "handedness": you can't turn a left hand into a right hand by sending it along some path in space. Our space is "orientable." But some possible spaces are non-orientable as the surface of a Möbius strip demonstrates. Likewise, in our space, there's an absolute distinction between inside and out, but that's a fact about our space, as the concept of a Klein bottle illustrates.