> > Intuition suggests that, under most circumstance, they should pass
> > each other. Our real life experiences reinforce this. However, given
> > the current movement rules in Olympia, unit [a] could move West then
> > South, while unit [b] moves East then North -- thus exchanging places
> > yet not encountering each other.
> This has nothing to do with ortholinear movement. It's true in every
> movement system known to man. Even with diagonal movement, there will
> be many equally good movement paths between two locations. For example,
> from aa01 to ab03, one might move aa01-aa02-ab03, or aa01-ab02-ab03,
> paths which do not intersect except at the endpoints.
You miss my point. Perhaps, i did not state it precisely enough.
First of all i did not use the term 'ortholinear movement'. Given that, your
initial statement has nothing to do with this discussion.
Secondly, i am not concerned with how many possible paths there are from point
A to point B.
I am concerned with the case where the 'most direct' route (ie. the shortest
route) would be the diagonal and where the 2 possible orthogonal routes are
of equal distance.