It's kind of funny to reflect that we fly along designated air routes (railway tracks in the sky) at set altitudes within +/- 50 feet vertically and +/- 100 metres laterally to such an extent that two a/c pass each other head-on at 1800 km/h in the middle of absolutely nowhere on a regular basis with only 1000' of separation. The much reduced probability of this happening if aircraft used random tracks and altitudes in remote areas (no ATC) would seem to be a far better option sometimes.
Someone with a brilliant theoretical, but practical mind will solve this problem sometime in the future and we will all sit back and say, why didn't I think of that?
David Gunson summed it up beautifully... "We force them down narrow corridoors, therby greatly increasing the risk of collision, while at the same time justifying the job of the Air traffic controllers to keep them apart."
Flying on North Atlantic routes, pilots now have the approved option of flying 2nm off track (to the right!) this beautifully solves the head on case and the difference in speeds of following traffic should really make it a non-event.