Directional speaker cables - switching direction

Some time ago I started a thread regarding speaker wire directionality and my inability to understand how it could have any affect on sound quality. The question was inspired by the fact that, after quite a few years using them with my Martin Logan Odysseys, I discovered that the cables (Straightwire Octave 2) had arrows printed on them. Not surprisingly the opinions expressed were pretty strong on both sides of the argument but those supporting directionality were the most vociferous and in greater numbers, one to the point of being downright insulting. In no case, though, was an explanation given by those supporting the importance of cable direction for how this phenomenon occurs except that it should be obvious that when a cable is broken in in one direction only someone with an uneducated ear would be unable to discern the difference.

Even though I still don't get it I'm not taking the position that there is no validity to the directional claim; if there truly is I just don't understand how. This leads me to my two part question. I haven't been using the Octaves for a few years but now, because of cable length issues, I want to put them back in my system partly to avoid the cost of new quality cables.

IF, then, the directionality theory IS valid and I don't recall which way the arrows originally pointed or which direction they were "broken in" do those in support of directionality think I should install them with the arrows pointing toward the speakers