This is a much debatable topic, but some "facts" should be considered.
First, as Grant Petersen (from Rivendell Cycles) pointed out in his text, for hard, paved roads the best tread pattern is zero, because the tire rubber deforms around the asphalt or concrete texture, and so the zero-thread offers a greater total area of rubber-pavement surface to interlock.
The extreme opposite, the super-knobby MTB tires, are intended to use off-road, where the surface deforms, having a visco-plastic mechanic behaviour. Instead of only the tire rubber conforming to the road texture, actually the soft terrain is indented and "flows" around the tire knobs, which are required to transmit reaction forces to the ground without slipping, while tractioning, braking and cornering.
In the middle, we have all other kinks of pavement (sand, gravel, hard-pack) and thread patterns (grooved, semi-slick, etc.)
In my experience the directional pattern is only found in Mountain Bike tires intended to be used off-road or in specific kinds of trail terrains. There are tires with a single directional pattern that should be inverted between front and rear. There are tires whose rear-front pair are dedicated counterparts. My favourite ones were the IRC Mythos Kevlar 1.95 and the Pararacer Smoke/Dart 2.2 (beware kids, this last one is VERY OLD!).
Also I found out sometimes it doesn' matter that much if you put a rear tire in front (Specialized Cannibal, a typical rear tire, was great in the front), or commit other heresies. In the end, the general thread pattern, knob size and spacing, overall tire width, and MOST IMPORTANT, rubber characteristics, count more than the orientation of the thread.
But that's not what Ritchey's "vector analysis" line of tires would try to say to you. By the way, those tires were KING!! (mostly because of their structure and rubber, I'd say).
Well, this is a lot of chatting, but the bottom line would be:
- In the front, always watch for the direction of the tire;
- In the rear, you can choose, depending if you traction more (uphill) or if you brake more (downhill);
- Don't believe in magic too much.