Learned this turn in the winter of 68-69 at Arctic Valley outside of Anchorage, AK. This is how I remember learning it, forgive any technical miscues, I have not taught skiing professionally for 30 years, so read at your own risk.
Was taught the serpentine on the gentle blues, some things do not change much. The boots were softer and lower, the skis a were a world apart in shape length and flex; so there ended up being a considerably more skidding in the turns, carving was a turn with a minimal skid. Even the poles for most of us were longer, my 54" poles got cut down to 48" as I learned this turn, and keep me out of the back seat. It is a short radius linked turn very similar in appearance to skiing a fall line flush on a slalom course.
From the fall line the knees were driven forward and into the turn, this caused a leg retraction, this in effect became the unweighting. At the maximum point of divergence to the fall line your COM was compressed over the skis. The knees were pushed down the hill changing edges and initiating new turn, the legs extended laterally keeping the head at a constant level from the snow. At the fall line your COM was inside the line of the skis, and you begin leg retraction (this is the first turn that I remember the idea of tightening of the abs in a ski turn) continue edging and steering; repeat upon completion.
Things that were critical in a pair of leather boots: maintain pressure in the front of the boot (if your ankles straightened there was no edging or steering), keep your navel pointed at the lift shack (quiet upper body was actually a fairly easy concept after learning the old wedlen), keep constant pressure on the snow (up unweighting was a tenant of the American Ski Technique at the time, was told I needed to display more up unweighting in free skiing while getting my associates (L2) pin that year), steer and edge positively with both skis simultaneously (very radical concept for a young 60's PSIA trained type).
As more challenging terrain was introduced the terrain absorption, edging, lateral projection, rebounding obviously became a bigger factor and the skiing became more dynamic( this unfortunately is where the jet-stick came from, that is a whole different misguided tale).
Still consider this a mother turn of modern skiing. Once you get past the leverage factor on the front of the boots, it seems that much of the fall line and bump skiing discussed here share some very common threads with this turn.
Thanks for putting up with the ramble down memory lane.