How the Correct Stretch Relates to being Correctly on the Bit

So, I've been trying to figure out this dressage thing for a while.  30+ years actually.  During this time, one of the big things that has eluded me is why the stretch circle or long and low leads to the horse being correctly on the bit.  How can being stretched out lead to easy compression?  I can remember watching Reiner Klimke school his horses long and low and then in the same session in highly collected work and wondering what the secret was to shifting between the two.  Was it the mysterious invisible half-halt?  Was it a magical German seat perfected on the longe line?  Was it just inherent talent on the part of the rider?  How does the green colored horse pictured above turn into a horse doing a correct piaffe?

Well, I finally have the answer, and of course, it is really pretty simple.  When the rider has stop, go, turn, and the forehand and hindquarter yields from the seat only, with a relaxed horse, THEN the rider can ask for lateral alignment on the circle with a light rein connection.  When this alignment on the circle is correct, with a relaxed yet energetic enough horse, the horse will start to offer the correct stretch because he is in the right place biomechanically to do so.  The rider slightly softens her back alignment or lifts her seat like rising from a slightly sticky chair and the horse offers to stretch softly out to the inviting hand.  There is really not a lot of hand involved.  Seriously, it is mostly lateral alignment and seat aids.

Because the stretch is coming from the alignment and because all the direction and speed control are from the rider's seat, there is no yanking, pulling, or hand sawing and no heavy contact.  It can even be bridle less like the above photo.  It is an exercise of alignment and subtle rider seat aids.  The reins can just limit how far the stretch is allowed to go.  When the stretch is done like this, the horse's back is up and free swinging, the shoulders are lifted, the neck stretched, and the throat latch is open.  And of course, he is already pretty straight because the lateral alignment led to the stretch in the first place.  

So, this is all fine, but how does this stretch lead to the horse being correctly on the bit and eventually to collection?  Think of the horse being like a bridge after basic direction and speed controls off the rider's seat are in place.  When the horse is green the stretch done correctly ensures that the horse's back is free swinging, the shoulders are lifted, and the head and neck are stretched out.  As the horse becomes stronger the rider gradually changes the height of the neck, bending of the haunches, and lifting of the shoulders through months and years of work, including many gymnastic exercises, to get to an end product that looks like the above illustration.

The correct stretch is essential because it ensures that the back/shoulder/neck mechanism are working properly unlike the above or behind the bit illustrations with dropped shoulders and back.  If the stretch is incorrect or not present at all the horse will never be correctly on the bit.  There should be a hint of stretch even in the most collected work to be sure the bridge is always raised.  When the mechanism is working correctly, cadence and lift become possible, and that is where the magic starts to happen.