Actually, Homer is saying that something at the upper end of the Pivot -- not necessarily the Head -- must remain Stationary to stabilize the motion. He recommended the Head as the Pivot Center because you can tell when it moves (you can see more 'under' the Ball). However, you can alternatively choose to keep the top of the spine -- the point 'between the shoulders' -- stationary. Either way, there is no Sway. In both cases, there is a Centered Pivot Motion. It is all a matter of what the player monitors.
This is probably one of the best posts on the "through the head" pivot center or "through the base of the neck" pivot center debates.
Good stuff Yoda!
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I'm not a TGM or PGA certified Pro, but I did stay at a Holiday Inn Express last night