I think in the endless debate between the Pelz/Mangum school of thought [face of putter stays square to target during stroke and you, in essence, try to vertical hinge by rocking your shoulders and keeping the face always squarely facing the target with a putter that has a shaft attached to a clubhead at an angle] and someone like Utley [Utley does not explain it well in my opinion, but he is arguing that the putter swings like other clubs on a plane and you angle hinge on that plane board] -- that Utley has the much better of the argument. I'm not saying you can't do it either way, but there is actually a good deal of manipulation in the Pelz/Mangum approach and it isn't consistent with how you otherwise square a clubface and adapt to the fact that the club is attached by a shaft at a severe angle and is not a croquet mallet attached to a robotic single-arm pendulum. Rocking your shoulders to vertical hinge is not the easiest of things to do, in my personal experience. I struggled with that approach for a couple years and only got worse with time.
Also, the idea that Mangum puts out that you control how far you putt the ball by controlling how far away from the target your lead shoulder throws the putter is exactly the opposite of how most athletic motions work and seems just backwards to me. I don't measure my throw to first base by estimating how far backwards away from the target to throw my arm and then just let gravity take over. I think in most athletic endeavors one controls the distance something is hit or thrown by the feel of the motion of the body and the arm towards a target and you learn that feel. If gravity really controlled the speed of the putter going forward then you'd have to be unbelievably precise about how far backwards you threw the putter with your stroke. Picture it: "ok, I have a 25 foot putt on greens running 11 with an uphill 5 degree tilt, that means I'll just throw the putter away from the target exactly 6.575 inches (would one need a Cray to calculate this backwards throw energy?) and then just let gravity take over because that will be the exact amount of energy needed to take the ball four revolutions past the cup lip...." or would one just learn how to create a forward motion that fairly consistently applies energy to a golf ball as if you were raking it towards the hole?
Actually, Niblick, in the last paragraph, you've got it backwards. The thought process is that because humans have been dealing with gravity for several million years(6000 years for some

) then there is an in built sensor in how to deal with it, SO ....if you learn to trust it, then touch becomes very instinctive pretty quickly, and you look and respond.
Four revolutions is more Pelz like...Geoff recommends 2 for various reasons, and again, he is trying to get people to appreciate the speed they want the ball rolling as it approaches the hole so that it has the best chance of falling in the hole. To use your own logic(or Pelz's), how many athletic pursuits does one think about how far past the target one must think about to hit that target?
With respect to your first paragraph, if you want to discuss Geoff's stuff, great. Understand that he is one of the biggest critics of Pelz which must throw the red flag up on some level about the types of stroke espoused.
If you want to talk TGM lingo, do so but don't pretend that you can describe Geoff's stuff in those terms. By your language, it is plainly obvious that you have not studied Geoff's material on any level, and have not taken a lesson from anyone versed in what he teaches. So your analysis should be taken with a grain of salt!