Thanks for the reply. Let me address a couple of things, and then I hope to be done with these conversations.
Regarding the diagram above: Your interpretation of the results is flawed. I know you don't want to hear this, and will argue strongly against it, but if you take a step back and actually think about what I'm saying, maybe you will agree. The diagram you made uses the center of the cue ball as the origin for your two lines that go to the CTE line and to the ghost ball line. The two lines intersect at the center of the cue ball. At one end, where the object ball is, the two lines are separated by close to a half ball diameter (the sharpest angled shot) while at the other end, where the two lines exit the cue ball, the lines are very close together.
The fact that the two lines exit the cue ball close together is meaningless. Why? Well, the direction the cue ball travels does not depend on the contact point on the cue ball. It depends on the angle of the cue itself. A more accurate diagram would be to start your lines from the contact point on the cue ball. In that case, all the lines would converge at a single point on the back of the cue ball. Every shot has the same contact point - center cue ball. The difference from one to the next is simply the amount of pivot on the cue itself. (Of course there are considerations of the tip being rounded and the ball being rounded and the contact point being more of a patch than a point, but you get the idea).
I had hoped that we were on the same page in that the basic premise is that no matter the method used to aim (pick a line to put the cue on) that line MUST resolve to the 2d ghost ball line in order for a cueball traveling down that line to be able to pocket the ball (disregarding, throw, cling, and sidespin).
Since GB is touted as not only being geometrically correct but also "easy to use" it is therefore proper to go ahead and use GB for diagramming purposes since most of agree that a cueball which replaces the GB will send the object ball into the pocket for most shots at medium speed due to the margins present.
And with that premise it IS relevant that the SHOT LINE is in fact the center of the cueball facing the shooter and going from there to the ghost ball center position. IF one had a laser system that could engage and lay down a laser line that represents the shot line then that laser line would BE the ghost ball center line. In fact on youtube you can find videos of robots and projectors with ball tracking that do just that.
So no it's not meaningless that VISUALLY orienting yourself to the concrete CTE line puts you in a physical space that is a tiny movement away from the actual shot line. Not to me. Just that alone has a huge implication for helping people to get into the right space to address the shot. That's huge even if we just stopped right there.
Next, I wanted to push you to answer the central question as far as you could, and I think you've done that. In my opinion, you cannot answer the question, and I think we both know that your explanations are more like grabbing at straws. I appreciate the attempt and I promise not to keep harping on this stuff. I had not posted here in a long time when one day you posted a video of Stan on my youtube page. I noticed that Stan had been practicing his curtain shots as evidenced by the chalk marks on the table. You guys got all upset and then Stan admitted he had been practicing the shot before taking the video in which he definitively states that he made the shots "on the first try after setting it up." OK, fine. Next you make a long video to answer my question, which I actually was happy to see. Unfortunately, and we can agree to disagree, you did nothing more than repeat that it just works... Sorry, that's not an explanation.
Again, if you're look for math then I don't have it and neither do you. And if I did it wouldn't matter one bit to the PRACTICAL application. And the explanation I gave you, the explanations Stan and others have given are all far more than "it just works".
I have techniques to teach people to jump. I use language like "time to rebound" and "clearance angle" and "compression force" - what I am describing MIGHT NOT BE what is actually happening but it suffices to get the student into the right body position and frame of mind to understand the aim and stroke and force needed to control the cueball during a jump shot. The ACTUAL math behind the physics of the jump shot are totally and completely irrelevant. It just works is enough as long as how to make it work can be adequately transferred from one person to another so that the next person can experience it working. One does not truly need to know WHY a jump cue works but instead needs to know very well the proper technique to use it accurately.
The entire purpose of my video answer to you was to indicate that each shot is a task unto itself with literally no relation to any other shot. As I said all of the aiming happens inside 50% of the balls. In a very tight corridor a small set of perceptions is enough to handle the actual but unknown angle/shot line. One does not need to know HOW the discovered phenomena works physically in order for that discovery to be useful. That's my point all along. You seem to think that it's just self-delusion and that we blindly follow Stan and simply swallow whatever he pronounces as to HOW CTE works. No we don't but we are more inclined to take a good look at what he thinks is the reason it works and explore that because we know how much time he has put in with it.
And the purpose of the diagram was to show that while the aiming ABSOLUTELY happens inside 50% of the ball diameters the actual result of using the lines places the shooter onto an even tighter track than that, literally focusing to a space that is between .4mm and .07mm at the back of the cueball. This then results in shooter ADOPTING the right shot line consistently. And as added bonus it was further discovered that when the shooter uses the other perceptions from same cueball position then the resulting shot lines lead to bank shots which send the object ball in or VERY close to the pockets.
Why that happens mathematically is unknown. IF it happens as a result of some sort of neurological trigger that forces the subconscious to automatically PICK the correct line for a three rail bank then great. Since consistency is what we claim to want in pool I fail to see how anyone could knock any method that actually produces consistency.
Or is your fundamental problem that you THINK that CTE does not produce the consistency claimed?
Finally, my position is that if CTE helps some people like yourself, then great. I believe most supporters here have rose colored glasses when extolling the vitues of CTE - making crazy shots all over the table with no effort. OK, we can all do that, sometimes, but if it worked that great then you should all be on the tour.
Again you conflate aiming with execution. Aiming is getting on the shot line. Execution is making the shot and getting position to continue the run out. Just because I put you on the EXACT shot line does not mean you will be able to make the ball and draw the cueball four rails consistently like Mike Massey can. This "if it's so great why aren't you on tour" red herring is old and smelly. Why are YOU not on tour Dan? I assume you have aiming down and I assume your stroke is great so why are you not on tour?
Could it be that aiming and stroking are not ALL that one needs to "be on tour" (if there was a tour to be on)? That you continue to make this silly and irrelevant point shows again that you are ONLY interested in tearing down the systems by basically saying to the audience, "you don't need it".
As for making crazy shots, yes Dan any player can make crazy shots once in a while. But a CTE user can make them consistently without guessing. CTE users actually take on "crazy" shots more often BECAUSE of the confidence they have through experience that the shot line is highly likely to be correct. And no one said that CTE users are making crazy shots all over the table with no effort. No, they have a very clear effort involved to guide them to the shot line. That effort is stress and anxiety free because they know that even if they have never before tried that particular shot they have an excellent chance to get on the correct shot line through the very clear objective process for perceiving the likely key that is right for that shot.
I've used this analogy before: CTE might work with some subconscious adjustment at some point in the process, or it might simply be done by adjusting the pivot. What I mean is that in ghost ball aiming, you keep your stroke the same but you vary your aim point. For instance, if I have a 30 degree shot, I'll aim at the half ball hit. If the shot is a little thinnner, I'll aim just outside of the half ball hit. In both cases, I am stroking the cue straight through without any pivoting. The only thing I am changing is the aim point.
So I will tell you what Hal said to me. What's 30 degrees? How do you know that a shot is 30 degrees or 32 degrees or 29.3 degrees? The stroke in CTE doesn't change based on the aiming. Stop bringing stroke into it.
In CTE, on those two shots, let's say I am aiming with the CTELA perception. In both shots, I am now aiming at the same exact spot - the place where the CTELA perception tells me to aim the cue. But this time, I am not stroking straight through like I did above. This time I am pivoting the cue. I think this is probably what makes CTE work. You are changing the shot with a different amount of pivot.
I deliberately showed you the half ball pivot. The cuetip comes to rest with the center of the tip pointing at the edge of the cueball and the body makes a tiny shift causing the cue to swivel to center ball. At center ball the tip is then on the ghost ball shot line.
The FEELING for the CTE user is not one where the pivot is changing. Maybe it is to some ridiculously small degree...but the point is that through objective perception the shooter is able to do three steps and be on the shot line without guessing.
In a nutshell, with ghost ball you aim at different places with the same stroke. With CTE you aim at the same place with different amounts of cue pivot. Both require experience to get good at, and both depend on the shooters knowledge gained by time at the table (some call this feel).
What are you talking about stroke for. Everything I am talking about has to do with what happens up to the moment that the shooter is down on the ball and getting ready to shoot.
You are confusing the type of experience needed to get "good" at aiming using GB vs. CTE.
In GB you definitely have to acquire some major visualization (imagination) ability in order to "see" the GB properly positioned with no offset caused by illusion. I did an experiment and asked my staff to just put a ball down where the ghost ball should be and most of them could not even do that precisely.
For that matter when you see people actually placing a real ball in the GB position they fidget with it, they use their cue to check the alignment, they back away to eye it up....all this to place a PHYSICAL ball behind another PHYSICAL ball in line with the clear pocket. And you want to tell me that it's "easy" to do this in an imaginary way????
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