I have the answers I need concerning the big CTE questions....
Does CTE really work as described? It might, or it might not. I don't care.
Does CTE work? Yes, then as described doesn't really matter. Does fire burn? Yes, the actual chemical composition of the fire doesn't matter as long as you know that you shouldn't stick your hand in it.
Where's the proof that it only works on a 2:1 table? I don't care.
We only play on 2x1 playing fields with the pockets at fixed positions so that point doesn't matter. So no, I don't care because it works on the ONLY competitive playing field that is the same all over the planet. Shots directly to any point though MUST have a CTE aim because any point with lines emanating at 90 degrees to each other form a corner of a perfect rectangle.
I actually do not agree with Stan on the 2x1 thing and have told him so and he feels that he is right and yet it makes zero difference in our relationship and zero difference in my assessment of the value of CTE aiming to the user.
How can 2 balls spaced the same distance apart provide a different ccb perception based on where they are on the table? I don't care.
because they are now in a different position relative to the fixed target. The CTE line and the shot line are emanating from the cueball. No matter the shot the variance between the two lines as they exit from the back of the ball goes from about .003" or .01mm to .022" or .4mm. What does that mean or why would that information be of any use? It means that when the user sights the cte then they are never more than about a tiny fraction of an inch or mm away from the shot line. That's just step one. So with step two being selecting a perception the body position gets closer still to the unknown shot line which is already so very close to the CTE line from the user's perspective looking at the back of the cueball.
So what then is "different" with the balls parallel-shifted? the angle to the target of course but when it is said that the target doesn't matter then you all contend that the same input cannot produce a different outcome and the object ball MUST also travel a parallel line. But we know that the human mind is NOT a linear computer that strictly interprets code and so it is possible that the being so close to the unknown shot line is what allows the "same" input 15 degree perception inside sweep to work for a range of same distance shots along an axis. In other words the system gets the user crazy crazy close to the unknown shot line OBJECTIVELY and the teeny teeny tiny difference between the edge to abc lines is so small by that point that the user is simply on it by objectively and deliberately following the steps. Fact is that we don't know and we really don't care because it works. IF the brain is making some kind of "leap" to close the gap from linear input to abstract choice I submit that the "guess" that the subconscious makes at that last millisecond is ONLY possible because of the OBJECTIVE STEPS followed prior to that "shot line" appearance for the user. So if I am right the brain is informed and guided consistently by the objective CTE steps. It is those objective steps that make it work and not the subconscious taking credit for closing a teeny gap at the very end of the process. One would almost say WELL OF COURSE the brain can EASILY find the shot line once the user has consciously and objectively narrowed down the available choices to a tiny point.
How does the numerology (15+30+45=90, and therefore the system connects to 90° angles) make sense? It doesn't, but I don't care.
Right, like the 2x1 claim it simply doesn't matter. Just like I don't need to care whether or not your system is based on the inscribed angle theorem or not. Maybe it is and maybe it isn't but it doesn't matter at all IF it is because it works within the playing field consistently. Now, IF I have trouble picking out the starting point and thus am getting inconsistent results with your system does it invalidate the system? OF COURSE NOT. The system is valid regardless of the skill level of the operator and the results they get. A very experienced operator who has really mastered your system is going to get the best results possible.
The same applies to CTE or any other valid system. The input is actually biased based on the user's initial parameters and the users who reduce that bias and move towards mastery through practice and knowledge tend to speak the same language and act on that code consistently from user to user.
So whether or not the idea of 15/30/45 resolving to 90 degree corners is valid or not the overriding point is that it is immaterial to the problem that the system solves. As an example last night at the Pool Dojo the instructor was showing a diamond system to figure banks and kicks. I stepped up and nailed the bank shot using CTE instead of the also valid diamond system. With CTE I had no need to find the shot line through a diamond system but if I knew a diamond system I could certainly use it if I wanted to. I personally find those math-y type systems cumbersome and others gel to them instantly.
So bottom line, when the improvement is measurable and noticeable and my joy when playing is increased and my frustration decreased then you're absolutely right, I don't care about what protons and isotopes are doing on the quantum level.