Dave,I'd like to hear from anyone in the world reading the thread who thinks CTE is geometrically incorrect - to prove why it is.
If you are serious about this, we would first need to clearly define what "geometrically correct" means, as applied to an "aiming system." I'll take a stab so others can help expand or improve the definition:
geometrically correct aiming system: a method involving a clear and reproducible set of steps that, in theory, accurately locate the line (the required aiming line) passing exactly through the center of the ghost-ball target for any shot.
Vision, alignment, perception, judgment, feel, conscious or subconscious adjustments, stroke accuracy or consistency, etc. are not part of the test for "geometric consistency." Geometric consistency refers to the theory of the system, not the implementation of the system. As I and others have pointed out, some of the systems that are geometrically consistent in theory (e.g., bisect-pivot-and-shift aiming system and contact-point-to-contact-point or parallel-lines system) aren't always easy to implement perfectly in practice (due to the long list of elements above). But this long list of "elements" present challenges to any system. The challenges of perception, vision, and alignment are ever-present at the pool table, regardless of the system one might be attempting to use.
Now, to judge whether or not your version of CTE is "geometrically consistent" or not, we would need a clear description of your version of CTE. I have heard and seen many versions of CTE over the years. Several descriptions, and one demonstration, of versions of CTE that have been offered over the years, can be found here:
None of these versions of CTE satisfy the definition of "geometrically consistent" above. I'm not saying your current version of CTE even closely resembles any of the posted versions, nor am I saying that none of the versions of CTE actually work "in practice" for some people. However, no version of CTE I have seen or heard to date can be described as geometrically consistent, IMO. I would still like to read a description of your version of CTE. How is your document coming? Weren't you working on something? Would you be willing to post a short and clear set of steps (with or without diagrams) that describes how you version of CTE works in theory? FYI, here are examples of the style of description (and illustration) that enable a "system" pass the test of "geometric consistency":
FYI, the version of double-the-distance described at the beginning of this thread is NOT "geometrically consistent." It breaks down as the balls get closer. Therefore, even "in theory," the system isn't perfect. Any system can break down in actual implementation.
I hope you don't take any offense with this post. I mean no disrespect whatsoever. I hope we can continue this discussion and better understand how your version of CTE works (in theory and in practice), whether or not it is "geometrically consistent."
Looking forward to your thoughts (and the thoughts of others),
Dave