I don't believe I ever said can't be diagrammed. I said has not been to Dan's satisfaction. I am of the opinion that anything that can be done in the physical realm can be diagrammed. In fact we have diagrams for many things which are not in the visible realm.
I have NEVER EVER said that math doesn't underlie CTE. What I have said is that it is likely that CTE must be able to be mathematically represented. I have thought about this many times and done diagrams of my own but I have always been math challenged. Really I OFTEN makes simple addition mistakes so higher-level math is well beyond my ability. My point of view here is that CTE is counter-intutitive and works so well that there just has to be something there.
The issue as I see it is that the few folks here with the math skills and the engineering skills arguing against CTE won't even try to reconcile this on the table with those who know the system best. There are engineers and computer science folks who use CTE. They just don't spend their time here arguing about it. They use CTE like it is supposed to be used, as a tool for aiming without ideology imposed on it.
If it makes you feel better I am a dunce at basic mental math (especally if i had to do it in a race, I would lose to a normal 3rd grader...) and I'm pretty good at higher level math. Higher level math is a whole different ballgame and based more on applying concepts vs rigid memorization.
You didn't answer my question (well I didn't really phrase it in the form of a question) about what is seen after the eye shift. Does the ball fraction appear in the corner of the eye or is it the aim line or is it both? I find a I definitely 'see' something different after the shift, and I find that if I mess around with placing either edge or center of the cue ball on the chosen letter of the object ball I see something differently, and normally one of those choices does look like i see a line into the pocket.
Validating (not proving) normal manually pivot CTE mathematically should not be very hard. Pro1 is a different story because the descriptions of how it works are so vague they leave much up to the imagination.
The way I see it Stan's videos are totally disorganized and more of esoteric sales literature than teaching material. For one he never seems to give definitions of the nomenclature. If you watch all of stan's videos and watch your videos and watch lil chris's video and read dr. dave's information (without which all of the other videos are basically useless because they don't include the tables) you get a rough idea of how pro1 works.
I tried to buy Stan's Pro1 DVD a year and a half ago or so and they were out of copies so I was told to wait for the book and by the time the book was out I had already solved many, but not all of my aiming issues. I was taught some (what i consider useless) version of CTE which I posted about here before by a BCA instructor. Patrick quickly (and correctly) shot down its validity. This made me much more skeptical about aiming systems. I tried Fractional Ball aiming and it didn't seem to do that much to help me.
And as I said before the changes in fundamentals that Geno taught me, did more for my aim than any of the other (Pivot CTE, BCA instructors CTE, Fractional Ball, tip contact point aiming, etc) aiming systems I tried. It is worth noting that I had figured out a (what i considered weak) way to fix some of my aiming problems, and using it won some tournaments. I told geno about it before my lesson and he said 'oh, so you figured that out,' so he left it out of the lesson.
So now I'm just trying to figure out a way to fix the remaining shots that I miss the same exact way over and over again and am willing to give CTE Pro1 a shot regardless even though I am somewhat sceptical due to the fact that no compensation is made for distances as is done with Pivot CTE.