The question was to use science to disprove the CTE can work as described. Geometry is a part of science. In geometry, balls don’t have edges, therefore you cannot use something that does not exist.
Oh yeah, you really proved that in real life balls have edges.
Balls having edges is all in your mind, good grief, how hard is it to accept this?
Geometry is necessary to prove anything graphically or spatially. But there is a lot more to geometry than most people realize. Have you ever built video games? Or written software to do 3d modeling and visualization? What about 3-d geometry?
If you are trying to map a system into two dimensions that exists in three, you cannot do it properly.
Perspective and the way things line up in 3 dimensions can produce completely different results than you could come up with on paper, in 2d.
I have done all those things and I have spent a lot of time on a pool table looking at how to 'see' things differently than most people. CTE is one of those things. Poolology is a good translation from 3 dimensions to 2. CTE doesn't lend itself to that. Not because it's incorrect or wrong, but because it simply can't be described in 2 dimensions in a way that will lead you to the same results.
Just because your perspective changes and that changes how things look and line up doesn't make a system subjective. Perspective is an objective part of geometry just like tangent lines are. It's just not terribly useful in 2d for this type of discussion.
Computer simulations like virtual pool as it is does not work for CTE because it is a 2d representation. No matter where your eyes are, the aim points look the same. You can shift the perspective in the game, but you can't really simulate 3d.
When I'm playing my best pool I am seeing the CB and OB as spheres, not discs. I believe that most, if not all, pro level players do the same. Even if they are aiming in 2d, they are still seeing in 3d.
I spent a lot of time (8-10 hours) aiming like Busty as an experiment. With the tip of the cue offset and low. And you know what? I shot GREAT! I couldn't believe how well that made me play. Even though I have no idea what he's looking at. Something about placing the tip there helped me visualize the CB and path to the OB in a way that was incredible. Great depth perception. Great spatial visualization.
I don't have any formal training in CTE so I'm not the best to answer questions about it but what I know if it works well. It's amazing to have the shots snap into place visually and just be able to stroke and watch the balls go in the hole.
Because of my 3d modeling experience I know the value of perspective and I know how CTE can work and how it can be objective. Claims that "Science" says it's impossible don't hold water with me. Especially when the 'science' is a 2d drawing with compass and protractor.
There are other things going on when you start using pivots. BC21 did a good job of summarizing these in a post about a year ago IIRC. For one thing, the amount of pivot changes depending on the length of the shot and the amount of offset between the initial point and the final point. So longer shots result in smaller pivots. When balls are close, there can be very large pivots.
When you pivot, if you leave your head position the same instead of re-aligning your eyes with the new cue position, that gives you a different perspective and a different vision of the shot. I've experimented with this a lot. If you align your eyes to the new line before you pivot that gives you a different perspective and vision of the shot.
And balls do most definitely have edges. On one side of the edge is ball. On the other side of the edge is not ball. That's the definition of an edge.