Many years ago (1998?) in the middle of a previous aiming war, I posted this, which I think still applies.
My experience is that the majority of people cannot make the connection between abstract geometry (such as a half-ball hit) and what happens while they play pool. It may be true that cut angle is a continuous function of the fullness of hit, but most people have neither use for nor understanding of a concept such as "function of".
For such people, I think it is not helpful to go into any more detail in a system than is required to draw their attention to the shot. It is not important what the system is as long as they believe in it and it sort of gets them into the right ball park. Their subconscious will do the rest, as it does for all players who can play a lick, Iron Willie and Virtual Pool excepted.
Ask players what the cut angle is for a half-ball hit and the majority (or a substantial minority) will say 45 degrees. This is in spite of their having shot hundreds of half-ball hits and hundreds of 45-degree cuts but never in the same shot. Many people need an explanation of what a "right angle" is for the kiss-line for position play -- people have even built special fixtures for the pool table to illustrate two perpendicular lines. Most people are not geometrians.
Aiming is as much psychology as it is physics. Arguing that the physics of a system is wrong doesn't prevent the psychology from
working, one way or another. On the other hand, it's not clear to my why people who know a system works for them psychologically argue it to be valid physically. There's no point.
Bob,
A great post from someone that understands the physics and geometry of pool as well or better than anyone else on the forum. If we go down to the pool hall we will find that most everyone or everyone there is in error in terms of physics and geometry. Could you imagine trying to talk about these things with Efren? However, like Efren, most of the people at the hall have figured out how to pocket balls and navigate around the table.
It took me a very long time to understand that there are many things that we can simply "black box" and forget about details. A very good friend and very smart person genuinely believed in witches and witchcraft. These were core beliefs, as real as what he gained from church on Sundays. I could have spent a lot of time trying to convince him that witches and witchcraft weren't real but two things stopped me. First, these things filled large gaps in his understanding. The other thing, I can say with over 95% certainty that these things aren't real, maybe even above 99%. I can't quite reach 100% though because there are things I know and have seen with my own eyes that are unexplained.
Hu