Miscommunication is the biggest problem in these CTE threads, and you're miscommunicating here by overstating your case. It's obvious to you and me that CTE describes no precisely programmed steps to an accurate aiming solution, but it's also obvious to CTE's users that it provides something objectively positive and useful for them - objective because it produces concrete results (they shoot better). If you want to communicate you have to be careful not to conflate or confuse the two concepts.
I agree that miscommunication is an enormous problem in such debates (I've engaged in them before, on other issues!). In this case, the definition of "aiming" can mean slightly different things to different people.
But I'm not sure what the cause of your apparent "fear" is for calling BS for what it is.
In looking through ancient threads that are spread all over the internet--many of which feature YOU, saying EXACTLY the things I'm saying now--I've learned that the main publicized version of Houle's work is a flurry of INSANE SOUNDING numerology, into which the approximately CORRECT cut angles for 15, 30, and 45 degree shots are inserted. AND that hitting the object ball at the appropriate one of those 3 places will make ANY SHOT!
But of course, THEN, there are those here who say things like "You have to be shown to really get it," and "The actual system is NOT public knowledge."
So no, it's not exactly obvious to me what CTE does and doesn't do--even if it is obvious that Houle was apparently some kind of lunatic.
Nevertheless, I CAN with complete confidence tell you what I DO know: I know the contents of my PM inbox. I know there are people who have taken paid instruction on the variants of CTE that are now for sale, who feel what they learned is total crap: that there are only 3 (or 6) numbered shots, that you learn the angles for those, and you're good to go.
Again you're conflating/confusing terms. A system can be geometrically undefinable and yet be a rational choice for a player because it produces objective results.
Now here I have to accuse you of being a bit confused--about the definition of the term "rational." It's not rational to believe it's only necessary to hit the object ball in 3 different places to make all pool shots--when that is WRONG information.
I know you've "convinced yourself" that some people are "helped" by believing something that is false. But I wonder what EVIDENCE you have about the helping part. It's a known fact of psychology that people will say things have helped them when in fact they didn't--especially if they've already paid for them.
I think the "objective results" you must be referring to are that, as people continue to play more pool they begin to make more shots. Who's the one being irrational if you're trying to draw a connection between a lesson to aim in one of three places vs people simply and naturally improving their motor skills and coordination by playing their sport over time? I question the objectivity of that--your information and your conclusions. Have you heard from all the people who say they WEREN'T helped by the Houle system? Or did those people just wander away, their pockets less full--perhaps thinking that they lack some capacity to learn?
I have seen or heard NO objective evidence that learning CTE helps people. I question your understanding of the phrase "objective results."
I don't think it's valid to assume that a system can't be objectively useful (or even "a system") because it isn't useful in ways we prefer.
I wonder: Do you think it's valid if I say that there are many ACCURATE systems of aiming available for free (Dr. Dave's website and elsewhere), or at minimal cost (the MANY pool books written over the years by the best to ever play), while very EXPENSIVE lessons in an INACCURATE system are touted as "special, secret information?"
Would it be valid if I said it's a travesty that the implication is being floated by some who wish to profit, that the famous pool players for generations who have written books have actually LIED about how they aim, but that for a large fee, you can be taught how they REALLY aimed?
I'm not arguing against you; just trying to draw you closer to a middleground that's more productive for discussion. My motives are selfish: we've been all over this ground many times already over several years and several versions of this system, and I'm tired of talking past each other.
If you're tired of the discussion it would be best if you didn't take part, no?
I know the feeling. My main intention in starting this thread was actually to pass along the Excel data (with formulas) that I originally posted. I had always intended to sit down and generate that data for myself, and this CTE business prompted me to get off (or onto) my ass and do it. Not only are 3 or 6 different shots not enough to make all shots--neither are 64! It's good, solid information that objectively shows exactly the hurdles that need to be cleared in making different shots at different angles and distances. It can help people to work harder on shots they SHOULD make, and worry less about missing those that require accuracy to a hair's breadth. It can give people the fodder to make objective choices in safety strategy, based on their level of play.
As to the "middle ground," I must have missed that being an important part of internet forums. I had the idea that forums were meant to collect the many DIFFERENT ideas from different minds--to compare and contrast, without trying to turn them into a single muddle in the "middleground."
What's the "middleground" between those who wish to sell to others the notion that only 3 shots are needed vs those who know differently, anyhow?