I assume this is regarding my post where I define backhand english here, or Dr. Dave's page discussing backhand english here.
In both places, the correct method of pivoting the cue by moving your back hand to create english while automatically compensating for squirt is described. In order for it to work correctly, the bridge must be at the pivot point of the cue when it is pivoted.
Apparently, Hal was on the right track, but didn't quite get there (or scoffed at the idea of a pivot point, as you say), so he may have popularized the term backhand english to describe an incomplete (and therefore incorrect) method of applying english and compensating for squirt at the same time. It sounds good and is easy to remember, so the term became well known and was used to apply to a method where your back hand is moved to pivot the cue.
Anyhow, whether Hal believed in the existence of a pivot point or not, the correct method involves bridging at a particular point on the cue while pivoting. Eventually, the correct method and catchy name were paired together on the internet and it stuck. In my opinion, it's better that way. Why waste a good, memorable term on a broken method?
Maybe if you go around and convince everyone that "backhand english" actually refers to a method that doesn't work, we'll call the working method something else and the term "backhand english" will just be a footnote in pool history, but it doesn't seem worth the effort. Maybe we should just specify which version we mean, as in "Hal Houle's broken backhand english" or "backhand english that works". I know it's a mouthful, but it would avoid confusion.
I did a video where I demonstrated that BHE is not dependent on either bridge length nor pivot point to be effective.
I was asked this very question two days ago at the BCA event here in vegas. I suppose the reason might have been spurred by your definition or this thread.
In any case I agree with Fred. Forget about who originated the term BHE. Hal popularized it and the meaning was the application of spin (with zero regard for pivot point) by using the grip hand to pivot around the planted bridge from a center ball address. This is how I learned it directly from Hal.
Anything else should be referenced with a different term such as ppbhe for example to denote a form of BHE that relies on the pivot point. (Which is pretty much a practical impossibility anyway since you can't always have your bridge planted at the shaft pp during the course of the game).
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