maybe this will be of some help in the process of people understanding better. i found this on an old billiard digest thread. i post it because i agree with 100% of what is said, and it supposedly came from Hals mouth. i can't prove that hal made the below statements, but if you call him this will give you a good few questions to ask him with respect to the topic at hand.
I posted a problem in another thread with two different shots that were
first proposed by George McBane and subsequently diagrammed on wei's table
by Pat Johnson. The answers I received, from Houle followers, defied the
laws of geometry and, as such, were absurd. I commented that, from my
recollection, Hal Houle was a decent guy and had always been forthcoming in
our prior discussions. I hoped that he would chime in and help explain
away the apparent dilemma. Thankfully, Hal sent a private email inviting me
to call him at home and indicating that he would be happy to answer any
question that I might have.
I took Hal up on his offer, called him tonight, and we spoke about these
matters for about an hour.
First of all, Hal Houle is a delightful gentleman, pleasant, conversational,
responsive, reasonable, intelligent, knowledgeable, and insightful. From
all that I can tell, he is not a mystic, magician, charlatan, eccentric, or
otherwise disposed to offer up systems or ideas that defy the laws of
physics or geometry. He is painfully aware of the normal behavior of
ball-to-ball collisions and like matters. Hal was quick to agree with me
when I asserted that his devotees were not helping his cause especially
well. He acknowledged that many of them are beginners and, as a routine
teaching practice, he does not provide explanations for why things behave as
they do. He wishes that many of them would just keep their silence rather
than attempt to explain things that they do not understand.
OK. On to the specific problem...
When presented with the Case A (30 degree shot to a corner) and Case B (36
degree shot to a corner), notwithstanding the contentions of his devotees,
there is a reasonable and relatively straightforward explanation.
1) Hal states unequivocally that for both Case A and Case B, if the
center of the cueball is aimed at the object ball's exterior edge, and
propelled with no spin on the cueball, the object ball will move in a 30
degree angle after contact, collision-induced throw notwithstanding (meaning
that we'll ignore that effect for the sake of the examples). As far as I
understand it, being a non-mathematician, this object ball behavior follows
the laws of geometry precisely.
2) Here comes the only tricky part to describe. Hal explains that,
when shifting from Case A's position to Case B, the focus spot on the object
ball has moved; that is, if we slide the cueball to the right several
inches, leaving the object ball in its original position, the spot (on the
object ball's edge) we are seeking has rotated "n" degrees to the right of
the original spot. This shifting of the relative aiming spot, from one shot
to the next, is what has been termed rotating edges. Similarly, from the
perspective of Shot A, the center axis has also slid to the right in Shot B
when aiming to the edge of the fixed object ball. This is what is meant by
"apparent centers." In other words, all that is being said is that, from
the perspective of one fixed shot, any other shot does not use the same
exact center or precise edge as the reference shot. The centers and edges
will have rotated relative to the original points. Truthfully, I have not
yet figured out the significance of this observation, but I am now quite
certain that this is the explanation of the otherwise mysterious "rotating
or apparent centers" and similar verbiage.
3) Now, having established that each shot has to be aimed the same way,
i.e., center ball axis to outside edge of the object ball, how is it that
the object ball can split the pocket in two different situations (6 degrees
apart), if the cueball is stuck the same way? The answer, according to
Houle, is that "THEY CANNOT." At least not without some adjustment. When I
mentioned that his followers were claiming that they could "split the
pocket" in both cases, he laughed. The truth is that his system is based on
the understanding that the pockets are typically twice as wide as the ball
and that, with a 1/2 ball hit, there is an error allowance (in degrees)
which will accommodate variations up to some limit that depends on the
particular table conditions (pocket width, cut, facings, etc.). When that
limit is exceeded, you have to switch to 1/4 ball up to its allowable error,
and so on... If players are using the fractional ball aiming system and
splitting the pocket for both 30 and 36 degree angle shots, they are
obviously making minor adjustments when aiming/shooting.
Clearly, Hal Houle is NOT CLAIMING TO DEFY THE LAWS OF GEOMETRY. According
to Hal, this particular system is usually provided to beginners because they
need approximate methods. After a while, they learn to make minute
adjustments (a hair this way or that) which allows them to split pockets
with shots that are within the allowable error range.
People -- there is no mysticism, magic, or other voodoo involved here