Proofs of the EXACTNESS of Pivot Systems

[Jal]

Jim -- What I said in post #121 was my take on what Spidey said a few posts before that. But my interpretation of what Stan said in the DVD is really a bit different. When I commented on Dr. Dave's review of the DVD, here's what I wrote (11 days ago):

The way I interpret what Stan says is that, essentially, one needs to find the sighting position where he can simultaneously view both the CTEL and the secondary alignment line (to A/B/C). This sighting position will be between those two alignment lines, and this sighting position will define the relevant edges of the cue ball and, therefore, the relevant face (now think of it as a flat disk) of the cue ball. From this sighting position, move straight in toward that cue-ball face (perpendicular to the flat disk) with the 1/2-tip offset needed.​

So I felt Stan was saying you're not looking straight down either the CTEL or the edge-to-A/B/C line -- you're between those lines, sort of optimizing the view of both, rather than directly on either one. After all, if you are to look straight down either one of those lines, there is no need for the other one (other than some consistency of set-up reason, perhaps).

I hope Dave can tell us which interpretation is the right one. And it would be great if Stan could confirm it. As you say, it's quite possible your earlier interpretation of 11 days ago is correct. That's why I did the graph for the cut angles where edge to B is appropriate, because it and the CTE line are parallel (though appear to converge), and any line between them radiating from the point of convergence is also parallel to them. We shall see.

Thanks for the additional comments......even though I was pulling for your interpretation in post #121.

Jim

 

[NewStroke]

Not by what you say you're doing while aiming. You've proved too many times that you don't understand the questions being asked.

pj
chgo

Will you believe it, if I kick your butt using CTE? I will tell you that I am not sure how it works exactly but my shot percentage has increased by at least 20%. I take shots I never would have taken and I am making them. If I miss, I know why and how to correct it for next time. Regardless of your arguments or anything else, I'll continue using CTE until it fails or I find something better.

Thanks

Dan

 

[jwpretd]

That's why I did the graph for the cut angles where edge to B is appropriate, because it and the CTE line are parallel (though appear to converge), and any line between them radiating from the point of convergence is also parallel to them.

Thanks again. That's a clear statement of what I was trying to babble in the post last night. I believe SpiderWebComm was talking about a

"... line between them radiating from that point...."

that goes directly to the center of the cue ball as seen from that point, by which I meant AtLarge's

"From this sighting position, move straight in toward that cue-ball face (perpendicular to the flat disk)....".

Except that it's displaced laterally (e.g., AtLarge: "...with the 1/2-tip offset needed.").

 

[Patrick Johnson]

Me:
Not by what you say you're doing while aiming. You've proved too many times that you don't understand the questions being asked.

Newstroke:
Will you believe it, if I kick your butt using CTE?

LOL. I don't know what I was talking about in that quote so I definitely have no idea what you're talking about. But if I had to guess I'd say no, I doubt that I'll believe it, whatever it is.

pj
chgo

 

[LAMas]

Jim -- What I said in post #121 was my take on what Spidey said a few posts before that. But my interpretation of what Stan said in the DVD is really a bit different. When I commented on Dr. Dave's review of the DVD, here's what I wrote (11 days ago):

The way I interpret what Stan says is that, essentially, one needs to find the sighting position where he can simultaneously view both the CTEL and the secondary alignment line (to A/B/C). This sighting position will be between those two alignment lines, and this sighting position will define the relevant edges of the cue ball and, therefore, the relevant face (now think of it as a flat disk) of the cue ball. From this sighting position, move straight in toward that cue-ball face (perpendicular to the flat disk) with the 1/2-tip offset needed.​

So I felt Stan was saying you're not looking straight down either the CTEL or the edge-to-A/B/C line -- you're between those lines, sort of optimizing the view of both, rather than directly on either one. After all, if you are to look straight down either one of those lines, there is no need for the other one (other than some consistency of set-up reason, perhaps).

Sounds correct to me, but there isn't an exact location for being in between.

 

[LAMas]

What are the cut angles +/- X degrees achieved by the secondary aim points A, B, or C and 1/8 with pivot in and pivot out?

 

[Jal]

Yes, that's the post to which I was referring. As for the rest... Please accept my apologies. I thought I'd found a way to make use of the fact that the CTE and ETC lines can appear to converge in the visual field even though they are actually parallel in the plane. The idea was fuzzy at the time, and gets fuzzier the more I think about it.

Jim: Saw your 03:09 post #124 immediately after submitting this one. That contains the general idea I was trying to grasp. Thanks for throwing some light in that direction.

I didn't mean to suggest or imply earlier that I thought you were speaking unintelligibly, and I'm sorry if I gave that impression. At this point we're all speculating as to the really fine details of the procedure. Until we hear from the architects, it'll have to remain as such. At any rate, it looks like we were thinking along the same lines. As a fellow babbler, we understand each other.

Jim

 

[SpiderWebComm]

My mind can't take in any more discussion on CTE. I'm numb

That's why you've posted recently in every single CTE thread on the main page. See.... that's what trolls do. Antagonize, instigate and then golly-gee -- they can't take anymore.

 

[MOJOE]

My mind can't take in any more discussion on CTE. I'm numb

Who's forcing you to participate??

 

[jsp]

You answered your own question. Draw it out yourself and you'll be quite surprised by the result. Oh, there might be extremes that effect workability, but the process seems to hold up with different pivot lengths. I just tried it out on my home table.

I'm still trying to figure out how to post my scan. What holds the process together is starting out at the contact point and pivoting to CENTER.

I don't think anyone took the time to reply to your drawing richard.

The problem with your drawing is that it shows it working for only that one GB location. Keep the exact same contact point location, initial cue offset, and CB location, but simply rotate the OB-GB locations around the contact point by an arbitrarily small angle. "Pivoting to center CB" using the exact same pivot point results in the same aimline but it will no longer go through the exact GB center since the GB has moved a small amount. The pivot point has to change to accomodate the new GB location.

For any pivot system to be "exact", the system must systematically tell you exactly where the pivot point should for EVERY shot.

 

[jsp]

Here's a tentative plot of the pivot lengths for three different CB-OB separations against cut angles in the range of about 15-30 degrees (the graph goes from 14 to 34 degrees). There are three curves for each CB-OB distance: a central black one showing the geometrically correct pivot length, surrounded by two red ones indicating the pivot lengths producing +/- 2 degree errors in OB direction.

View attachment 172904

According to this, the only pivot locations that roughly agree with those suggested on the DVD (7"-9" according to Dr. Dave's summary), are for the 18" separation at cut angles within a few degrees of 16. The pivot distances move down the stick (and ultimately beyond it) as the desired cut angles approach 30 degrees. This is because the stick, according to the interpretation of the pre-pivot alignment used here, is oriented parallel to the CTE line prior to pivoting. It thus requires a pivot looking ever more like a parallel shift as the cut angle nears 30 degrees.

I used the term "tentative" because there is considerable ambiguity as to where one's cue should actually be pointing in the descriptions of the method (I don't know if that's been resolved yet). At least in the interval of about 15-30 degrees, the CB edge to OB center (ETC) direction is parallel to the CTE direction. Although they converge in the field of vision, any line running between them so to speak (radiating from the point of convergence), is also parallel to them. Another possible interpretation, however, ala Lamas, is that the pre-pivot direction should run parallel to the ETC in the field of vision (image plane of the eye). If that is what's meant, then that would make it dependent on eye position, orientation of the optic axis, and a few other things, but would tend to squeeze the pivot locations into a tighter range (judging from similar graphs based on center to contact point alignments). Before attempting ones based on that interpretation, perhaps we can get more precise descriptions of this aspect of the method?

Jim

Once again, you're the man Jal. I was about to undertake a similar analysis until I saw this post and your work on Dr. Dave's site. Sometimes I wonder why I bother even pondering to attempt such things, considering either you or Dr. Dave have already done such analyses/proofs and have them documented somewhere online if I look hard enough. Lol.

 

[richard s]

I don't think anyone took the time to reply to your drawing richard.

The problem with your drawing is that it shows it working for only that one GB location. Keep the exact same contact point location, initial cue offset, and CB location, but simply rotate the OB-GB locations around the contact point by an arbitrarily small angle. "Pivoting to center CB" using the exact same pivot point results in the same aimline but it will no longer go through the exact GB center since the GB has moved a small amount. The pivot point has to change to accomodate the new GB location.

For any pivot system to be "exact", the system must systematically tell you exactly where the pivot point should for EVERY shot.

I'm glad someone answered my disjointed series of posts. The principle seems to hold up for me at many different cut angles. While the pivot point might be a factor (I'm certainly open to suggestions and observations), I really believe the principle shown to be geometrically provable as described in one of my previous posts. I also suspect this is a principle that has been known for some time by some of the better players. I just happened to stumble upon what I diagrammed after being highly intrigued by the reliability the aim and pivot systems produced. My first exposure to these systems was a ball proportion process given to me by Hal over the phone. I hope the pool community can arrive at some kind of consensus regarding this interesting subject.

 

[richard s]

Addendum to Last Post

Actually, the length of the pivot changes, given a static pivot point, with the contact point and center ball aim requiring a longer or shorter arc.

Remember, the starting point is the contact point and the end point is center ball.

 

[Jal]

Once again, you're the man Jal. I was about to undertake a similar analysis until I saw this post and your work on Dr. Dave's site. Sometimes I wonder why I bother even pondering to attempt such things, considering either you or Dr. Dave have already done such analyses/proofs and have them documented somewhere online if I look hard enough. Lol.

Thanks Jsp. I'm glad you mentioned Dr. Dave, since, after all, he does try to contribute something every now and then. At least we have to give him credit for that.

I've been waiting for the opportunity to welcome you back to the forum, and since you complimented me, hey...No, seriously, it's great to see you here once again, even though it means we won't be able to get away with some of the BS so easily (or at all).

It wouldn't hurt to have you do the math in your own style. It may very well be clearer than mine, or offer up some nuances in a novel way. All views are certainly welcome. I always look forward to reading your take on things.

Jim

 

[champ2107]

Stan suggests a precise bridge length for each CB-OB distance. He also clearly defines 6 and only six different lines of aim for each CB-OB distance. All of this is clearly summarized here:

http://billiards.colostate.edu/threads/aiming.html#ProOne​

Regardless of where you position your eyes and how you perceive things at the table in 3D, there are still only 6 different lines of aim for a given CB and OB placements (at a certain distance apart). These 6 different lines of aim create six different cut angles. Depending on where the pocket is relative to the OB, one of the 6 angles might pocket the ball. The chances for success are better if the OB is closer to the pocket and if the pocket is large. However, 6 cut angles is not sufficient to cover the wide range of shots that occur at a table, especially a full-size table with tight pockets. For more information, see:

http://billiards.colostate.edu/threads/aiming.html#limited​

The proof that 6 lines of aim is insufficient is irrefutable. Regardless, align-and-pivot "aiming systems" like CTE and 90/90 can still have potential benefits for some people. Many of these benefits are summarized here:

http://billiards.colostate.edu/threads/aiming.html#benefits​

Regards,
Dave

I see 9 lines of aim and 10 if u count a straight in twice or am i confused and you guys are talking about something else, i am to lazy to read all this stuff you guys are posting?

 

[dr_dave]

Stan suggests a precise bridge length for each CB-OB distance. He also clearly defines 6 and only six different lines of aim for each CB-OB distance. All of this is clearly summarized here:

http://billiards.colostate.edu/threads/aiming.html#ProOne​

Regardless of where you position your eyes and how you perceive things at the table in 3D, there are still only 6 different lines of aim for a given CB and OB placements (at a certain distance apart). These 6 different lines of aim create six different cut angles. Depending on where the pocket is relative to the OB, one of the 6 angles might pocket the ball. The chances for success are better if the OB is closer to the pocket and if the pocket is large. However, 6 cut angles is not sufficient to cover the wide range of shots that occur at a table, especially a full-size table with tight pockets. For more information, see:

http://billiards.colostate.edu/threads/aiming.html#limited​

The proof that 6 lines of aim is insufficient is irrefutable. Regardless, align-and-pivot "aiming systems" like CTE and 90/90 can still have potential benefits for some people. Many of these benefits are summarized here:

http://billiards.colostate.edu/threads/aiming.html#benefits​

I see 9 lines of aim and 10 if u count a straight in twice or am i confused, i am to lazy to read all this stuff you guys are posting?

For each CB and OB distance, Stan's version of CTE provides only 6 different lines of aim. If you read the description again, with this in mind, it should be clear that this is the case. So for any particular shot, there are 6 and only 6 different cut angles from which to choose, assuming you use a fixed-bridge pivot at the bridge length suggested by Stan.

Regards,
Dave

 

[champ2107]

i made a mistake on the ccb/robe/b/lp and ccb/robe/A/lp they should be reversed.

is this wrong?

 

[Patrick Johnson]

is this wrong?

Stan's DVD instructions say to substitute the 1/8 aimpoint for the "A" or "C" aimpoints with thin cuts - he says this is because if you use the "A" or "C" aimpoints you're aiming into space beside the OB.

I don't know how it's better to aim even farther into space using the 1/8 aimpoint, but if you follow his instructions to bypass the "A" and "C" aimpoints for thin cuts, then you get only 6 cut angles (the straight-in shot isn't a cut).

pj
chgo

 

[dr_dave]

is this wrong?

The 6 lines of aim apply to each cut direction (right or left), and they vary from straight-in to very thin. If you want to include all possible cuts in both directions, then there are 11 lines of aim (because straight-in shouldn't be counted twice). You're only showing 8 lines of aim in your diagram (or 9 if you include "straight in").

Regards,
Dave

 

[jwpretd]

I don't think anyone took the time to reply to your drawing richard.

The problem with your drawing is that it shows it working for only that one GB location. Keep the exact same contact point location, initial cue offset, and CB location, but simply rotate the OB-GB locations around the contact point by an arbitrarily small angle. "Pivoting to center CB" using the exact same pivot point results in the same aimline but it will no longer go through the exact GB center since the GB has moved a small amount. The pivot point has to change to accomodate the new GB location.

For any pivot system to be "exact", the system must systematically tell you exactly where the pivot point should for EVERY shot.

Does this drawing differ from the pivot system described by LAMas in posts #94 and #95 of this thread:

1. Aim center of cue ball at object ball contact point.
2. Parallel shift the cue to point at the center of the object ball.
3. Pivot the cue back to the center of the cue ball. The cue will now be pointing directly at the center of the ghost ball.

For a given cut angle, the position of the pivot point varies directly with CB-->OB distance. For a given CB-->OB distance, the pivot point position is constant for all cut angles.

NB: The leftmost drawing in post #95 is showing what happens if you hold the pivot point constant (i.e., at 12.88 inches) while varying CB-->OB distance; note the other 89 degree cut drawing. Given the distances and narrow angles involved, it's very difficult to make images that are small enough to post in this forum and that are also close to scale and show things accurately.