Proofs of the EXACTNESS of Pivot Systems

[Jal]

The pivot length needs to be shorter than the CB OB distance. Not a problem for long shots, but it is a problem up close and personal shots.

Someone suggested on one of the CTE threads that this distance should be about 3/4 of the CB OB distance. I have seen recently that it should be 1/2 of the CB OB distance.

The 3/4-ths seems to work for me.

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.



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

 

[AtLarge]

... 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 ... perhaps we can get more precise descriptions of this aspect of the method?

Jim, here's a post from Stan Shuffett today in another thread. Does it help you at all?

http://forums.azbilliards.com/showpost.php?p=2883073&postcount=107​

 

[Patrick Johnson]

Jal:
...there is considerable ambiguity as to where one's cue should actually be pointing
AtLarge:
Jim, here's a post from Stan Shuffett today in another thread. Does it help you at all?

http://forums.azbilliards.com/showpo...&postcount=107

Stan's post doesn't settle it, but it seems that the cue is placed in relation to either the edge-to-aimpoint line or another line somewhere between it and the CTE line. It's not yet certain whether the cue is placed parallel to this "aim line" or at some unknown angle to it (although it's a good bet that it's parallel).

It's interesting to quantify the variance, but I don't think it's necessary in order to conclude that pivoting can't be systematically accurate for a workable range of shots. That seems preposterous on its face.

pj
chgo

 

[Jal]

Jim, here's a post from Stan Shuffett today in another thread. Does it help you at all?

http://forums.azbilliards.com/showpost.php?p=2883073&postcount=107​

Thanks AtLarge. Thus far I'm with Patrick (and likely you as well), that it doesn't really settle it.

Jim

 

[Jal]

....
It's interesting to quantify the variance, but I don't think it's necessary in order to conclude that pivoting can't be systematically accurate for a workable range of shots. That seems preposterous on its face.

Of course, I agree Patrick. It's great to see you swatting the curves balls once again!

Since, according to him, Dave Segal has gone some way in attempting to put it on a mathematical basis, and other proponents are likewise interested in doing so, I thought that maybe we might eventually come to some sort of agreement as to its quantitative predictions. Maybe then, and possibly only then, will everyone accept its conclusions. So a part of my purpose is to show that it can be done. But, as you (and others) have been attempting to elicit, we could use clearer descriptions.

Jim

 

[JoeyA]

Drawing by Richard s

 

[JoeyA]

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.

 

[jwpretd]

Although they [the CTE and ETC lines] 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?

I took SpiderWebComm's post of last night to mean that the pre-pivot cue position is parallel to, and displaced laterally from, a line running from the CTE-ETC perceived convergence point in the field of vision to the center of the cue ball as perceived from that point. ("ETC" should probably be "CB edge to appropriate division of OB" since Shuffett's method doesn't use the OB edge). The post by Stan Shuffett that AtLarge pointed out also seems to indicate that it's the perceived convergence point in the field of vision that's being used.

 

[SpiderWebComm]

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

Jim:

This is excellent. Nice work. The cue is never offset parallel to the CTEL, even on an edge to B alignment if there is some distance between the CB and OB. Your eyes would come off the CTEL at different distances based on the same offset at different shot distances (that's what I was trying to get at earlier). I hope that makes sense.

Dave

P.S. As the distance changes, the cue's angle into the CTEL changes due to perspective. Figuring the cue to be parallel to the CTEL on all shots and distances / alignments wouldn't be right. If we can figure OB size changes (with perspective) and how that affects visual offsets from the CTEL (so we know the cue's alignment to the CTEL), we'll be able to figure a more definitive graph. This data is really interesting to me.

 

[SpiderWebComm]

Stan's post doesn't settle it, but it seems that the cue is placed in relation to either the edge-to-aimpoint line or another line somewhere between it and the CTE line. It's not yet certain whether the cue is placed parallel to this "aim line" or at some unknown angle to it (although it's a good bet that it's parallel).

It's interesting to quantify the variance, but I don't think it's necessary in order to conclude that pivoting can't be systematically accurate for a workable range of shots. That seems preposterous on its face.

pj
chgo

Stan used a 1/2 tip pivot because it mitigates pivoting errors and is objective for people learning the system for the first time (it's hard to mess up).

Arcing the pivot along the "shot circle" (even for small pivots) will ensure you're hitting the correct center. I think this is often missed in discussions. I think if you combine both topics (perspective / OB-plane pivots) --- we're at a much better place.

Dave

 

[Palmerfan]

Pivot System

I just had my first 90/90 lesson which is a variation on CTE but a pivot based system..after the lesson I spent 3 hrs at the table hitting different cut shots with the system and since it was my first day using the system there were plenty of misses..but the misses were the exact same (hitting thick)..after making an adjustment I was pocketing balls form all over..it simply works for me and I'm not a teacher or coach so I cant explain why it works..but when I have my sightline right and that small pivot moving the tip to the center of the cue ball..I feel like I cant miss. And to make sure, I was hitting balls hard to make sure they went in clean as they did..had a few rattle but most went clean at the end.

It works for me so I'm sticking to it. Helps that Ron V was coaching me and saw my mistakes and corrected them no doubt, but I believe in the system, I saw it improve my pocketing

 

[mantis99]

Jim:

This is excellent. Nice work. The cue is never offset parallel to the CTEL, even on an edge to B alignment if there is some distance between the CB and OB. Your eyes would come off the CTEL at different distances based on the same offset at different shot distances (that's what I was trying to get at earlier). I hope that makes sense.

Dave


This is also partly why the math is so challenging. It is difficult to objectively put down exactly where the line of aim will be with each sight line, expecially since it changes with CB distance to OB. It is not hard to find the sight lines, but to correctly ascertain where that puts you from a math stand point is the hard part. Thus why so many people are happy to just make balls and not worry about the math.

I for one really want to know the math because I think it will really help to determine some baselines for sight line and pivot selection instead of having to slowly learn them over time. I really like how much more consistently I ammaking difficult to aim shots, but am quickly growing tired of having to try a few different sight lines and pivots before I get to the right one with certain shots. That is what will keep from using the system right now in any competition. I can't be guessing on a shot, only to learn I picked wrong as an oponent comes to the table. From my experience at the table so far, I believe the mathematical answer is out there instead of an illusion of feel.

 

[mantis99]

Being able to pocket balls with a system doesn't make it exact. Even if you never missed any ball on the table, that still does not make it exact. Exact is a very specific definition that requires CTE to be mathematically proven before it is considered as such.

If the CTE proponents would just admit that CTE is NOT exact and relies on intuition and feel rather than discrete mathematics, all the "naysayers" would not have anything to criticize about CTE and there would be much less negative publicity about it.

Instead proponents of CTE keep insisting that it is exact and crying foul when "naysayers" tell them that its not.

They also seem to resort to insults and personal attacks far more often than the "naysayers", probably due to frustration in not being able to provide any evidence that CTE is exact.

Honestly, those trying to hype CTE up by saying it is exact are probably hurting Stan's sales because potential customers read your statements and then read the statements by Dave and PJ proving them wrong. If you just passed it off as a system that allows you to pocket balls by making alignment more intuitive, you would be much better off.

I find this to be an interesting statement. Certainly CTE is not proven mathematically yet, however, it is far from disproven. Many naysayers put down math and say, hah, it is disproven, but the CTE'rs say "not so fast" because they see errors in the perceptions of the system to create the math. Also, when you pocket balls center cut everytime you do it right, especially on shots that you would normally feel uncomfortable with, it starts to make you think that there is more than just feel going on. If I have a hard time making a shot with feel, then use CTE and it goes in, how can that be feel. There have been a number times I have gotten down on a shot and thought "this aim line can't be right", but then the ball goes center pocket (shows how much I suck at feel aiming). That really isn't why I find the post interesting though. You make a statement that CTE'rs should just admit that the system isn't exact so as not to draw flack. Personally, I will not say that it is certainly exact until it is mathematically proven, although my experience at the table thus far makes me lean that way. That is the nature of proof. At the same time, you probably should not say with such vigor that it can not be exact, because that simply remains to be seen.

I think the value of the system will be improved either way if we can figure out if it has an exact mathematical system, or if it gets you close and feel does the rest, as one can hone their skills with a better understanding of the system. One thing that can't be denied is that people are making balls better than they have before with the system, so it has validity for the game of pool. Given the info we have at this time, I think the best place to be concerning the exactness of CTE is somewhat neutral. Obviously people will ride certain sides of that fence, but to close yourself to the idea that it could work when it has not been disproven is to completely close yourself to the ability to see things other than what you are biased to already. I don't know anyone who can consistently do that and be correct with all of their current ideas. It certainly wouldn't bode well for inginuity if everyone did anyways.

 

[Mikjary]

I just had my first 90/90 lesson which is a variation on CTE but a pivot based system..after the lesson I spent 3 hrs at the table hitting different cut shots with the system and since it was my first day using the system there were plenty of misses..but the misses were the exact same (hitting thick)..after making an adjustment I was pocketing balls form all over..it simply works for me and I'm not a teacher or coach so I cant explain why it works..but when I have my sightline right and that small pivot moving the tip to the center of the cue ball..I feel like I cant miss. And to make sure, I was hitting balls hard to make sure they went in clean as they did..had a few rattle but most went clean at the end.

It works for me so I'm sticking to it. Helps that Ron V was coaching me and saw my mistakes and corrected them no doubt, but I believe in the system, I saw it improve my pocketing

Ron is a good guy and welcome to the forums. :thumbup:

Best,
Mike

 

[Jal]

I took SpiderWebComm's post of last night to mean that the pre-pivot cue position is parallel to, and displaced laterally from, a line running from the CTE-ETC perceived convergence point in the field of vision to the center of the cue ball as perceived from that point. ("ETC" should probably be "CB edge to appropriate division of OB" since Shuffett's method doesn't use the OB edge). The post by Stan Shuffett that AtLarge pointed out also seems to indicate that it's the perceived convergence point in the field of vision that's being used.

I appreciate the input and looked up some of Dave's posts yesterday. I think you might be referring to this one (post #40) in the thread on Patrick's review of the DVD?:

"With your eyes "straddling the ctel" as your starting position...you move your eyes until the cb inside edge hits a b or c (touches the same vertical line in your field of vision). At that point, the 180 deg view of the cb is what you slide into with your tip offset."

I'm still a little fuzzy on the meaning of his second sentence, but it looks like Dave himself might be able to clear that up. If you're referring to another post, any further clarification would be appreciated.

As to your interpretation, it's also not quite clear (to me) what using the convergent point means. That is, if you place the cue down along one of the lines radiating from that point, it will be parallel to the edge-to-B and center-to-edge lines, which are "physically" parallel to each other - in other words, from a non-perspective point of view. But when you say "displaced laterally," it could mean "physically" parallel, as per the last sentence, or parallel in the image formed by our eye (perspective view). In the latter case, it would not be "physically" parallel to the edge-to-B and center-to-edge lines. So I'm sorry, but I'm not quite sure of your meaning.

Jim

 

[Palmerfan]

Ron is a good guy and welcome to the forums. :thumbup:

Best,
Mike

Thanks Mike,

Nate

 

[justnum]

This thread would serve its readers if someone explained a pivot system and discussed the features of using one. Otherwise there is no source material to debate.

The best system is physics and probability. The probability of a player hitting the cueball dead center everytime for dead center shot is infinite, shooting in a region around and containing the dead center is more likely to happen.

As long as the debate is about physics and collisions and not about people who do not shoot straight or on the intended line, then arguing in the language of physics with equations and diagrams would be better. Cooking up the formulas for scrutiny they are loaded in all billiard simulators.

If OP JSP does a math proof please state which form of a proof you intend to use, Direct ,Induction, Contradiction, Derivation or other.

I've been working out my own system but it is tough because I don't always shoot the way I want to.

A pivot occurs in a bank shot, kick shot, combo and straight in. Two things pivot the cue stick (aim the cue at the center of the cue ball then pivot the back end of the cue there are infinitely many different lines, and the path line the cue stick follows after that everything is physics and pre-determined. I've been considering the cue stick and cue ball at the moment of rubbing to act as a lever. Yes a lever. Because of this I get angular and linear velocities and torque. Once the proper initial conditions, stroke speed and cue ball contact and stroke follow through, are set physics and gravity does the rest.

Electrostatic forces do interfere because they attract hair to the CB, I've been meaning to take a magnet to polarize the table or attract lose charges on the table, it is like combing your hair and then pouring water on the comb, the electrostatic charges can create a bridge for the water to ride. On the table it has the effect of smoothing the polarity of the table. Maybe its related to the pivot system in some roundabout way.

 

[AtLarge]

... "With your eyes "straddling the ctel" as your starting position...you move your eyes until the cb inside edge hits a b or c (touches the same vertical line in your field of vision). At that point, the 180 deg view of the cb is what you slide into with your tip offset."

I'm still a little fuzzy on the meaning of his second sentence

My take: With your eyes at the point Dave "defines" in the first sentence, you can then think of the CB in front of you as a flat disk ("180 deg view"). Slide your hand toward that disk with the cue perpendicular to the disk and offset 1/2 tip from the center of the disk in the appropriate direction.

 

[Masayoshi]

I find this to be an interesting statement. Certainly CTE is not proven mathematically yet, however, it is far from disproven. Many naysayers put down math and say, hah, it is disproven, but the CTE'rs say "not so fast" because they see errors in the perceptions of the system to create the math. Also, when you pocket balls center cut everytime you do it right, especially on shots that you would normally feel uncomfortable with, it starts to make you think that there is more than just feel going on. If I have a hard time making a shot with feel, then use CTE and it goes in, how can that be feel. There have been a number times I have gotten down on a shot and thought "this aim line can't be right", but then the ball goes center pocket (shows how much I suck at feel aiming). That really isn't why I find the post interesting though. You make a statement that CTE'rs should just admit that the system isn't exact so as not to draw flack. Personally, I will not say that it is certainly exact until it is mathematically proven, although my experience at the table thus far makes me lean that way. That is the nature of proof. At the same time, you probably should not say with such vigor that it can not be exact, because that simply remains to be seen.

I think the value of the system will be improved either way if we can figure out if it has an exact mathematical system, or if it gets you close and feel does the rest, as one can hone their skills with a better understanding of the system. One thing that can't be denied is that people are making balls better than they have before with the system, so it has validity for the game of pool. Given the info we have at this time, I think the best place to be concerning the exactness of CTE is somewhat neutral. Obviously people will ride certain sides of that fence, but to close yourself to the idea that it could work when it has not been disproven is to completely close yourself to the ability to see things other than what you are biased to already. I don't know anyone who can consistently do that and be correct with all of their current ideas. It certainly wouldn't bode well for inginuity if everyone did anyways.

Dr. Dave has disproven it. Basically, with one set bridge length, there are 6 discrete points of aim in Stan's version of CTE. 6 points of aim are insufficient to pot many shots.

The shots in between these points of aim must be corrected by (either conciously or unconciosly) adjusting where you pivot the cue. The bridge length must be adjusted by feel and intuition. Therefore CTE is not exact.


The CTE'ers say "not so fast" because they seem to believe that not being exact is a bad thing.

 

[Palmerfan]

From the lesson I got it seemed the pivot came with either the slight straightening of the right knee or left knee depending on which side you started on the CB/OB path. Head, Bridge and shooting arm stays dead straight and the 2-3 tips to bring the tip back to center from the edge is a slight..almost unnoticeable "shift" that I saw Ron V. do by basically straightening a knee..so slight you would have to stare at it to remotely see it, but thats what brought the tip to center..and it worked non stop for hours with very few mistakes..and I would imagine more of the mistakes came from poor cue stick movement as once that tip turns toward that CB from the edge of the OB, kinda feels like you cant miss. Of course you do sometimes but for someone struggling with a ball pocketing system that is reliable and "Ghost Ball" just isn't really getting the job done..90/90 aiming system is fantastic. If I learned it 10 years ago I would have never stopped playing out of frustration. It works for me, I don't know if its for everyone but if you do the 2-3 steps the ball goes down...isn't that good enough?