Proofs of the EXACTNESS of Pivot Systems

[jsp]

The pivot def matters. The larger the pivot, the more it matters in order to hit the correct vector through the core (correct "center").

The pivot must always be executed from the tip-back, not the bridge-forward. This is figured from the edge of the shot circle (OB edge of circle, bridge at center--- you must pivot along that arc, which many times forces an effective pivot point behind the bridge).

Then you have perspective adjustments--- the OB gradually getting smaller than the CB with greater distance. When the OB/CB are close, your eyes must move MORE than when the OB/CB are far away (on the same alignment).

None of the above is every really though-out well in these threads.

I believe with a laser pointer, I can show a tolerance that's VERY small with no adjustment (one movement to the final position). This system is very math-based.

The guy who I had helping me got busy with other things. If guys like Dr. Dave / PJ really wanted to know the math--- we'd figure it out together. I have diagrams showing the pivot point offsets in 2D, but I believe they calibrate as the OB size decreases--- that's where I left off.

When I say "I believe it's exact" -- that's based on the info I have and the amount of adjustment needed when I play. I'll continue to say that because I'm confident that with the proper math-help, it'll be proven out in time. I'd rather be unpopular and right (for now) than in the "cool aiming police" group and flat wrong.

Spidey, what you're attempting to do is to figure out the mathematical formula to calculate the exact pivot distance by working backwards from the the ghost ball aim line to the pre-pivot aim line (as determined by the pivot system in question). If the system is exact to begin with, then this formula should already be an intrinsic part of the system itself.

In other words, you're not trying to prove the exactness of the pivot point system. Rather, you're attempting to make an imperfect system (the pivot point system) perfect (ghost ball) by introducing an impractical fudge factor formula (pivot point calculation based on CB-OB distance and other things) into the system in question.

 

[Patrick Johnson]

Spidey:
Why is the offset greater for short shots vs long shots (same alignment) if this is all 2D math as you say.

To address that we'll need to describe a particular short and long shot with alignment, offset and pivoting steps carefully defined.

pj
chgo

P.S. We can do this by PM if you like.

 

[SpiderWebComm]

Not really. Shot angle is a moot point. If your eyes strattle the ctel...the distance your eyes move to get to either the inside quarter or even the center is a variable based on distance. you guys describe alignments as constants- they're not.

Sent from my SPH-M910 using Tapatalk

 

[mantis99]

Lets say for an instant that cte is exact.

Well it all measured points off of the object ball right?

The protocol you chose these 6 different ones you choose them based on the lay of the pocket to the ball right?

So what does the ball know about the pocket?

Nothing so you are basing everything you do on judgement to arrive at a fairly generic contact point that takes into account the width of the pocket, is found by going off the object ball and has not a thing to do with the pocket.

What the pocket got to do with it? Got to Do with it?

Everything especially when you consider you have put a 2 and a 1/4 inch wide object in it and not a contact point.

Your feel is being dicatated by a non visual system which on another thread here its been established that visuals play a part in the system for angles in between the 6.

Geometric exactness is something that doesnt exist of on a shot when you have to throw one in with English to get your ball somewhere else to do it again.

Its just the system gives one a way of making balls.

All the ball making in the world is subject to getting shape, getting out and leaving yourself the easiest shots.

That is why my friend is robbing another one of my friends who plays with cte on a regular basis.

You have to be able to attain feel at some point. Your reference system has to readily allow you to do that or youre in deep doo plain and simple.

If you get there to the right place to make the shot.

Are you tuned in thick or thin? How do you get to the next ball with English to get you there?

336robin :thumbup:

aimisthegameinpool@yahoo.com

Its fairly obvious that aiming is not the only part of pool. No one claims otherwise, and no one claims that learning CTE will be the end of people's pool problems, and that really has nothing to do with the original question. Of course throw and english will come into play, and CTE makes no claims about adjusting for it. It is simply said to get you into the correct line to make the ball. Other factors such as spin and throw will have to be accounted for by the player.

The pocket only matters for the initial set up. The math of the system does the rest.

 

[mantis99]

Then you're having a difficult time visualizing basic geometry. You don't think pivoting at 24'' from the cue tip will result in a different aim line compared to pivoting at 2'' from the cue tip (given the same same pre-pivot cue line and CB placement)? Simply draw it out if you still have doubts.

You are moving the tip a set distance. Whether you have a 5 or 10" bridge, you are moving the cue one half tip. Changes in bridge length will change the amount of excursion of your hand needed to get to the desired spot, but will not change the final spot.

 

[mantis99]

Not really. Shot angle is a moot point. If your eyes strattle the ctel...the distance your eyes move to get to either the inside quarter or even the center is a variable based on distance. you guys describe alignments as constants- they're not.

Sent from my SPH-M910 using Tapatalk

This falls to the point I have made in different threads. It is not the angle of the shot from center CB to OB to pocket that matters. That will not change as the CB is moved in or out from the OB. It is the angle from center CB to the ghost ball that matters.

 

[mantis99]

The issue here is not about whether its mathematically correct or not. The issue is that proponents of CTE such as yourself claim that it is mathematically correct without first backing up your claims with actual math. To make a claim in science you need proof, until then you are wrong. If you do end up proving CTE to be mathematically correct, opponents of CTE were not wrong for asking you for proof to back up your claims.

Incorrect. Nothing is wrong because it is not proven, it is just not proven. All of you are yelling to have proof, however, the math of this system is beyond most people's ability to prove. Sometimes the best way to find the proof, is to try and show why it is not true. Thus, I would like someone to show me why this is just rehashed junk like PJ said. Pj just watched the DVD, so I would love some mathematical proof as to why it does not work. That may be a good place to start for now.

 

[mantis99]

Not really. Shot angle is a moot point. If your eyes strattle the ctel...the distance your eyes move to get to either the inside quarter or even the center is a variable based on distance. you guys describe alignments as constants- they're not.

Sent from my SPH-M910 using Tapatalk

Agreed. This is part of what makes the math so complicated. It is also part of what makes the system much more variable than people are giving it credit for. It is not a 12 line system. It is 12 lines at any one given point that will vary there effect on the OB anytime the cue balls position in relation to the OB is changed. Thus it has infinite points where it can actually hit the cue ball. The math is there, but very complicated. It just hasn't been properly described yet.

 

[JoeyInCali]

I was going to go shoot tonight until I read this thread. Now I don't want to go anywhere near a pool table for some reason.

If you shoot jacked up one handed, how do you pivot ?

 

[SpiderWebComm]

People on this site don't understand how COMPLICATED the math is with these systems. This IS NOT Wei-style 2D 9th grade proofs. The OB size changes which changes offsets from CTEL, pivot points are variables based on distances, etc. This is tough.

We need to agree on core issues before tackling the math.

The good news is.....execution is cake. As easy as it gets. The "WHY" of the matter is nowhere close.

Like I said, I believe it's a perfect system. With some CAD help from someone like LLAMAS or someone else who can help simulate perspective based on ratios, I think we can get this to the finish line.

If someone thinks the CTEL is the same based on distance (or any line), they have a lot to learn based on perception/perspective.

For example, with CB/OB "touching" and back to back.... that's a center to center alignment and a left edge to left edge (or right edge alignment). As the distance increases, the OB shrinks in size and before you know it--- you no longer have an edge to edge perspective/alignment. If you realign - you're def no longer center to center. Furthermore, if you're aligning edge to "A" when the balls are touching and you move the OB 8' straight back--- you're no longer perceiving edge to "A" on that "same line" in your field of vision. You must move to re-acquire that alignment.

I have the 2D CAD diagrams worked out...but I need to convert them to a "perspective" model (simulate perspective with size vs distance ratios). It's NOT a "proof" in a pure sense. I'm not capable of doing that, for sure. However, if we all worked together--- we'd eventually get there and end the partisan bickering.

Dave

 

[Not Dead Ted]

Incorrect. Nothing is wrong because it is not proven, it is just not proven. All of you are yelling to have proof, however, the math of this system is beyond most people's ability to prove. Sometimes the best way to find the proof, is to try and show why it is not true. Thus, I would like someone to show me why this is just rehashed junk like PJ said. Pj just watched the DVD, so I would love some mathematical proof as to why it does not work. That may be a good place to start for now.

You should consider starting your proof by addressing this issue:

Mechanical CTE does not consider the pocket location other than by forcing the user to select one alignment from a small set of available options. For the same CB-OB distance, the same set of available alignments and cut angles are identical. It is easy to show that moving the CB-OB a small distance (while maintaining CB-OB distance), say 2" of translational motion, will result in a miss. Since CTE is a "center pocket" system, how do you reconcile this?

As it was presented, there are only 6 available cut angles for left cuts and 6 for right. It is very easy to prove by contradiction that this is not sufficient for all table positions of a fixed CB-OB relationship.

 

[Masayoshi]

Incorrect. Nothing is wrong because it is not proven, it is just not proven. All of you are yelling to have proof, however, the math of this system is beyond most people's ability to prove. Sometimes the best way to find the proof, is to try and show why it is not true. Thus, I would like someone to show me why this is just rehashed junk like PJ said. Pj just watched the DVD, so I would love some mathematical proof as to why it does not work. That may be a good place to start for now.

No, Positive claims are considered incorrect unless you have proof. If you answer does sasquatch exist with "yes", you are wrong unless you drag its carcass to the nearest zoo. Sasquatch could exist, but you couldn't positively say that sasquatch exists without being wrong.

 

[horton129]

Many posters here have claimed that these pivot systems are "exact" or "perfect" or that they require absolutely no subconscious adjustments if systematically followed.

Well, I created a the thread for these posters to PROVE these claims. If a particular system is EXACT as claimed/advertised, then it can formally be proven mathematically.

So let's start seeing these proofs! Otherwise, the exactness/perfectness of these systems will continue to be considered as unsubstantiated claims by the "detractors".

1-a~<€ . [b/z {£} a] < b+ (a*1) . (g2:45) = x

This proves mathematicaly without a doubt that pivot systems are perfect for center pocketing.

 

[cleary]

who said there existed any form of mathematical proof that pivot systems work. There are a hell of a lot of bank shots that go, though mathemaically they don't.

Some things just work, because they do. for some people.

Exactly. A good stroke will pocket a ball. Aim a cut shot or bank shot and poke the ball, it may not fall.

 

[jsp]

Duplicate Post...

 

[jsp]

You should consider starting your proof by addressing this issue:

Mechanical CTE does not consider the pocket location other than by forcing the user to select one alignment from a small set of available options. For the same CB-OB distance, the same set of available alignments and cut angles are identical. It is easy to show that moving the CB-OB a small distance (while maintaining CB-OB distance), say 2" of translational motion, will result in a miss. Since CTE is a "center pocket" system, how do you reconcile this?

As it was presented, there are only 6 available cut angles for left cuts and 6 for right. It is very easy to prove by contradiction that this is not sufficient for all table positions of a fixed CB-OB relationship.

^^This.

Though, moving the OB an arbitrarily small distance (say 2") on the same pre-pivot alignment won't necessarily "result in a miss", but it would no longer result in an EXACT center pocket shot anymore. Since the claims are that these system are exact, the exactness proponents MUST reconcile this. The way these systems have been presented, they can't.

In order for these systems to be even remotely considered as potentially exact, the system must have a way to compute the exact pivot distance based on the exact CB-OB distance on the same pre-pivot alignment.

For example, for one particular pre-pivot alignment with a CB-OB distance of x'', the pivot distance is y''. If the CB-OB distance is now (x+d)'' (moved a distance d'') on that same pre-pivot alignment, the new pivot distance should now be (y+f(d))'' (the change in pivot distance is a function of the change in CB-OB distance).

And even if the system does have mathematical formulas or look-up tables to determine the precise pivot distance, actually executing it in practice would be highly impractical.

 

[DangerousDave]

Incorrect. Nothing is wrong because it is not proven, it is just not proven. All of you are yelling to have proof, however, the math of this system is beyond most people's ability to prove. Sometimes the best way to find the proof, is to try and show why it is not true. Thus, I would like someone to show me why this is just rehashed junk like PJ said. Pj just watched the DVD, so I would love some mathematical proof as to why it does not work. That may be a good place to start for now.

Usually I wouldn't be too keen to shift the burden of proof in this way but since the CTE believers generally ignore theirs, this might be the way to go - as long as everyone is clear on the fact that CTE is not deemed valid until proved otherwise. Still, it almost goes without saying that if someone did the math and could demonstrate that CTE could not possibly work, most of the believers in the system would ignore or deny it - "It don't have to work on paper, it works on the table!"

This commonly-seen rationalisation aside, the CTE crowd generally have too much invested in the system to publicly denounce their old views. They've spent hours online arguing with anyone who expresses any doubt over the value of CTE, and to concede that they were incorrect in their assertions and fervour would be too painful for them. Admitting when you're wrong is hard to do. That's why I tend to avoid being wrong in the first place.

 

[mantis99]

You should consider starting your proof by addressing this issue:

Mechanical CTE does not consider the pocket location other than by forcing the user to select one alignment from a small set of available options. For the same CB-OB distance, the same set of available alignments and cut angles are identical. It is easy to show that moving the CB-OB a small distance (while maintaining CB-OB distance), say 2" of translational motion, will result in a miss. Since CTE is a "center pocket" system, how do you reconcile this?

As it was presented, there are only 6 available cut angles for left cuts and 6 for right. It is very easy to prove by contradiction that this is not sufficient for all table positions of a fixed CB-OB relationship.

Ugh! This perception is a lot of the reason people fail to see why the math is there for this, and continues to be repeated. Your statement, however, is incorrect. There are 2 variables for this reason. 1st, while the angle of the shot may remain the same, the angle going from center CB to center ghost ball (required spot to shoot center CB to make the shot), or even the CTE line WILL CHANGE with any CB movement away from the original spot. This will result in the sight lines putting your aim point at a slightly different spot, so you will not miss, at least not within a certain range. You will eventually, of course reach a position where you will need to use different sight lines, thus the 12 line system (6 for each cut direction). Also, as has been alluded to a number of times, any movement of the CB in relation to the OB will make the viewers perception of the OB size in relation to the CB change, thus, when you sight the same lines and pivot, their will be some variation in the resultant aim point from the one done from a different spot.

 

[mantis99]

No, Positive claims are considered incorrect unless you have proof. If you answer does sasquatch exist with "yes", you are wrong unless you drag its carcass to the nearest zoo. Sasquatch could exist, but you couldn't positively say that sasquatch exists without being wrong.

Ugh! Where did you learn your science. I am not trying to be rude or difficult, but there is just so much misinfo on here. I have a bachelors degree in Biology and a Masters degree in Physical therapy. The scientific method and proof of effectiveness of treatment are things I deal with daily. The sasquatch example does not fit at all here. No one has ever seen a sasquatch or had any real proof that one exists, thus no one will believe its existence without strong proof. However, people are routinely and consistently pocketing balls with CTE, they just can't yet exlpain why. There is proof right at the table. Heck, spidey made a video shooting balls without seeing the pocket. Proof of the system's abilities is at the table already, it is the explanation of why that is missing. This certainly does not make it wrong. Gravity is obvious, but I bet you can't explain it mathematically off the top of your head. Is it wrong? Of course not.

I treat people daily using a variety of techniques to help heal injuries. Some are well proven, and some aren't yet. Thus I have to combine to the best of my abilities the empirical evidence in the research with clinical reasoning based on my experience. I guarantee you I have helped heal injries with techniques that we haven't been able to fully explai nthe whys of yet. Should I stop using them? Research shows that people get better with spinal manipulation, yet there is fierce debate as to why it works. Should we stop using it even though data suggests it works because we can't fully explain it? Of course not. CTE's results are obvious, why is not. Because it has not been proven mathematically, one can't rule out PJ's ascertions that it is a subconscious feel based system, or other theories to explain it. It certainly is not considered wrong though.

 

[dr_dave]

Many posters here have claimed that these pivot systems are "exact" or "perfect" or that they require absolutely no subconscious adjustments if systematically followed.

The systems can be "exact" and "perfect" if you place your bridge hand in the correct place and use the "effective pivot length" necessary for a given cut angle.

If a particular system is EXACT as claimed/advertised, then it can formally be proven mathematically.

In my opinion, others and I have already done this here:

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

For full context and understanding, please see the entire page containing basic descriptions of various versions of CTE along with explanations, illustrations, article links, and quotes from me and others who have already studied these concepts in depth.

First of all, it is obvious that 2, 3, 4, or 6 lines of aim (from CTE Versions 1-4) are not enough to pocket balls over a wide range of cut angles. This is mathematically proven here:

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

However, if you vary the "effective pivot length" during the pivot, these shortcomings can be overcome. Jal posted all of the math necessary to understand how the "effective pivot length" must vary to achieve a range of cut angles. Here it is:

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

His results show that the "effective pivot length" must vary quite a bit, and in a complicated way. His math applies directly only to Version 2 of CTE, but the concepts and conclusions apply to all "align-and-pivot" methods (e.g., any version of CTE or 90/90). I illustrate and explain how the "effective pivot length" can be changed, and why it must be changed, here:

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

The problem is: To be able to place the bridge hand in the right place and/or use the "effective pivot length" necessary for a given shot, you need to be able to visualize the aim required for a given shot. And, IMO, if you already have this ability, you have no need for a procedural "aiming system." Although, align-and-pivot "aiming systems" do offer many potential benefits to some people.

Regards,
Dave