Proofs of the EXACTNESS of Pivot Systems

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.

If you can show me anywhere on Stan's DVD where it suggests that the mechanical CTE method depends on the CB table position, I will gladly review it. I did not see anything on that video (or in the many other CTE descriptions) that suggests that it depends on anything other than CB-OB distance.
 
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.
Sorry, Mantis, but this is nonsense. Changing the distance between the CB and OB doesn't change the number of cut angles defined by CTE, and that's the problem being discussed. No matter the CB/OB distance, and no matter what aim lines you use to find them, there are only six (maybe 8 with the 1/8 fraction included) unadjusted cut angles available with CTE, and this simply isn't enough to cover the whole 90-degree range of possible shots - not even close.

CB/OB distance and changing apparent size of the OB are red herrings that don't address the question of how to aim the shots that fall between CTE's 6-8 defined cut angles - which, by the way, are most of the shots on the table.

Continuing to raise this red herring argument shows a failure to understand the question and a general difficulty with the subject matter.

pj
chgo
 
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.

:D
So if we are at a table and I describe CTE to you, then I demonstrate CTE over and over so your exactly sure what I am doing, and there is a way to mark the CB so its verified that I am hitting center, and I'm having a very good day and doing everything perfectly, ball after ball is going center pocket, I still have to go get pencil and paper, do the math before CTE is valid?
By the way, the people who express doubts are people that haven't put any time on the table to learn CTE.
 
So if we are at a table and I describe CTE to you, then I demonstrate CTE over and over so your exactly sure what I am doing, and there is a way to mark the CB so its verified that I am hitting center, and I'm having a very good day and doing everything perfectly, ball after ball is going center pocket, I still have to go get pencil and paper, do the math before CTE is valid?
Yes, if "valid" means "works without adjustment by feel". Nobody can tell exactly what you're doing to make shots, even if they're looking over your shoulder while you're doing it.

By the way, the people who express doubts are people that haven't put any time on the table to learn CTE.
By the way, that's still irrelevant.

pj
chgo
 
Yes, if "valid" means "works without adjustment by feel". Nobody can tell exactly what you're doing to make shots, even if they're looking over your shoulder while you're doing it.


By the way, that's still irrelevant.

pj
chgo

So you'll never be satisfied, and it's not irrelevant that people argue without a complete understanding of the subject.
I vote valid even if while playing I make some adjustments by feel, although sometimes I wish I didn't.
 
So you'll never be satisfied
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.

...it's not irrelevant that people argue without a complete understanding of the subject.
So stop doing it.

I vote valid even if while playing I make some adjustments by feel, although sometimes I wish I didn't.
Voting on the definition of "valid" is irrelevant.

pj
chgo
 
Sorry, Mantis, but this is nonsense. Changing the distance between the CB and OB doesn't change the number of cut angles defined by CTE, and that's the problem being discussed. No matter the CB/OB distance, and no matter what aim lines you use to find them, there are only six (maybe 8 with the 1/8 fraction included) unadjusted cut angles available with CTE, and this simply isn't enough to cover the whole 90-degree range of possible shots - not even close.

CB/OB distance and changing apparent size of the OB are red herrings that don't address the question of how to aim the shots that fall between CTE's 6-8 defined cut angles - which, by the way, are most of the shots on the table.

Continuing to raise this red herring argument shows a failure to understand the question and a general difficulty with the subject matter.

pj
chgo

Let's start here. I believe edge to "a" alignlment at 1' provides a different solution than edge to "a" at 5'. Explain why you think it's the same.

Sent from my SPH-M910 using Tapatalk
 
Let's start here. I believe edge to "a" alignlment at 1' provides a different solution than edge to "a" at 5'. Explain why you think it's the same.

Sent from my SPH-M910 using Tapatalk

Yes, the CB-OB distance is critical to the cut angles determined by the method. The problem is that this is all it depends on. The pocket location is not considered. For a given CB-OB distance, you are stuck with the same handful of discrete cut angles, and they cannot suffice for all locations of the OB.
 
Dave:
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.
...
However, if you vary the "effective pivot length" during the pivot, these shortcomings can be overcome.
The pivot length must change in order to be able to make all shots at a fixed CB/OB distance. But the DVD isn't clear about this (or about a lot of things, unfortunately. It specifies a small range (about 3 inches) of possible pivot lengths for each CB/OB distance, but doesn't say whether to choose one distance within the range and stick to it or to vary the pivot length within that range for different shots. The most obvious interpretation, given what's said and not said, is to choose one pivot length for each CB/OB distance.

By the way, there is no discussion of pivot length in the video presentation - what little there is has to be discovered by reading the "glossary".

pj
chgo
 
Yes, the CB-OB distance is critical to the cut angles determined by the method. The problem is that this is all it depends on. The pocket location is not considered. For a given CB-OB distance, you are stuck with the same handful of discrete cut angles, and they cannot suffice for all locations of the OB.

Slow up - we're not there yet.

Just to clarify to the room and show people how perspective changes the result:

exampled.jpg


This is an example of two balls touching and how your perspective of an edge to edge alignment changes with distance. Although the geometry is the same, your brain sees the geometry differently; thus, you align differently to offset the perspective illusion.

Therefore, if a true edge to edge alignment changes greatly with distance, all alignments change (except true center-to-center). So, even something basic like a CTE/EDGE TO B (parallel lines on two touching balls)--- the shooter must offset different distances based on CB/OB separation in order to maintain a true overlap (both points touching the same vertical line in your field of vision). This means a different vector through the core of the CB.

Dave

P.S. Looking at Dr. Dave's aiming site-- most of his diagrams are wrong. The OB is NEVER the same size as the CB perceptually speaking, so the player NEVER aligns the same for many of his examples. Players always look at overlaps based on vertical lines in their vision - not skewed lines.

PPS--> It'd be fascinating to have Dr. Dave find a CTE solution that works or a 90/90 solution that works (figuring a smaller OB at all times - based on distance / size ratios) and then calculate the offsets required to maintain the same visual alignment as you increase the distance and see if those also yield a solution to the pocket.
 
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So if we are at a table and I describe CTE to you, then I demonstrate CTE over and over so your exactly sure what I am doing, and there is a way to mark the CB so its verified that I am hitting center, and I'm having a very good day and doing everything perfectly, ball after ball is going center pocket, I still have to go get pencil and paper, do the math before CTE is valid?
By the way, the people who express doubts are people that haven't put any time on the table to learn CTE.

I believe that the players that are questioning CTE have put in many more hours at the table on average than the players that feel CTE it is the best method for aiming. Johnnyt
 
I believe that the players that are questioning CTE have put in many more hours at the table on average than the players that feel CTE it is the best method for aiming. Johnnyt

Doubt it. Most CTE users play all the time and play well. CTE is something they evolve into after years of playing with another method. No one really just learns CTE from day 1 unless they're fortunate, imo.
 
... 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:

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:

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:
...
The pivot length must change in order to be able to make all shots at a fixed CB/OB distance.
Agreed!

But the DVD isn't clear about this (or about a lot of things, unfortunately. It specifies a small range (about 3 inches) of possible pivot lengths for each CB/OB distance, but doesn't say whether to choose one distance within the range and stick to it or to vary the pivot length within that range for different shots. The most obvious interpretation, given what's said and not said, is to choose one pivot length for each CB/OB distance.
I think Stan's version of CTE presented on the DVD is very clear on this. For each CB-OB distance, there are 6 (not 8) precise CB-edge/point-to-OB-point alignments to choose from. Also, a precise bridge length is specified for each CB-OB distance range. The DVD does not suggest or imply you should vary the "effective pivot length" for different cut angles within each of the alignment ranges. I think it is clear that the "effective pivot length" for every shot is the selected bridge length, since a "fixed-bridge" pivot is being used.

By the way, there is no discussion of pivot length in the video presentation - what little there is has to be discovered by reading the "glossary".
It would have been nice to see examples of the different bridge lengths required for different CB-OB distances, but at least the information is clear in the glossary.

To me, the most important thing that remained unclear after watching the video several times is: How do you choose the appropriate alignment for the amount of cut needed on a particular shot at the table. In other words, how do you judge the required ball-hit fraction? The specific examples provided are useful; but, IMO, there was no guidance on the DVD concerning how to do this yourself, other than: "You will learn with experience." But maybe that's the most important message on the DVD: We all learn how to aim "with experience." You must practice a lot at the table to learn to aim accurately and consistently, regardless of which "system" you might or might not use.

Regards,
Dave
 
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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.


So stop doing it.


Voting on the definition of "valid" is irrelevant.

pj
chgo

Really PJ, seems I answered alot of your questions. You either chose to not change your closed minded thinking or said we don't speak the same language, what a joke.
 
Me:
Changing the distance between the CB and OB doesn't change the number of cut angles defined by CTE, and that's the problem being discussed
.
Spidey:
Let's start here. I believe edge to "a" alignlment at 1' provides a different solution than edge to "a" at 5'. Explain why you think it's the same.
Read what I said above and explain how you're addressing the question. Changing the CB/OB distance changes the angles of the edge-to-aimpoint lines (compared to the CTE line), but it doesn't add any new cut angles. Six angles at 1 foot distance and six different angles at 5 feet is not 12 angles to choose from - you only shoot each shot at one fixed distance.

Here's another quote from above that applies here too:
Continuing to raise this red herring argument shows a failure to understand the question and a general difficulty with the subject matter
.

pj
chgo
 
I believe that the players that are questioning CTE have put in many more hours at the table on average than the players that feel CTE it is the best method for aiming. Johnnyt

I think the big three have spent thousands of hours on forums speaking against it and very little time on a table trying it. CTE is real easy to learn if your willing too, but more fun to argue against apparently.
 
Looking at Dr. Dave's aiming site-- most of his diagrams are wrong. The OB is NEVER the same size as the CB perceptually speaking, so the player NEVER aligns the same for many of his examples. Players always look at overlaps based on vertical lines in their vision - not skewed lines.
Spidey, a diagram can easily be shown with 3D perspective, but this doesn't change the meaning or information provided by the diagram. In other words, I could add perspective to every diagram on my aiming resource page, and absolutely none of the explanations or conclusions would change!

For a given CB-OB distance, there is a very clear meaning for each of the CTE alignments. For example, for a given CB-OB distance and a given cut direction, there is only one true inside-CB-edge-to-OB-center line, regardless of how you decide to draw it on paper (with perspective or not). For given CB and OB locations, a given distance apart, Stan's version of CTE suggests 6 and only 6 different possible lines of aim. Each of these will create 1 and only 1 cut angle, assuming you are using a fixed-bridge pivot at the bridge length suggested by Stan. These 6 cut angles will allow you to pocket a fair number of shots at the table, but there will be many shots that can't be made with these 6 cut angles. Now, if you vary the "effective pivot length" as you suggest on your blog, you can make every shot at the table. However, as Jal has clearly illustrated, it is extremely difficult to learn how to judge the "effective pivot length" needed for a wide range of shots.

Regards,
Dave
 
Spidey, a diagram can easily be shown with 3D perspective, but this doesn't change the meaning or information provided by the diagram. In other words, I could add perspective to every diagram on my aiming resource page, and absolutely none of the explanations or conclusions would change!

For a given CB-OB distance, there is a very clear meaning for each of the CTE alignments. For example, for a given CB-OB distance and a given cut direction, there is only one true inside-CB-edge-to-OB-center line, regardless of how you decide to draw it on paper (with perspective or not). For given CB and OB locations, a given distance apart, Stan's version of CTE suggests 6 and only 6 different possible lines of aim. Each of these will create 1 and only 1 cut angle, assuming you are using a fixed-bridge pivot at the bridge length suggested by Stan. These 6 cut angles will allow you to pocket a fair number of shots at the table, but there will be many shots that can't be made with these 6 cut angles. Now, if you vary the "effective pivot length" as you suggest on your blog, you can make every shot at the table. However, as Jal has clearly illustrated, it is extremely difficult to learn how to judge the "effective pivot length" needed for a wide range of shots.

Regards,
Dave

True alignments - you're correct. However, in practice...real life results are different. With the same aligment and pivot - perspective mitigates your reported "off" results.

If you recreated many of your graphs in 3D...you'd see the vector through the core of th cb changes in order to maintain an alignment with the cb/ob points residing on the same vert line.
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True alignments - you're correct. However, in practice...real life results are different. With the same aligment and pivot - perspective mitigates your reported "off" results.
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"Perspective" ======> Unconscious correction for pocket location
 
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True alignments - you're correct. However, in practice...real life results are different. With the same aligment and pivot - perspective mitigates your reported "off" results.
*******************

"Perspective" ======> Unconscious correction for pocket location

That's not unconscious correction--- that's VERY conscious correction. When you sight an "overlap alignment" it's based on light of sight (vertical line in your field of vision). That's not unconscious - that's conscious precision.
 
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