Proofs of the EXACTNESS of Pivot Systems

Without doing all the math, I don't understand where you come up with only six angles. Pick a spot for the cb and ob. There is one angle. Now, move the cb over 1/16" to either the right or left. You now have another angle. This new angle will have a different CTE line by a little bit, and a different A.B,or C line by a little bit. I don't believe you are taking that into account.

What changes in your scenario (of moving one of the balls by 1/16" to the right or left) is the cut angle needed to pocket the OB. But if the CB/OB separation is the same for the two set-ups, Stan's CTE prescription would yield the same set of 6 cut angles (in either direction) that could actually be achieved. One of those 6 angles might or might not pocket the OB's in the two set-ups.

Neil, please read again Dr. Dave's summary of Stan's CTE (it's version 4 on this page: http://billiards.colostate.edu/threads/aiming.html#CTE). If you really think that summary is incorrect, I'd appreciate your telling us how it is incorrect. And I don't mean by using any math. This point requires no math. And please remember that Dave Segal criticized Dr. Dave for disclosing the entire DVD in this summary, so that must mean that Spidey felt it was reasonably correct.
 
Jim, if the CB and OB are far apart, the OB appears significantly smaller than the CB. In that case, the CTEL and the secondary aim line appear to converge in the distance (not at the player's eyes) regardless of whether the A/C or B point is being used.
Yes, that's true, AtLarge. But even though they appear to be converging in the forward direction (on the eye's image), they're still converging (in the absolute sense) in the rearward direction in the case of edge to A (left cut) or edge to C (right cut), and are parallel with edge to B. With edge to A or C, I don't believe I've read anything yet that pins down how the cue is to be aligned in relation to them and the CTEL. As we've long grown accustomed to, such ambiguities are the life-blood of these methods, allowing traditional aiming adjustments to sneak in through the back door.

Jim
 
I went to the pool hall and tried out the tilting of the head.
From the starting CTE line to the right side of the OB on the spot and the CB in the center of thee kitchen to cut to the upper corner pocket on the left.

I noticed that my left eye was looking at the left edge of the CB on a secondary line to the left ¼ on the OB. I then moved my stance to the left until the left edge of the CB was on an aim line to the center of the OB (B). My right eye was now off of the right edge (CTE) of the OB a bit to the right of the edge.

I then tilted my head at an angle to the right until my right eye was again looking at the right edge of the OB. Tilting my head, put my right eye below and closer to my left eye. I proved to myself that I saw the 2 aim lines that verified that I was in the correct position/stance for the secondary line from the left edge of the CB to the ½ point (B) on the OB.

From that stance I brought my cue into position under my chin with my bridge aiming the tip of the cue ½ diameter to the left side of the center of the CB.

This put my cue at a slight angle and not parallel to the secondary aim line. This cue location was established by where my shoulder and arm was in this (new) stance behind the bridge. My stroke is “always” with my arm directly below my shoulder and perpendicular to the floor.

So as my secondary aim line moves from A to B to C to 1/8 toward the right edge of the OB – so does my body and shoulder or stance moves incrementally to the left with the left edge of the CB at the axis. Since my shoulder is at a new location based on the secondary aim point, my cue and stroke will be at a different angle for each.

I finished the aim by rotating the cue at my bridge until the tip of the cue is aimed at the center of the CB. I stroke the shot from that stance and the OB went into the pocket at a 45 degree cut angle. I repeated this shot making 8 out of 10 with 2 near misses.

I then tried a secondary aim at the ¼ (C) point to the right of the center (B) of the OB and missed the pocket consistently to the left by 10 degrees or a 55 degree cut angle.

I then tried a secondary aim at the 1/8 point inside of the right edge of the OB and achieved a thin cut of about 70 degrees. Since I was hitting the part of the OB where the cut angles are very close to each other, if I wasn’t careful, I would miss the edge of the OB. I need more time at the table and my eyes were getting tired.

I conclude, for me, that I don’t need to tilt my head to bring the CTE line back on line for I don’t shoot with my head tilted and as long as my left eye was on the secondary aim line – I got the same results. I even cheated by laying my cue on the secondary aim line to make sure that my left eye was on line and not affected by a parallax view.

I find that this CTE aiming method can be/is useful.

I will persist with CTE for those shots over a 30 degree cut angle where my GB/double distance aiming is off of the edge of the OB and on the felt where things get blurry for me.

The distance between my eyes from pupil to pupil is 2.25 inches so the distance form my left eye to the position of the cue under the center of my chin would be 1.125 inches to the right of the secondary aim line pre pivot and almost parallel to the that line after the pivot.

May I offer this diagram of the secondary aim points sighted from the left edge of the CB.

CTE Stan A 1.jpg


I have diagramed this earlier and with a 12 inch bridge distance behind the CB; the angle of the secondary aim line and the 1.125 ince offset from that line pre and post pivot, it may be geometrically documented.

Again with time at the table, I may fill in the other angles in between the points by moving my bridge forward or back; less or greater tip offsets when necessary. :):thumbup:

Just saying.
 
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You have proved nothing! do you not understand that? show the math to the system or dont talk about it!

If Dr. Dave is correct (and I agree) that Stan's CTE prescription (if carried out with robotic precision) provides for exactly 6 cut angles in either direction for any given CB/OB separation [no math needed for agreeing or disagreeing with this]

and​

If PJ's calculations of the number of cut angles needed to pocket all shots at various distances from the pocket are correct [math is needed to confirm or refute this, but it has been established fact for a long time]

then​

You have the proof you deny exists.

Example: for an OB 4 feet straight out from a 4.5" pocket, PJ's math says you'd need 34 cut angles to pocket all such shots. Stan's CTE provides for 6. 34 is greater than 6. QED.
 
I went to the pool hall and tried out the tilting of the head. ... Just saying.

What you're "Just saying" makes me wonder about the efficacy of sighting the CTE visuals for people with a straight-on snooker alignment.
 
What you're "Just saying" makes me wonder about the efficacy of sighting the CTE visuals for people with a straight-on snooker alignment.

What I am saying isn't parsimonious. :)

After my trial with CTE tonight, I finished by reverting to my double distance/GB aiming and ran a few racks of 9 Ball.

Just being academic.:wink::thumbup:

Thanks.
 
LOL! You say opinions don't matter, yet you really mean only the opinions of the naysayers matter! The only proof you have that it isn't exact is from those that don't even understand how to use it! How can their math possibly be right??? Oh yeah, it can't, but that doesn't matter.:banghead:


It seems like all these threads play out the same way.

Naysayers = Math
Yaysayers = Non Math

The Naysayers all seem to say that the Yaysayers don't understand the math...therefore can not explain why it does or does not work......The Yaysayers all seem to say that the Naysayers don't understand the system....therefore can not explain (through math) why it does not work.

However...I find it hard to believe that not one of the Yaysayers understands math.....I also find it just as hard to believe that not one of the Naysayers understands the system.

On top of that...I feel like I get the vibe that the Naysayers are trying to confuse the Yaysayers with an incredible amount of math......and the Yaysayers are trying to confuse the Naysayers with an incredible increasing amount of jargon and seemingly more and more "method" being added

what really surprises me with the Masters event going on is that the Yaysayers have not come forward and said "hey look at Stevie Moor's shot making % compared to the other top pros" ......and the Naysayser have not come forward and said "hey look at Stevie Moor's shot making % compared to the other top pros"...
 
It seems like all these threads play out the same way.

Naysayers = Math
Yaysayers = Non Math

The Naysayers all seem to say that the Yaysayers don't understand the math...therefore can not explain why it does or does not work......The Yaysayers all seem to say that the Naysayers don't understand the system....therefore can not explain (through math) why it does not work.

However...I find it hard to believe that not one of the Yaysayers understands math.....I also find it just as hard to believe that not one of the Naysayers understands the system.

On top of that...I feel like I get the vibe that the Naysayers are trying to confuse the Yaysayers with an incredible amount of math......and the Yaysayers are trying to confuse the Naysayers with an incredible increasing amount of jargon and seemingly more and more "method" being added

what really surprises me with the Masters event going on is that the Yaysayers have not come forward and said "hey look at Stevie Moor's shot making % compared to the other top pros" ......and the Naysayser have not come forward and said "hey look at Stevie Moor's shot making % compared to the other top pros"...

Show the math to the system, anyone? help me understand it ok :) theres a piece to the puzzle missing and nobody knows what it is!
 
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Show the math to the system, anyone? help me understand it ok :) theres a piece to the puzzle missing and nobody knows what it is!

Here is the formula.

(C+E)1/2t-(PC)+{f}=pOB


Study it and you will find that it is really pretty simple:wink:
 
Show the math to the system, anyone? help me understand it ok :) theres a piece to the puzzle missing and nobody knows what it is!

I can do the geometry for a given distance between the OB and CB from the edge of the CB to the secondary aim points on the OB back to the aiming eye two feet behind the CB.

Fom that line, I can draw a line from the center of my chin (between my eyes) 1.125 Inches from that line to a point 1/2 offset from the center of the CB and another line post pivot approx. parallel to the original secondary aim line that sends the CB to the GB.

What isn't mathematically demonstrable is how the secondary aim points on the OB relate to the cut angle that sends the OB to the pocket/target.

I guess that one can document what cut angle can be achieved by several fractional aim points (more than 6) on the OB and commit that to one's memory and employ that knowledge to solve the shot to the pocket/target.

This is what (look up table) can be programmed into a computer processor to solve the shot. The human brain is capable of this.

Again, just saying.:thumbup:
 
Seems like Andrew Cleary..with the help of Ron V. and Dave Segal put it the easiest way on his short "aiming voodoo" video..thick cuts CTE..thin cuts ETE..and super thin cuts E to opposite E..looked easy and sounded easy. And if tomorrow it works for me then I'm done and no need to figure out how or why.
 
This is what (look up table) can be programmed into a computer processor to solve the shot. The human brain is capable of this.
You could do it that way, but it's not what you'd do in practice. The robot knows exactly where the object ball, cue ball, and center of the pocket opening all are. Thus, it's trivial to calculate the point over which the cue ball must be driven to pocket the object ball (essentially, calculate the ghost ball position). This is much easiest way to do it and probably the fastest.

A week or so ago, I posted a link to a video of a self-propelled pool-playing robot and included the relevant comment from the shot planning code. The post is here: http://forums.azbilliards.com/showthread.php?p=2878716#post2878716
 
I think, what jsp has successfully shown with this thread is, that advocates of pivot systems really don't care whether it's exact or not. They just tell themselves that it is. And in case anybody gives a counterexample and shows that you can do all the steps accurately and still come up with the wrong angle, then there is obviously this nonexistent referenceline that hasn't been considered in the calculation. But that line cannot be shown on paper, it's only in your head.
It's so frustratingly stupid. To all yaysayers, if you want to contribute to this thread: It's not just about CTE, it's about all pivot systems. Please present any pivot system and its method including clear steps that are supposed to lead you to the exact line of aim that will send the ob into the center of the pocket. Then I'm sure some naysayer will be happy to give an example.
 
I think, what jsp has successfully shown with this thread is, that advocates of pivot systems really don't care whether it's exact or not. They just tell themselves that it is. And in case anybody gives a counterexample and shows that you can do all the steps accurately and still come up with the wrong angle, then there is obviously this nonexistent referenceline that hasn't been considered in the calculation. But that line cannot be shown on paper, it's only in your head.
It's so frustratingly stupid. To all yaysayers, if you want to contribute to this thread: It's not just about CTE, it's about all pivot systems. Please present any pivot system and its method including clear steps that are supposed to lead you to the exact line of aim that will send the ob into the center of the pocket. Then I'm sure some naysayer will be happy to give an example.

There is know system that can produce(the correct line of aim for the player) the exact line of aim .If you took away the margin of error away from the pocket and made the pocket just big enough for the ball to fit through. And then you took a gb aim trainer , place it behind the ball so you could see the actual ghost ball(this is the exact line of aim)now we shoot through the gb with the different type of hits ,hard, soft ,right ,left,high and low,or what ever we would hardly ever pocket a ball if we didnt make any adjustments.(good thing for margin of error and rails)


Guess work will always be involved when it comes to pocketing
balls.The only shot in pool that has exactness would be a straight in
one.
I could be wrong about these things, but that's the way i feel.
 
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There is know system that can produce(the correct line of aim for the player) the exact line of aim .If you took away the margin of error away from the pocket and made the pocket just big enough for the ball to fit through. And then you took a gb aim trainer , place it behind the ball so you could see the actual ghost ball(this is the exact line of aim)now we shoot through the gb with the different type of hits ,hard, soft ,right ,left,high and low,or what ever we would hardly ever pocket a ball if we
didnt make any adjustments.(good thing for margin of error and rails)

Guess work will always be involved when it comes to pocketing
balls.The only shot in pool that has exactness would be a straight in
one.
I could be wrong about these things, but that's the way i feel.

It is true that we have to make adjustments due to friction, even for ghost ball, but the special thing about ghost ball is that it is geometrically perfect and thus a good starting point to base your adjustments off of. There are several other geometrically perfect systems such as double the distance and contact point aiming.

The downside to these geometrically perfect systems is that not everyone can properly visualize them. In that case, a less accurate, but easy to visualize system like CTE could be of benefit.
 
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What I am saying isn't parsimonious. :)

After my trial with CTE tonight, I finished by reverting to my double distance/GB aiming and ran a few racks of 9 Ball.

Just being academic.:wink::thumbup:

Thanks.

Lamas,

I respect academics who don't attempt to ridicule non-academics. You seem to be an exception and make no attempts to look down your nose at other people.

I'm curious. You apparently play nine ball rather well. Are you able to use CTE/Pro One at a similar level? If not, how much worse or how much better do you play with CTE/Pro One? (just making a funny about the "better")

Thanks,
JoeyA
 
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What I am saying isn't parsimonious. :)

After my trial with CTE tonight, I finished by reverting to my double distance/GB aiming and ran a few racks of 9 Ball.

Just being academic.:wink::thumbup:

Thanks.

LAMas,

Again, for clarity, when you say tilting your head, are your eyes on the same level with your left eye forward? Or is one eye above the other? By the sideways alignment, I was proposing that you turn your head and still keep your eyes level. It will close the distance between your eyes. This alignment works better for B or thinner cuts.

I start out by aligning my eyes to the Cte line and shifting my eyes to the reference point. I will shift my head slightly back and forth until my eyes pick up the second point. You can be somewhat square to the shot. It doesn't matter. It shouldn't be an extreme change to what you did previously before Cte. It will be a slight adjustment as you look at the object ball.

Everyone has an individual setup. Do what's comfortable and mechanically correct for you. Your body should fall into place naturally with accurate visuals. I turn sideways on some alignments and am more squared up on others. It varies with each shot. You can reverse engineer your Cte system and reverse pivot to see where your visuals start out at. Compare the starting alignment with with your present aiming system and you may gain some insight as to your visual and physical set up that is natural for you.

I set up a known angle and reverse Cte to see if I am setting up correctly with my pivot, bridge placement and visuals. When I teach a baseball swing, I use reverse engineering to show how you get there.

Best,
Mike
 
Lamas,

I respect academics who don't attempt to ridicule non-academics. You seem to be an exception and make no attempts to put look down your nose at other people.

I'm curious. You apparently play nine ball rather well. Are you able to use CTE/Pro One at a similar level? If not, how much worse or how much better do you play with CTE/Pro One? (just making a funny about the "better")

Thanks,
JoeyA

No.
There are too many incremental steps to Hal's CTE. I am now learning that with what I think Pro One is, I can just step into the secondary aim points within +/- a couple of degrees, but this isn't as accurate as double distance aiming and contact point to contact point aiming when the CB and OB are close together.

I am looking at CTE/Pro-1 for shots over 30 degrees where the aiming can be referenced to points on the OB and not on the felt or the rail behind.

You know what I am talking about.

I am not proficient at Pro-1 yet, but I persist and am getting better at it. I only use it academically and revert to DD and CP to CP to finish my practice sessions and run intermittent racks of 9 ball.

Thanks.:):thumbup:
 
LAMas,

Again, for clarity, when you say tilting your head, are your eyes on the same level with your left eye forward? Or is one eye above the other? By the sideways alignment, I was proposing that you turn your head and still keep your eyes level. It will close the distance between your eyes. This alignment works better for B or thinner cuts.

I start out by aligning my eyes to the Cte line and shifting my eyes to the reference point. I will shift my head slightly back and forth until my eyes pick up the second point. You can be somewhat square to the shot. It doesn't matter. It shouldn't be an extreme change to what you did previously before Cte. It will be a slight adjustment as you look at the object ball.

Everyone has an individual setup. Do what's comfortable and mechanically correct for you. Your body should fall into place naturally with accurate visuals. I turn sideways on some alignments and am more squared up on others. It varies with each shot. You can reverse engineer your Cte system and reverse pivot to see where your visuals start out at. Compare the starting alignment with with your present aiming system and you may gain some insight as to your visual and physical set up that is natural for you.

I set up a known angle and reverse Cte to see if I am setting up correctly with my pivot, bridge placement and visuals. When I teach a baseball swing, I use reverse engineering to show how you get there.

Best,
Mike

Mike,
Thanks for your help.
As a lazy engineer, I look for the easy way to solve problems so that I can have time to post on AZ Forums.

I don't think that I need two lines of aim to position my body/stance to find the secondary aim points. I only use my eye closest to the edge of the CB as you have posted before. As long as the secondary aim points force me to move my body/stance, I can shoot different cut angles over 30 degrees by aiming at fractions on the OB and not on the felt or the rail behind.

Using the closest eye to the relevant edge of the CB is more parsimonious and for me is all that I need for now.

I am memorizing the fractional points on the OB to achieve more than the 6 discrete cut angles.

Thanks for your and others help. It has made shooting more interesting.

PS,
I also think that 90/90 aiming is more parsimonious.:):thumbup:
 
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