Proofs of the EXACTNESS of Pivot Systems
- Thread starter jsp
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But when you sight an alignment with the CB and OB in set positions, for a cut in a given direction, your line of sight is well defined, right? And after you pivot with a given bridge length (or "effective pivot length"), don't you end up with a well-defined cue alignment? And don't you end up with a different cue alignment for each of the other 5 initial alignments and pivots? And don't each of these cue alignments create a different cut angle?
To be clear, the CB and OB relationship (alignment and distance) and direction of cut are the exact same for each of these questions.
Now, the following (based on a previous post) should make more sense:
For given CB and OB locations, a given distance apart, and for a given cut direction, 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 (based on the CB-OB distance). These 6 cut angles will allow you to pocket a fair number of shots at the table, especially if the pockets are large and/or the OB is close to the pocket, but there will be many shots that can't be made with these 6 cut angles.
I'm not saying this is a bad thing, and I'm not saying there aren't ways to deal with this (... several are suggested on my CTE resource page, including the "shot arc" method you suggest on your blog). I'm just trying to be clear about what Stan's version of CTE yields both in theory and at the table if the procedure is followed precisely. Despite all of this, I still see the benefits of such systems for some people.
Regards,
Dave
...is that you completely don't understand the purpose of this thread.
The purpose of this thread is NOT to contest the claims that these pivot systems "work" or that they can actually help people pocket balls, but rather to contest the claims that these systems are EXACT. Saying that an aiming system is exact has a very precise meaning.
Just because a system works for you doesn't mean it's an exact system.
Likewise, just because a system is exact doesn't mean it can help you pocket balls.
Now unless you can provide proof of the exactness of these systems (no, personal testimonials that they can help you pocket balls is NOT proof of exactness), then your contributions in this thread aren't productive for the purpose of this thread.
That's because it's obvious without trying it how it works and whether it will be useful. I've now seen the DVD, and there are absolutely no surprises. The way we've always assumed it works (by approximating aim lines and finishing with feel) is exactly the way it really works. Actually, there is one small surprise: there's less to the systematic part of the system than I thought there would be.
The ones who have used CTE the most are the ones who understand it the least.
pj
chgo
I've watched the DVD and the only thing it makes crystal clear is that "the naysayers" have been right all along. Plenty of people have been talking out their asses here - but they all seem to be CTE users.
pj
chgo
I have tried CTE at the table more than one time and couldn't make a ball. But I'm not important. That doesn't tell you anything about exactness either.
Again in your mind you decide right and wrong, but trying it at the table, hell why would you bother to do that. Not surprised by this post from you.
I thought this thread was about proving (by math) the "exactness" of the CTE method.
I don't think it would be something proved (on a table)....I think it would be something proved on a chalk board.
The whole problem is....even if it could be proven by math....it would never transfer to the table.....Let's say that you came up with a set number for pivot lenth for a particular shot of say 8.333" .......how on earth is a player going to know that they have measured out that specific distance without turning thier pool cue into a ruler?
Instead it would get transformed into something like..."About 8" is the best pivot lenght for a specific shot....from there the player is now able to feel what is "about" 8" on thier cue.....It then becomes very close...but not "perfect"
Maybe, though off hand, it seems to me that drawing the object ball at, say, half the size of the cue ball (simulating a distance of about three feet) would give the same results. However...
Added 11Mar2011: The above statement about drawing the object ball smaller was incorrect. - jwpretd
In the absence of complete and rigorous drawings and rigorous definitions of the terms used for and at each step of the methodology, there's the chance that, say, parallax or the use of multiple sight lines accounts for the apparent geometric discrepancies. Some of the more recent descriptions remind me of Houle's "rotating edges" (I think that's the term he used), among other things.
So I've grabbed and installed Truespace (it's free now) and I'll see if I can remember enough about how to use it that I can draw this stuff in 3-space. I may not be able to do that in the amount of time I'm willing to spend on it. It's been a very long time since I used Truespace, and a great deal has been added and possibly changed.
By the way, this illustrates one of the niggling problems with retirement. When I was still working I'd have just gotten a couple of six packs of Anchor and bribed one of the grad students to do it. Grad students will do nearly anything for free beer. Now if I want this sort of grunt work done I've got to do it myself.
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jwpretd,
I diagramed another pivot system in Autocad and showed the relation to the smaller appearing OB down table and thee replies were from chirp, chirp to huh????
If there were requests for clarification of the diagram on the left, I would have persisted with what was diagrammed...chip, chip. LOL
I hope that you will fare better. :thumbup:
This is a simple pivot system where you aim the center of the CB at the contact/impact point (that sends the OB to the pocket/target), then parallel shift the cue/bridge to the center of the OB and pivot back to the center of the CB and shoot
It isn't exact because the CB and OB are round, but adjustments can be made with hours of practice...what's new?:grin:
Just sayin.
I diagramed another pivot system in Autocad and showed the relation to the smaller appearing OB down table and thee replies were from chirp, chirp to huh????
If there were requests for clarification of the diagram on the left, I would have persisted with what was diagrammed...chip, chip. LOL
I hope that you will fare better. :thumbup:
This is a simple pivot system where you aim the center of the CB at the contact/impact point (that sends the OB to the pocket/target), then parallel shift the cue/bridge to the center of the OB and pivot back to the center of the CB and shoot
It isn't exact because the CB and OB are round, but adjustments can be made with hours of practice...what's new?:grin:
Just sayin.
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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.
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.
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Thanks for the images. Around 1997-98, at the height of one of the periodic Houle-storms on RSB, I did a bunch of drawings that wound up looking very similar to the ones you have on dr_dave's site. One of my feelings then was that "center of cue ball" didn't always mean the same thing at each of the stages of some of the pivot systems, particularly the CTE variants. That was mostly driven by Hal's reference to "rotating edges", which seemed to imply a shift in alignment from one step to another, giving a different (rotated) perception of the cue ball center from one step to another.
It never occurred to me to look at the CB_center-to-OB_contact_point line. That was probably because I assumed that the point of the various pivot methods was to find an aim line if you couldn't "visualize" the OB contact point. I mean, if you can accurately visualize the OB contact point from your shooting position, why in the world would you care about anything else? Just do the CB-OB overlap and shoot the damn shot.
The pivot-based methods in essence assert that there is a functional relationship between some easily seen path(s) (e.g., CB center to OB edge line, that line shifted to someplace, etc) and the actual aim line necessary to make the contact points come together (equiv., to drive the center of the cue ball directly through the center of the ghost ball). And that they also assert that this functional relationship is such that the cue can be placed on one of these easily seen lines and then pivoted to the cue ball center (whatever center might actually mean) about some convenient point on the cue that is easily discerned "on the fly", after which the cue will point along the needed aim line.
In any case, thank you again for all of your effort in producing your drawings. They are interesting and useful.
Hi,
the main thing is, that PJ and Dave ve had exactly questions. And the responses weren t exactly. I still don t think that Dave or PJ just having questions to tease somebody. They still just want to understand- like many others. I m also always interested in *new* things which i could learn. Was just able to test some shots with the descriptions i found here. Not to forget a 1 on 1 video conference JB. It was really interesting and he tried to answer each question- but i must say that it didn t work for me.
As long as no *guru* s appears here which would try to explain me exactly how to use cte/or whatever i won t try again, would be senseless for me.
But! If it works for other guys, i m happy for them. They don t need to explain me why it works for them. But from that what i read, some questions are really still not answered clearly.
Perhaps i m too oldfashioned to understand- i learnt to detect the target-setup a proper/perfect alignment-and then go down *into the stance*-- at this point in my opinion it doesn t make sense to move eyes/head or the hip again......then in my opinion i m not aligned perfectly anymore.
lg
Ingo
the main thing is, that PJ and Dave ve had exactly questions. And the responses weren t exactly. I still don t think that Dave or PJ just having questions to tease somebody. They still just want to understand- like many others. I m also always interested in *new* things which i could learn. Was just able to test some shots with the descriptions i found here. Not to forget a 1 on 1 video conference JB. It was really interesting and he tried to answer each question- but i must say that it didn t work for me.
As long as no *guru* s appears here which would try to explain me exactly how to use cte/or whatever i won t try again, would be senseless for me.
But! If it works for other guys, i m happy for them. They don t need to explain me why it works for them. But from that what i read, some questions are really still not answered clearly.
Perhaps i m too oldfashioned to understand- i learnt to detect the target-setup a proper/perfect alignment-and then go down *into the stance*-- at this point in my opinion it doesn t make sense to move eyes/head or the hip again......then in my opinion i m not aligned perfectly anymore.
lg
Ingo
Thanks for the astute reply.
I wanted to learn a more accurate way to aim/shoot those cut angles over 30 degrees where I have to aim off of the CB outer edge to somewhere on the felt or a rail behind. I tried the early parallel shift offsets descriptions of Hal’s version of CTE.
I saw that some use ½ tip offset (you know what I’m saying) or one tip, or
Edge of the CB…etc. I had a hope that I would find the Holy Grail with a pivot system for all of the components are related to tangible points on the OB and not on the cloth.
You say:
“I mean, if you can accurately visualize the OB contact point from your shooting position, why in the world would you care about anything else? Just do the CB-OB overlap and shoot the damn shot.”
just sayin:thumbup:
I would like to see what you have. If it is a matter of posting the diagram in the thread.
Then follow the old link on posting. It is quite simple. It involves posting your image onto another site. Then linking that to the forum.
http://forums.azbilliards.com/showpost.php?p=1967931&postcount=1
Al
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.