Proof discrete aiming methods can't work

E

enzo

Banned
Az member John, whom i very much respect, led me to the following conclusion during one of our pm conversations. I'll just go right into the explanation.

Think of two pool balls on a pool table. If a player approaches the table, and hits one ball into the other, there is an infinite number of possible directions, or degrees, that the object ball can be cut. Now, to understand the problem with discrete aiming systems, you must realize that as you line up your shot based on the system, a pool table can also be situated in an infinite number of positions on the plane that it rests on. Look at it this way, what if a player lines up his shot using his system, it goes dead in the pocket, well, what if the table were rotated a tad just enough so that the shot would have missed? You see, since the table can be rotated in any of an infinite number of angles along it's plane, there must be an infinite number of thicknesses or degrees to which a player needs to cut a ball. What that tells you is there is no way a system with a only certain number of "thicknesses" or cuts (discrete systems) can work, there is literally no possible way.

As my friend John states however, these systems work for people. I believe him, and i give people that use systems to better their game all the credit in the world, even though i know the systems are based on fallacies.

Over.
 
ah no not really. the table would be a constant. maybe its just too late for me but this really makes no sense at all.

brian
 
So your saying that the shooter and his alignment on the shot are a constant and the table rotation on a given plane is a variable ??

I'm not understanding this........

Oh Lucy!!! You got some 'splaining to do!!!
 
enzo said:
Az member John, whom i very much respect, led me to the following conclusion during one of our pm conversations. I'll just go right into the explanation.

Think of two pool balls on a pool table. If a player approaches the table, and hits one ball into the other, there is an infinite number of possible directions, or degrees, that the object ball can be cut. Now, to understand the problem with discrete aiming systems, you must realize that as you line up your shot based on the system, a pool table can also be situated in an infinite number of positions on the plane that it rests on. Look at it this way, what if a player lines up his shot using his system, it goes dead in the pocket, well, what if the table were rotated a tad just enough so that the shot would have missed? You see, since the table can be rotated in any of an infinite number of angles along it's plane, there must be an infinite number of thicknesses or degrees to which a player needs to cut a ball. What that tells you is there is no way a system with a only certain number of "thicknesses" or cuts (discrete systems) can work, there is literally no possible way.

As my friend John states however, these systems work for people. I believe him, and i give people that use systems to better their game all the credit in the world, even though i know the systems are based on fallacies.

Over.
Click to expand...

A Zeno-like paradox. Cool.

TxSkin
 
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several things

First, we are very limited in the range of degrees that we can hit a ball. It doesn't matter if the angle can be split into degrees, minutes and seconds and endless fractions of a second because the width of the pocket and the shape of the balls both create slop. A fairly small number of angles will pocket almost all straight in shots if we can actually hit these angles. Sailor Barge was reputed to break the cue ball down into sixteen target spots. Those sixteen spots will make over 90% of shots if not all shots, or will at least provide a shot that can be made if you choose to shoot it.

The real catch is that no aiming system takes into account the variables in cushion, cloth, and balls, even lighting, so there never has been and never will be a perfect aiming system for human beings to use. We have to add judgment and touch to any starting point an aiming system gives.

One thing about the finite systems, you can grow them over time. Once you get rock solid at dividing a ball into say seven parts, then it is very easy to use those seven parts as new references to divide the ball again. Start with center ball, half ball, quarter ball, and very thin hits, slightly more than edge to edge. Once you can see these shots reliably you can split them in half. Once you can hit all of the points found splitting them in half any further refinements are tiny adjustments.

Without allowing for blocking balls I used software to test and found that 13 to 15 aim points would pocket any typical shot on the table assuming we had made some effort to play shape. If these aim points wouldn't pocket a particular shot a better shot was offered by using another pocket.

Ultimately all aiming systems give way to the ultimate computer, our minds. "Feel" is the ultimate aiming system for humans. Free out minds and bodies to work together without interference from thought in words and we are playing at maximum potential. The conscious mind presents the problem, a much lower level can solve it without effort once we have given it enough background data.(experience)

Hu


enzo said:
Az member John, whom i very much respect, led me to the following conclusion during one of our pm conversations. I'll just go right into the explanation.

Think of two pool balls on a pool table. If a player approaches the table, and hits one ball into the other, there is an infinite number of possible directions, or degrees, that the object ball can be cut. Now, to understand the problem with discrete aiming systems, you must realize that as you line up your shot based on the system, a pool table can also be situated in an infinite number of positions on the plane that it rests on. Look at it this way, what if a player lines up his shot using his system, it goes dead in the pocket, well, what if the table were rotated a tad just enough so that the shot would have missed? You see, since the table can be rotated in any of an infinite number of angles along it's plane, there must be an infinite number of thicknesses or degrees to which a player needs to cut a ball. What that tells you is there is no way a system with a only certain number of "thicknesses" or cuts (discrete systems) can work, there is literally no possible way.

As my friend John states however, these systems work for people. I believe him, and i give people that use systems to better their game all the credit in the world, even though i know the systems are based on fallacies.

Over.
Click to expand...
 
Not for nothing, I agree an infinite number of angles do exist...however, after a certain tolerance these angles are relegated to hundreds of thousandths of a degree and are imperceptible by even the greatest, most accurate and most expensive tools of measurement.

Your logic is faulty sir. What you're attempting to do is replicate and explain "Chaos Theory" and that can't be done. Specifically not in a pool game.

Pool is a game that is comfortably explained by the laws (or theorems) of Euclidian geometry with some Newtonian mechanics thrown in for good measure.

Long story short....line it up and shoot it...if you miss it's your fault not the universe and an imagined rotated table.

Hell, I could be the guy at the bar that talks too much and doesn't know his ass from his elbow...but if you'd like to have a "Scholastic Scrimmage" I'll spot you the 7.

Mattie
 
ShootingArts said:
Ultimately all aiming systems give way to the ultimate computer, our minds. "Feel" is the ultimate aiming system for humans. Free out minds and bodies to work together without interference from thought in words and we are playing at maximum potential. The conscious mind presents the problem, a much lower level can solve it without effort once we have given it enough background data.(experience)

Hu
Click to expand...

Couldn't put it any better. Human's perform better when acting on instinct and muscle memory. You have to allow youself to do what you've trained yourself to do.
 
mattiefingaz said:
Not for nothing, I agree an infinite number of angles do exist...however, after a certain tolerance these angles are relegated to hundreds of thousandths of a degree and are imperceptible by even the greatest, most accurate and most expensive tools of measurement.

Your logic is faulty sir. What you're attempting to do is replicate and explain "Chaos Theory" and that can't be done. Specifically not in a pool game.

Pool is a game that is comfortably explained by the laws (or theorems) of Euclidian geometry with some Newtonian mechanics thrown in for good measure.

Long story short....line it up and shoot it...if you miss it's your fault not the universe and an imagined rotated table.

Hell, I could be the guy at the bar that talks too much and doesn't know his ass from his elbow...but if you'd like to have a "Scholastic Scrimmage" I'll spot you the 7.

Mattie
Click to expand...

The new AZ billiards SCHOLASTIC SCRIMMAGE Champion:grin:

good post Mattie
 
enzo said:
Think of two pool balls on a pool table. If a player approaches the table, and hits one ball into the other, there is an infinite number of possible directions, or degrees, that the object ball can be cut. Now, to understand the problem with discrete aiming systems, you must realize that as you line up your shot based on the system, a pool table can also be situated in an infinite number of positions on the plane that it rests on. Look at it this way, what if a player lines up his shot using his system, it goes dead in the pocket, well, what if the table were rotated a tad just enough so that the shot would have missed? You see, since the table can be rotated in any of an infinite number of angles along it's plane, there must be an infinite number of thicknesses or degrees to which a player needs to cut a ball. What that tells you is there is no way a system with a only certain number of "thicknesses" or cuts (discrete systems) can work, there is literally no possible way.
Click to expand...
The situation isn't quite as bad as your description might imply, especially when the OB is closer to the pocket (where the pocket is "bigger"). However, you overall message is valid, IMO. Here's a pertinent quote from my fractional-ball aiming FAQ page:

For a given shot, with N different lines of aim, assuming you can hit where you are aiming, the object ball can go only in N different directions. Depending on where a pocket is and how far it is from the object ball, the cut shot may or may not be makable with one of the selected aiming lines.

Even with English effects (squirt, curve, and throw) and cling (collision-induced throw), the object ball can still go only in N different directions for N lines of aim for a given cue stick elevation and shot speed, and for given ball and table conditions.

See TP A.13 for background and specific results. Here are some highlights (for people who don't like the math):

  • To be able to pocket an object ball into a pocket about 3 feet away, with an average angle to the pocket, and for any cut angle, the required number of aiming lines is about 19!
  • If you consider cut shots only within a typical range (e.g., 7.5 to 52.5 degrees), and use only three equally spaced lines of aim (e.g., the 15, 30, and 45 degree aims):
    • If the object ball is less than a foot from the pocket, every shot can be pocketed with the three lines of aim.
    • If the object ball is more than two feet from the pocket, less than 50% of all cut shots in the limited range can be pocketed with only three lines of aim.
Now, I still think the three fractional aiming references (1/4, 1/2, and 3/4) are very useful because they are very easy to visualize. And having easy to identify references is always useful (e.g., as with the tangent line and the 30 degree direction for predicting CB motion), so I agree 100% that the aim points (from fractional-ball aiming or any other system) provide a good framework from within to work, especially for people that have difficulty aiming accurately and consistently.

Regards,
Dave
 
TxSkin said:
A Zeno-like paradox. Cool.
Click to expand...

Zeno's paradox was (and is) solved with calculus. And BTW the faster runner behind actually passes and wins--the same one would get by using their head.

But throwing around the word infinity; as if this, in and of itself, makes the problem more unsolvable; is also meaningless. Consider that the OB is placed a distance from a pocket such that if it is rolled along a line within a 1 degree angle; it will still drop in the pocket. Here, in that 1 degree, are another infinite number of unique angles. So, in effect the infinities cancel out and we return to discrete math.
 
cte does not have a fixed number of aim points. it has an infinite number of solutions. you only have a fixed initial reference point.

as the table rotates, the side of the ctel from which you setup might shift. the outermost edge shifts.

by saying cte has a fixed number of aimpoints demonstrates how little you know about the information you're attemping to disprove. the aimpoint is unknown until after the pivot is complete. the pivot itself is an exact ratio based on the length of the shot...the shot arc.
 
SpiderWebComm said:
the aimpoint is unknown until after the pivot is complete. the pivot itself is an exact ratio based on the length of the shot...the shot arc.
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It seems like this is the real key to CTE ... the "pivot." You can start with a ball-park alignment (e.g., edge-to-center) as long as you pivot relative to an effective pivot point (achieved by deforming or shifting your bridge slightly if necessary) to achieve a specific shot angle within the range appropriate for the initial alignment. I can see how somebody could learn to play effectively using CTE, provided they have practiced a lot with how to vary the pivot from one shot to another of similar but slightly different angle.

Regards,
Dave
 
Is aiming so hard???? I truly understand that using different methods to visualize your shot can be helpful at times but what exactly is an aiming system doing. You are not a machine. Is this just a method of tricking your brain into being more confident in your natural abilities? How long do you have to play pool to know where to hit the cue ball on a cut shot? I think it has more to do with how consistantly you execute a shot then where to aim.

If you put two balls directly inline with a pocket 4 diamonds away from eachother and mark their location so you can shoot this shot over and over again what percentage do you make it? When you hit the ball in a straight line there are no angles to calculate no ghost ball to visualize just hit the ball full into the other ball. if the only issues in your game are your aiming system you should make these a very high percentage.

If your consistancy is simular on a straight in shot as a half ball cut I would argue this has nothing to with aiming and everything to do with mechanics, rythm and being relaxed/focused and aware of your mental game...

Clouding your head with systems of how to aim might not be the answer you're looking for. Maybe your brain knows how to make balls better then you give it credit for.

Dudley
 
What's so wrong with the Ghost Ball?

With minor adjustments for throw effects, it is geometrically sound and 100% dependable.

For you fractional aimers, I personally can "see" the GB much easier than I can estimate if the cut angle is "17 degrees" or "23 degrees."

GB allows for infinite angles - versatile enough to "thread the needle" between one (or two) almost-blocking balls, or to cheat a pocket.

The GB technique is possible to explain quite simply to 99% of the pool playing world, whereas the process of clearly and unambiguously communicating CTE continues to elude even its most ardent advocates and its most interested potential converts (like me).

Of course, I still miss when using GB. As with any method for aiming, it can only be as good as your ability to execute what you are attempting to do. It's my $%#@@#!! side-winder stroke....
 
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