:wink:
Good Morning Larry,
That is flawed. You're saying the same type things that Stan's CTEers say.
Boy! Where do I start? Let's start with the word "different" & add in Einstein's Relativity.
We need to put the word "different" into the proper context & I guess the word "angle" too, since it is joined with "different".
Let's set an OB at center pocket sitting on the edge of the shelf at a corner pocket... & then place the CB down the long rail but on the same side of the side pocket & parallel to the rail so that the Center LINE is parallel to the rail.
I was unsure here so I drew a pocket hanger at the top corner pocket and put the cue ball just below the side pocket.
Now... let's move that CB one 'tic' at a time for 90* of rotation toward the other corner pocket until the shot line gets parallel to the short rail. We then have 90 straight in shots & we could have an infinite number.
Imagined cue ball rotating around OB by an invisible string at fixed distance from side rail to short rail.
They are all "different"... yet they are all the SAME.
They are all on "different" parts of the table. Yet... they are all THE SAME one ball RELATIVE to the other & the LINES between the balls are ALL the SAME... One Ball RELATIVE to the Other Ball.
Let me say that again.
THEY ARE ON THE SAME ANGLE & WITH THE SAME LINES RELATIVE ONE BALL TO THE OTHER. THE LINES ARE SET BY RELATIVITY... ONE BALL TO THE OTHER BALL.... Even though they each are on 'different' parts of the table.
They're all straight in shots and they use the same visual, a zero angle shot. I don't understand your position. There's been too many different types of lines mentioned too in other posts. I need you to define 'LINES' and when you mention relative to each other are you talking about the shot line?
Now do a similar thing... pull the OB straight out of the pocket toward the diagonal side pocket about a diamond's length... then set up a ghost ball on it. We now have a cut shot. Now extend a line through the Ghost Ball/OB center lines to the point on the shelf where the OB sat for ALL 90 (or infinite #) of the straight in shots.
Now rotate the whole mess, the 3 balls & the STRAIGHT LINES between them with that point at the pocket shelf as the apex point.
Rotate that whole set up, the 3 balls & especially the LINES between them 1 'tic' at a time toward the short rail until the LINE through the Ghost Ball/OB gets parallel to the short rail.
I do not know how many degrees of rotation that that actually is. So I do not know how many DIFFERENT shots that it is, but it is a significantly high number & it could be an infinite number.
They are all "DIFFERENT" but the LINES are the SAME... RELATIVE ONE BALL to THE OTHER.
It is the balls that SET the LINES & NOT where they are on the table.
Sorry for the Caps. I'm not yelling. I'm just highlighting certain words.
I certainly hope that you can understand what I am trying to say.
You just received a brief example of Einstein's Relativity.
I just wish the balls were travelling at the speed of light. Lorentz's contraction would turn them into disks and I'd finally be able to talk about my 2D stuff again.
You need to rotate your watch face.
I hope that you do not have any questions, but if so, I will do my best to answer them... For You.
I'm not inclined to waste time with 'haters' of the scientific truth.
All the Best for You & Yours,
Rick
I don't see your point yet. I hope you can provide some definitions to clear the matter.