Three Dog Night didn't pay enough attention I guess.

http://www.imdb.com/title/tt0069044/

A pair of numbers which are the sum of each other's proper divisors are called amicable, and larger cycles of numbers are called sociable. A positive integer such that every smaller positive integer is a sum of distinct divisors of it is a practical number.

Bruce, you are close to 10k.

I'm actually way over since it restarted counting when they updated the software at one point. So that's only posts in the Common Era.

Way to go. Feeling like a real noob right now.

But on the other hand, 4 years is something also, I guess


This is part of our life story, like it or not.


You must be one of the coolest mods btw. No customized undertitle. You're not bull****ting around!

Hello all,

We have a hell of a discussion brewing in the Golf Forum that may be of interest to people in this forum. It is a discussion of whether a straight putt or a breaking putt has a better chance of going in.

My stance is that straight putts and breaking putts have equal chances of going in. The physics of a ball falling into a hole do not change just because break is introduced, the speed and line of the putt still have to match and there is a finite number of speed + line combinations that allow a putt to go into the hole.

The counter argument is that breaking putts are easier to make because there are more lines to choose from. What the people backing this argument appear to lack in understanding is that when you increase the amount of lines, the speed required on all of those lines becomes much more exact. You still have the exact same amount of combinations of line + speed that will go into the hole, they are just more widely dispersed.

Anyone have any thoughts? If you go looking for the thread it's right here. This discussion starts a little ways down.

http://forumserver.twoplustwo.com/93...100-a-1398494/

You are meaning if the stick is there or not when putting? Not exactly infinite ways, imo. Have thought about the same. But apparently it's +EV to have the stick removed, maybe partly because it takes some space off the hole. And the bouncing effect is probably bigger than the "catching" effect if putting too hard, when the speed is randomized around a semi-average.

But maybe you meant something else?

Yes stick removed. And no not "infinite ways" I'm saying there are a "finite amount of ways" for all putts which is basically just a combination of line + speed and this number of combinations doesn't magically increase bc break is introduced. Basically when the ball gets to the hole it is unaware of the break that has occurred until the point because it has no effect on the physics of the ball dropping in.

What do you mean by a "break"? I mean, define it from scratch. Is it that damned stick or not?

You'd be amazed about how little we know about golf. But if we are knowing what you are talking about, you'll get some amazing calculations.

Ok.

The golf hole is 4.25" wide.

Let's take a 15 foot putt for example. Assuming it is a straight putt, you have .68 degrees of error on each side before you get outside of the hole. The closer you get to the edges of the cup, the more precise the speed must be bc if it's too hard it will bounce out. The dead center of the hole allows obviously for the largest margin of error in speed.

If you add up all of the different lines and all of the corresponding speeds along each line with which putts will go in there is your combo of makeable putts.

Now compare that too a 15 foot putt that breaks say 6" to the left if you hit it the "perfect" speed. Your margin for error of starting angle is a little bit wider, but each of the lines requires more exact speed. Again if you were to add up all of the different lines(you have more here) and all of the corresponding speeds(each line has a lower margin of error in the speed category) you will get the same total amount of combinations of makeable putts.

Make sense?

Probably to everyone except plaaynde. You'd get better answers if you made a thread on it IMO.

Seems like it would depend on the put as to which approach would be best. If a breaking put would allow it to hit the cup at a slower pace than a straight put, it should be less likely to bounce out. But I assume breaking puts are harder to judge, so it would be some variation of risk/reward.

By breaking putt NxtWrldChamp means this;



compared to the straight putt being more like




Now essentially this is a trajectories problem. There is a wide range of possible trajectories that take you in, some of them very curved if the terrain is appropriate. There is also friction and spin interactions. It is a super tough problem actually. Interesting however in the following sense;

A human brain can probably design a possible path with some uncertainty in speed and direction at start (and some times the brain messes up big in another more global way, imaging curvature of trajectory that never materializes or deceleration of ball speed that is too much resulting in too fast putts or underestimating deceleration resulting in putts that dont reach the hole etc) .

In general you have 2 kinds of errors. The bad scenario error and the good scenario initial conditions range error. The 2 work together interacting as it is possible to have the physics wrong in your mind for example and still get lucky because of significant initial conditions uncertainty. But if one is able to get at least the physics right, being able i mean to visualize to a good degree the correct families of paths, it will then become an initial conditions range problem.

You want to select the path that has the wider range of error allowed in all variables giving you higher probability to get in i mean over an alternative approach. Keep in mind in principle you may have several "islands" of distinct initial conditions sets (call each island the subvolume "cone" of initial conditions in speed and direction slightly around an ideal central curved in general but straight near the end path- that gets straight in during the very last segment of the trajectory=no impact parameter, i mean with the highest margin of final, ie at hole rim, velocity error) that take you inside especially if the terrain is very curved making it possible i mean to either go nearly straight fast in or in slight curvature or in very significant curvature if you go first higher to the right say and then rising higher you start curving to the left and going to the hole after having initially moved in a seemingly very different direction to the right of the hole (think of it as a potential plus kinetic energy plus frictions problem making it possible to follow even weird looking trajectories on occasion with substantial curvature)

So in case i wasnt clear before you want to first get the physics right. The physics in principle in a curved terrain with substantial friction sources can be very complex and can result in many islands of solutions. Each of these islands can be seen as alone, separate from the others (hence the term island) if the golfer is a very accurate player. On occasion however there may be some mixing due to significant chaos between 2 nearby islands making it possible i mean to think one way of going in, be off due to chaos =very big sensitivity on initial conditions, and having the errors in your initial strike delivery mechanism (your natural ability to be precise i mean and execute close to what the brain thinks is the proper values of speed and direction - or even spin lol) save you by landing your trajectory unintentionally into the other nearby island of solutions.

Anyway if the islands (people in golf may call those "lines" it seems) are seen as separate enough and your execution in each is very precise but still not perfect there will be for each island (or line) an ideal initial velocity and direction that takes you to the hole with 100% result. You can say deviate from that initial solution choice by some angle df or speed dv and still land inside (ignore spin for now) . But there will be some initial deviation that is big enough at some point that you start missing. So for every choice the brain makes there is a pair of errors df, dv in execution.

So you have 2 sources of errors. The get the physics right error which is super hard to quantify (its a brain estimate error) and the get the parameters of initial velocity and direction right error (body execution of brain command) assuming the physics was perfect. In real life you have both interacting together as only a supercomputer could get the physics right and have to worry only about the execution error.

So you want to select a solution island (or line) that allows the highest possible initial conditions "phase space" volume as it is called.

By that i mean for example that maybe one solution requires very roughly 1% error in velocity and 1% error in angle (the angle error is a function itself of the velocity value anyway so you get why this is is all very complex). Another solution (say a straight fast solution) may require only 0.25% error in angle but can tolerate 5% error in speed.
Now the human body will respond differently to these 2 methods. Each time it will fail to deliver the ideal central shot, it will deliver something else. If this delivery happens to be inside the initial conditions cone that lands ultimately inside the hole its great. Each initial solution cone or island or line therefore will naturally come with its phase space volume inside which execution by human body will have to "land" in terms of the initial strike in order to be successful.

So your mind/body has to jump in some "window" among all possible "windows" of solutions and select the window so to speak with the higher opening giving you the best chance to be good. I hope this clarifies it a bit more.


To make it very extreme for example imagine a situation that the terrain is very curved and you are only away from the hole 30 cm. Your best choice is to hit it straight in. However an alternative solution among many may exist that is ridiculous such as to hit it completely away from the direction of the hole with intention to take the ball first to a rising hill 3 meters away in the right say from where it will then drop down back to the left another 3.1 meters and into the hole. Those 2 are 2 islands of solutions basically. The second one is the most imaginative fancy one but it has such a small room for error in execution plus impossible to get right physics to begin with that it has to be avoided clearly.

In real life it wont be as extreme as that but it will still be possible to have different islands and you need to select the particular island where your execution uncertainty will be less penalizing for you. That obviously in general is a highly complex problem impossible to talk about without knowing the terrain and friction properties etc.



PS :i have never played golf a single day in my life although they have a ton of practice fields around campus where Tiger once was also lol.

And you have to time your shot to miss the revolving windmill blades.

Think you can't just calculate this, because the break makes it so much more difficult all in all to perform a correct put, because the direction has to be estimated, while a straight put needs "just" aiming.

I think the least problem is that the total distance increases a bit with the break. The speed factor will always be more forgiving than the direction factor, because the hole gives that flexibility as a stopper, distance will be paramount for if the put goes in. And you will also be able to regulate the speed factor better with shorter distance. Of course the distance is so paramount, because of that the correct angle decreases in direct proportion to the distance.

And the starting angle has to be as exact when you put straight as when there's the break, even theoretically.

Not to mention win also the teddy bear for your girlfriend in the 3 balls strike a cone game or whatever luna park variant lol. But it all ends up being about "holes" game. Ask Tiger who has tried all the variants including both static and moving ones...

Timed out. As to OPs question, think it's not really answerable. It's about how much of a change of aiming/speed you will accept as a "change" in the two quite different putting scenarios. With the break, the combo of aiming angle and speed decides if you hit the hole in the first place, and what's more, if it gets stopped by the hole when you hit it. The aiming isn't a factor that way when putting straight, you always aim the same, you are only regulating speed, as an independent factor.

To sum it up, it's like comparing pears and apples, imo. When putting straight the correct aiming/speed are independent factors, when putting with a break the correct aiming/speed are factors depending on each other.

http://mathworld.wolfram.com/DiskCoveringProblem.html

These disks are made very close to the minimal diameter to cover. They are sometimes made of metal, and you have to compensate for them sliding downhill. It's hard enough straight up, but some carnys have been known to cheat by stretching the fabric of the table to make the big circle larger, swapping out disks by slight of hand for ones that are too small to cover, or jostling the table slightly.

The ball doesn't travel 15' in a successful 15' putt with break.

So for 5 you place the first disk so that its circumference passes from the center of the main bigger disk call it O. It will then intersect the circumference of the main disk at 2 points A,B. The second disk now must be placed so that it also passes from the center O and the intersection point A say. Then follow with the 3rd disk similarly always passing from the center and the last intersection point of the main disk circumference with the prior disk circumference.

You can only hope then that you play a fair game where the minimum 5 disk radius allowed and the one you have available is not the same or lower or even a tiny bit higher. It must be a decent little bit higher maybe 5% at least to have room for error?

So to play the game you first measure the 2 radii and act accordingly if the small one is at least say 65% of the radius of the main disk. If its 62% or less tell the guy there to shove it!!!

Actually that is a nice real life game to see how much you need to price the ticket to play it as function of how close the r1/r is to 0.618... etc

They won't let you make a measurement.

Yes but you can creatively use your fingers to examine the disks and place your palm to the big disk asking questions playing the idiot lol. That can give you a way to gauge how much over 60% you are.

Tried that. Still got backed off.