Very interesting discussion. I read a book recently that talked briefly about convergent and divergent problems and how students solve each type. As a bit of background, problems with convergent solutions are those we would be most familiar with from grade school i.e.:
“I’m skiing. With every minute that passes my speed doubles. If I start at 1 mile a minute, how fast will I go after 5 minutes?”
A divergent thinking problem might ask how many uses one can imagine for various (often mundane) objects. What can you do with a pencil? A string? A rock?
I’ve always thought a golf shot is more of a divergent thinking problem. How many ways can I get this ball into range for a birdie put? I think golf rangefinders (and analogous systems for billiards) encourage convergent thinking which is great is you have perfect information and can comprehend all the variables within the system but most of us realize this is impossible in golf. So why do people pick use them at all?
Because feel is rediculously hard to teach! If a new golfer asked you how Hogan felt the wind in the trees to gauge distance what would you say? A big part of feel development is acquired subconsciously from extensive experience and if you don’t have that, or if you haven’t drawn properly from your experience, you are at a major disadvantage (even if you have impecable technique) if you go head to head against a guy like Lag who has been hitting golf shots under pressure for championships since his junior golf years and has that massive encyclopedia of sights, sounds, feels, that are calculating some unknown formula in his head before that golf shot.
to further answer your question, sang lee always looked at the cue ball last. players often debate whether it’s better to look at the cue ball or object ball last. sang lee was very big on gesturing the cue ball, that is all the subtle things he did with his various strokes. he would accelerate through the cue ball at varying speeds, depending on what type of shot he was playing. also he would often dip or raise or swerve his cue through the cue ball. moreover, it’s much more vital to contact the cue ball with your cue tip in a precise way in billiards rather than in pool, because of the effect spin has on the shot. for all of these reasons, i think this is why he always looked at the cue ball last. however, he would always have the entire shot in his mind before and during his stroke. in fact, the gesturing, or massaging, he would do to the cue ball implies how much he played by feel.
pavaveda,
yes, even pool players are surprised to learn that modern billiard tables are heated. also, it is customary in billiards–but not in pool–to have the table vacuumed and be given a clean set of balls before each and every game.
there is another way, i think, we can look at feel or intuition. within computer science there is a field called artificial neural networks, which is a model for the actual neural networks in our bodies. from a purely mathematical point of view (and one i am particularly more comfortable with), these networks are just numerical methods for approximating nonlinear functions of a great many number of variables.
the purpose of numerical methods is to get approximate solutions to functions for which we don’t know how to–or theoretically can’t–solve in a closed form exact solution. these methods are generally iterative, that is getting a very rough answer, making it better, and on and on. to make this concrete, let’s consider the following:
we are trying to determine how a ball will fly and where it will land if we know what club we’re using, how far we hit said club, the wind conditions, the temperature, the humidity, all the variables that make up the lie, etc., etc. in fact we’re trying to solve at least three equations that will yield distance and trajectory and direction, given tens or even hundreds of inputs.
the problem is that such equations–even if they do indeed exist–cannot be solved by simple closed form formulas (or at any rate, the formulas would be prohibitively complicated). but that is exactly what we are trying to do if we go about it by taking the distance and adding or subtracting for wind, and again for the lie, and so on. the actual formula is so much more complicated (and highly nonlinear to boot!). furthermore, relying on such an overly simplistic formula necessarily involves divorcing ourselves from what is actually happening.
now back to the neural networks. our brains come with this amazing ability to approximately solve such complicated nonlinear functions involving many, many inputs. in fact, we can get ourselves to continually perfect these solutions (i.e. make better and better approximations), by smartly applying trial and error, and practice, and astute observation, and so forth.
this is what i think feel and intuition really are: the results of our neural networks. the better we feed them, the better our feel and intuition become.
i’d like to add one other thought. lag often talks about lightbulb moments. a subset of these are what sang lee called clearing up misconceptions. he would always speak of finding and clearing up misconceptions. these misconceptions, i think, occur when your intuition is at direct odds with reality. when you can no longer lie to yourself about reality, you have a lightbulb moment, and your misconception is cleared up. and, your intuition and feel are greatly changed for the better. that’s when the big breakthroughs in learning are accomplished.
One thing that I have noticed, is that over the years of playing “pool”, I rarely have found a touring pro that didn’t have a fairly acute sense for the game… whether they played much or not… I only really compare this to pick up games in a bar with say your average patron. I have found many golf pros to be better than your average at pool.
I have never played pool seriously, never had a table in my home, as a kid or otherwise… but I have been able to run the table to my surprise on more than a few occasions (8 ball). I can only assume that spending years fixating on a target visually, and with a natural inclination to assess speed has been a huge factor in the few time I have walked out of a pool hall with everyone’s lunch money, even against guys that show up with their own stick… I have always gravitated toward the heaviest stick on the rack… only making sure it is somewhat straight, and has some kind of felt on the tip. I have also been aware that I have a loop in my right hand that forces me to aim slightly right, of my intended ball path, and I pull all my shots slightly left… being right handed… I just play for it… just like golf. I would assume this is not advisable or standard practice, but I would not be at all surprised if there have been some excellent players who hitched it a bit one way or another.
I can only imagine if golf was “call your shot only”. No slop… that would surely change the game a bit… and I would not be opposed to such a rule…
my guess as to why you and other touring pros do well at pool compared to regulars at poolrooms is that most casual pool players don’t accelerate through the cue ball, and i imagine that you are so accustom to doing it in golf, that it comes naturally to you in pool. just like golf, when you accelerate through the cue ball, the shot is much more stable. you’re pushing the cue ball rather than poking at it. i like to think of it like this: if one were to open one of those big heavy glass doors that opens in, you wouldn’t whack at it. no, you would push it, applying force (which implies acceleration) over a distance. if you whacked at it, you’d get all kinds of unwanted vibrations that make the door unstable. anyway, just like in golf, if you go to the standard pool forums (which i rarely do anymore) there’s always a debate about whether you can accelerate through the ball. i’d like to get my hands on a very high speed camera and put the issue to rest. i’d be highly surprised if the top billiard players are not accelerating at and through impact.
not until i started the modules have i considered over acceleration. understanding this has helped my billiard stroke immensely. it was a real “lightbulb moment” for me. it has reminded me of the few times sang lee gave me a lesson on how to stroke certain shots. since he was a lefty and i’m a righty, we would both hold the cue while he stroked it, so i could feel what the proper stroke feels like. he would say things like “not here…here!” now thanks to lag and abs, i understand what he was saying. he was telling me not to over accelerate at the beginning of my forward stroke and make sure i’m accelerating through the ball.
my friend ira, whom sang lee took under his wing, recalls many sessions where sang lee did this with him. but he would get much more nuanced with ira, getting him to accelerate at different rates and for different velocities. when ira did it correctly, sang lee would say to him “yes, that’s it! now keep doing it so you remember what it feels like.”
in billiards, but not so much in pool, you need to be able to put many spin to speed ratios, at many differing speeds, on the cue ball. so in billiards, the number of strokes you need to master are much greater than in pool. at the risk of making a silly analogy, i’d say that putting on a green with little or no break is like pool, and everything else in golf is like billiards. and the nine ball break with the modern break cues with phenolic tips is like driving with the modern titanium drivers. [getting off my soapbox now.]
lag, as to the loop in your right hand, when you say that you “aim slightly right,” do you mean that you hit the cue ball slightly right of center, when you intend to make a center ball hit? if so, i can explain why your shots go left. when you hit the cue ball left or right of center, not only do you get spin on the cue ball, but the cue ball also deflects in the opposite direction. for example, if you hit the cue ball right of center, you will get right hand spin (right english) and the cue ball will deflect to the left. the harder you hit it, and the stiffer the shaft of the cue stick, the more deflection you’ll get. playing pool you can get away with compensating for it, but if you played billiards you’d have a much harder time. the reason has more to do more with the amount of english than the direction of the cue ball. the direction you can compensate for by altering your aim, but in billiards you have to be very precise with how much spin you’re putting on the cue ball.
as to the weight of the cue stick, i have to think about this more. in golf the ball is being compressed, whereas in billiards (and pool and snooker), the leather cue tip is being compressed. also, a billiard ball weighs about 7.5 ounces (pool balls weigh less) and a cue stick generally weighs between 15 and 22 ounces. so the ratio of stick to ball is roughly between 2 to 1 and 3 to 1 in billiards, whereas it’s much greater in golf.
i know that straight rail and balkline billiard (older carom games involving no requirement to hit any rails) players use light cues, about 15 or 16 ounces. the reason for this, i think, is that they never have to hit the ball hard, and mostly all shots are very delicate ones. furthermore, a common shot (used to gather the balls) is to get a lot of draw (back spin) while hitting the ball very softly. with a lighter cue, you can achieve such a high spin to speed ratio at a very low speed. with a heavier cue, you would put too much linear speed on the cue ball in order to obtain the required amount of draw.
three-cushion players use heavier cues, usually between 17 and 20 ounces, since they often have to hit the ball hard. but there are enough delicate shots that they don’t want to use cues that are too heavy. i’ll have to think about this more. but it does make me think about why the more lofted irons are heavier than the longer ones. could part of it be that the more loft there is, the less of a direct blow on the golf ball, therefore a heaver club is desired to make up for it?
Regarding golf clubs… if you look at the step pattern on the shafts… they get lower and lower moving down toward the head as we move into the shorter irons. Typically they move down in 1/2 inch increments. This effectively is tipping or stiffening the shaft as the clubs get shorter. To then get a similar flex weight is added to the heads as the irons get shorter. This then counters by giving us a similar or even exact swing weight or balancing point between the various clubs in a bag. There are no absolute rules here… and you will see variations in how clubs are set up between tour pros, especially in the old days.
Since I have been playing again the last two years, I have learned a lot more about how I like my gear set up, because I don’t play often… so it is important that my gear is correct for how I swing the club… and I have made some changes that I always wanted to make during my touring years, but didn’t get around to.
I have found I get better response from my short irons by adding weight progressively from about 8 iron down into my wedges.
So I now a couple of my sets that say are D4 from the long and mid irons, then moving to D6, D8 E0 E2 for 8 - SW respectively.
I personally really like extra weight into the short irons… However… I don’t necessarily like the shaft super stiffening as most club fitters would suggest taking that route. I use tipped X shafts, but keep the traditional step pattern right through the short irons… so that the added weight effectively loosens the shafts of the shorter irons slightly. I like to be able to feel a bit more flex in the short irons as I can work the ball a bit better that way. I always have some kind of shaping in mind even with wedges… this wanting to work the ball more may be due to my subconscious discontent with the modern golf balls that don’t want to move. I can definitely shape the modern balls, but with much more effort in doing so. Unfortunately balata is not a viable option these days, even if you can get them, they will be old and have lost their compression significantly after 10 years or so. I always felt they could have made a better ball than the balatas, as we would have to pull out a new ball about every three or four holes as they would scuff by just looking at them wrong, and even get out of shape or round just by playing them a few holes…
I was hoping that a new material could be invented that would still offer the soft feel, but be a bit more durable. The surlyn balls were not the answer, and the modern low spin rate balls are not the answer either.
