Thank you for asking this tremendously important question, especially in light of the recent articles highlighting vision so prominently. I think the proper role or function of vision in putting in pretty misunderstood, and this misguided emphasis on vision hurts most golfers.
Let me start with a few key observations and then respond to each of your questions.
The fundamental character of golf is action, not information gathering. In putting, the action is three-staged:
1. [Reading the Putt]
First, the action is simulating the roll of a successful putt over the actual green surface into the cup in the mind so that the best-chance startline and the speed are comprehended accurately,
2. [Aiming Putter and Body]
Then the action shifts to orienting the body setup to the startline for a straight stroke,
3. [Making a Straight Stroke with Good Touch]
And then the action is executing the stroke movement with good touch or distance control.
The routine integrates these three fundamental phases into a unified, flowing, single action of "the putt" in a way that respects and enhances innate brain-body processes of targeting (perceptual processes) and stroking (movement processes).
The first phase (reading line and speed) is targeting with the effect of stroke movement in mind (how the ball will roll). The second phase (aiming putter face and body in setup to line) is moving and positioning the putter and body in response to continuing targeting, so it is a blend of perception and motion. The final phase (stroking straight with good touch) is pure movement, beyond targeting, made out of the setup position with the targeting in control of touch at a non-conscious level.
Once the path is accurately imagined with the "read," and the setup to the startline is adopted with the putter face aimed squarely down the startline, the only missing variable is touch. But touch is simply the length of the backstroke in a stroke executed with consistent tempo. And this aspect of the action is set non-consciously as a result of targeting in the first and second phases.
The role or function of the eyes is to assist the body in its process of learning to feel "aimed." The body is position and posture and forthcoming movement on the green in relation to the ball, putt line, target, cup, and stroke. The eyes obviously have a role in "reading" the putt and this role is pretty straightforward and is the normal way people think about the eyes and vision. But in getting the putter and then body setup in the second stage of action, the role of the eyes is entirely subordinate to the movement and positioning of the body as it uses targeting motions to square up to the imagined startline of the putt, aim the face down this line, and square the body to this face and putter-as-aimed for purposes of the ensuing straight stroke movement in the final stage of "the putt." And in the final stage, making a straight stroke with the putter-as-aimed with good touch, the eyes have next to no role, apart from not hurting and mildly helping the body make the motion correctly.
People who have little appreciation for the neuroscience of action, as well as a limited exposure to elite putting technique / expertise, tend to misunderstand the role of vision in the second and third stages. Statements like "have a steady gaze aimed at the back of the ball" right before and during the execution of the stroke, all fancied up with the aura of "science," make golfers believe that there is more being done with vision at this point than really is the case. The important neuroscience at this point is proprioceptive and movement-oriented, not visual -- that is, "feel" and not "sight.". The main function of the eyes and vision now is not to harm the important processes, and there is very very little that vision contributes in a positive way to making a straight stroke with good touch.
Let me respond to your separate questions, and hopefull this will become clearer.
Q:"1) During the last 5-10 seconds before you stroke and the moment that you stroke, what exactly should you look at in what order and what should you think about, or imagine/visualize?'
RESPONSE: This is the final parts of the setup action leading into the stroke. These final 5-10 seconds are when the golfer has aimed the face of the putter and adopted his beside-the-ball position. he is looking one last time down the line to the "target," to make sure he really "feels" the putter face is accurately aimed, that his body is "squarely" setup for a straight stroke with that aim, and that he has a good sense of speed for rolling the ball into the cup with good touch. Picking the target to aim at based on the imagined "read" and aiming the putter's face after sighting from behind the ball have already been done. The golfer is transitioning from vision to body movement. He checks the face visually to make sure it looks and feels aimed where intended; he checks his setup in relation to the putter as thus aimed for purposes of feeling whether he can make a straight stroke rolling the ball straight away from the face as aimed; and he refreshes his sense of distance.
What is he looking at? First, the way the face aims thru the center of the ball. He has done this already in setting up to the face aim as established from sighting behind the ball, but now he does it again, this time to make sure he "sees" the line he has established for the forthcoming stroke by the face aim thru the ball. The golfer assesses the perpendicularity of the face and the line off the face thru the center of the ball, to make sure he knows where the face is actually aimed. This line thru and away from the ball out of the face is what the golfer now wants to follow with his vision to see where it ends up.
The golfer now assesses whether the eye line across his skull matches the line away from the face, and he assesses whether his gaze is aimed straight out of his face. (This step becomes a lot easier and with little or no thought as it is practiced.) This is the beginning position (eye line matches face-aim line and gaze straight) for accurately turning the line of sight out of a fixed straight gaze by simply turning the head to move the gaze.
The golfer then turns the head and monitors the turn with feeling and vision to make sure the head turn is progressing so the line of sight stays moving in a straight line along the ground, wherever it is going. If the line of sight ends up at the preselected "target" straight away from the way the putter face is actually aimed, then this process has successfully confirmed that the face is aimed squarely at the target. (In a breaking putt, for example, the "target" would be a spot to the side of the hole.)
From the target, the golfer keeps the head still with the same orientation to the target but shifts his gaze to the spot on the lip where the ball should enter the cup. From there he retraces the last segment of the curve of the putt (emphasized during the reading of the putt) backwards out of the hole in reverse realtime visualization with eye muscles only and follows this curve as it merges back into a straight line back to the ball. At this point, the golfer resumes the fixed-gaze head turn and retraces the line back to the putter face by keeping the gaze straight and re-turning the head. The golfer watches to see that the line of sight comes back into the face in a perpendicular way, just as it left to move to the target.
(This head turn with fixed gaze to the target is done while imagining the roll of a perfect-speed putt to the target. Doing this gives the body feel-knowledge in terms of the angle of neck turn and the pacing of the turn that calibrates the brain for making a stroke with good touch. That is, this checking of the face aim combines with the timing to establish the backstroke length of the forthcoming putt. This happens totally without thought and depends only on a persistent background sense of green speed and some accuracy of imagination is visualizing the perfect putt's realtime roll along the path to the target.)
As the line of sight arrives back at the ball, the golfer wants to "feel" the putter face's aim straight thru the ball. This means that the sweetspot of the putter face will be moved in a line straight thru the center of the ball along the line the face is now aimed. So the golfer looks at and feels this line thru the ball, starting at the back dimple on the equator closest to the putter face and extending thru the center of the ball and out the opposite front dimple on the equator that is closest to the target. As the eyes stop moving, the feeling of this aim is a matter of visiting your body to feel if all systems are go for the stroke necessarily implied by the ball-putter face relationship (aim) - do the posture and tension feel correct for the stroke to come, are you aware of how the motion will be started, with which body part moving how? This all happens subconsciously in a flash (or two).
Then the golfer stops moving the head. The gaze may have shifted about a little to get the correct feel of what is straight down the line and out the face of the putter, but now the gaze stops moving. It has to stop with the line of sight pointed somewhere, and the back of the ball is certainly one possibility. But the fundamental point is that the gaze should stop soemwhere along the line of the putt near the ball. You could look at the front dimple, a spot on the line in front of the ball, the center of the ball, the back dimple of the ball, a spot on the ground between the putter face and the ball, or the sweetspot of the putter (and probably other spots on the line near the ball). I personally like to look at a small blade of grass on the line right in front of the edge of the putter face between the face and the back of the ball. I identify this spot as the place for the (down)stroke motion to transition from perfectly flat and vertical at the bottom of the stroke to an upward finishing stroke. But that's because the bottom of my stroke is directly in front of my putter face. This is a little unusual, as this plus forward ball position makes a gap between my putter face and the back of the ball. I think this gap is a wonder way to emphasize the line and the body motion of the stroke, as compared to moving the putter head forward to the back of the ball and thus past the bottom of the stroke.
When gazing down at this blade of grass, the golfer does not think of anything at all, except perhaps to make a good straight stroke with good tempo.
Q:"1) What is best? "
"Thinking about the exact target/spot DURING THE STROKE or to think about the ball following the line?"
RESPONSE: Neither. Don't think about the target or the line; just think about making a straight stroke with good tempo. Keep the sweetspot moving on line simply by the shoulder movement and keep the face square to the target simply by keeping the hands '"dead."
Q:"And what about the spot on the ball where you want to hit it. Can you make yourself look at this point subconsciously so that you can actually think about something else, like the target or the line?"
RESPONSE: Yes, you can look at the back of the ball or another spot on the line, but you don't have to think about that or about anything else.
Q: "Cohn and Winters address this issue, but are very vague about it. They say (page 131):
“most players watch the ball during the stroke, but also retain the ball-target orientation and/or sight their line with peripheral vision”.
"I think they are addressing more or less the same problem, but do it very vague. Why do they say AND/OR?? What exactly is the ball-target orientation? What part of the line do they sight with peripheral vision. How does this change for longer putts? Etc. Etc. Etc."
RESPONSE: The "ball-target orientation" is the feeling that you are aimed square at the target with putter face and body and are set to make a straight stroke. I don't believe golfers should sight the line with peripheral vision. Doing so is diciding attention in a way that leads to peeking and head and eye motion during the stroke, which leads to poor stroke motions.
Q: "2) Another question I have also comes from reading their book. Should your eyes focus on the hole, a spot near the hole, or an intermediate spot on your line? How about using that imaginary spot for downhill/uphill putts (or putts that break)? "
RESPONSE: a spot on the ball or on the line near the ball in front or behind.
Q: "3) What is the correct order in which to look at things during the last 5-10 seconds?"
RESPONSE: ball and putter face; line; target; hole; curve backwards out of hole until it transitions to a straight line back into the ball; ball and putter face; spot of grass; sweetspot in downstroke arriving at spot of grass; spot of grass after putter head passes into impact.
Q: "4) Should I envision the entire line the ball is going to take?"
RESPONSE: Yes, but only during reading the putt and when retracing the path backwards out of the hole, but not when executing the stroke.
Q: "5) Should I look at the line from ball to hole or vice versa?"
RESPONSE: Yes, but be careful how the "looking" movement is performed in terms of gaze and head turn.
Q: "6) How does this all change for long putts?"
RESPONSE: It doesn't change at all for long putts. In fact, since there is more neck-turn angle and the hole appears to be a smaller visual object, there is reason to argue that long putts start out with more precise input for the targeting perceptual processes.
Q: "7) To what specific part of the ball should I look at? I look at a dimple on the right side (viewed from above, for a right handed player). Is this correct?"
RESPONSE: That's ok. It's also OK to look at another spot on the ball or grass that is on the line and near the ball, whether slightly in front or behind.
All of the above is a rather explicit, point-by-point description of what I think is a good way to use the body and vision in putting. But laying it all out explicitly like this should not lead you to think this is "paralysis by analysis." There are just a couple of things to learn, one of which is the fundamental approach to putting as "body action." Another is how the gaze has to be unchanging and straight for accurate perceptions. Another is to use the final check at setup for the dual purposes of checking that your aim feel right and of building in the correct neck-angle and pace of turn used for the touch system.
And probably the biggest on, contrary to a lot of existing putting lore, once you are happy that the putter face and body are aimed at a target selected in your read, you really want to KILL vision completely, get out of targeting mode, and go completely into stroke mode. At this point, you could close your eyes and pull the trigger with good tempo and an empty brain. About all a fixed and still gaze contributes at this point is a mildly useful visual stillness that helps make sure the body movement stays on track. Too abrupt a movement, and the visual scene might shimmer. Twist the torso out of square, and the scene at your feet shifts.
What I say is that once you are satisfied with the putter face aim and your feet are "happy" (thus signalling that the body from eyes to feet has settled into the square setup to the putter face aim, then it's time to stare blankly at one spot, live in the still scene at your feet, think of nothing at all except perhaps making a straight stroke with good tempo, and start the stroke.
Let me know what needs better clarification.
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