The single plane theory part two- plus levers

(note that this had originally been the "two planes" theory- had you read part i, before I added slight corrections. Thanks to those who pointed out the careless error in distinguishing between the two dimensional nature of a "plane" and the one dimensional nature of an "axis". This has now been fully corrected, although I can assure you that this careless error in terminology does not affect any of the practical issues)

In this post, I will be looking at the results of the pencil experiment and exploring the nature of levers- all the way from the finger to the shoulder. In particular, at the end I'll be introducing an idea about how to balance the whole arm and finger as one unified mechanism- with low effort and very little inherent complexity. The specific aspect that I'll be describing this is not something that I have ever encountered in a book on piano technique or heard spoken of by any other teacher. However, I am absolutely convinced that I am looking at one of the single most important things that just about all great pianists have had in common- no matter how diverse their techniques might appear to be on the surface. In short, it's a way of relating the finger to the arm- within a sustainable quality of balance. In this balance it is possible to absorb the forces that the keys respond with despite scarcely any change in state- yet the finger does not have to support excessive levels of weight at the keybed.

Anyway, first it's back to the pencil experiment, for the results and analysis. Hopefully you will have found that the most efficient means of moving was to get the pencil to exert a kind of "pull" upon the key, in which the direction of the force was constantly changing- rather than a push that involved driving the pencil in a single straight path. If you didn't, that's nothing to worry about, however. I'll try to illustrate how this action can be acquired, right now. Note that, although we're sticking with the pencil for now, this gives a prior illustration of many of the concepts which we'll be applying directly to the finger, within future posts.

One thing that we can write off at once is the worth of adding a third axis of forces and movement. Mechanically, anything sideways contributes nothing of any benefit to the context of playing an individual note. This illustrates the value in generally striving to line up properly behind each finger, in order to keep the activity almost solely within a single plane (that consists of both the backwards/forwards axis and the up/down axis). Basically, it serves no purpose to direct any movement or forces sideways, and neither is there any reason to align the pencil anything other than parallel to the length of the key surface.

More about how the arm must be involved in the considerations later in this post, but the finger itself can make direct transfer of energy, when aligned to act within this plane. In fact, the closer it is to this alignment, the easier it is to integrate its action with the arm. This provides a very strong argument for judging the hand's alignment as a whole from the weaker fifth finger. It's a common fault to find pianists who put their strongest and most agile fingers in a perfect line to play- yet leave their weaker fourth and fifth fingers in a far less suitable position. Why would you want disadvantage your weakest fingers of all, by putting them in a position where their natural path of action is not even close to the plane of the key? Nowhere is it more important to fit the finger's path to the key's path than when it comes to the fifth finger. Slanting can easily lead to a vicious circle of inactivity that perpetuates the belief that perfectly capable muscles are weak- by preventing them from carrying out their natural purpose. Without adequate alignment in this plane, comfortable finger staccato from the fifth can become little short of an impossibility. Of course, you may not have the option of aligning right behind the fifth, at all times, however- especially if you have smaller hands. Keep the single plane action in mind as an ideal to strive towards whenever possible. However, in future I will talk in detail about the best way to set about activating the fingers effectively along less direct paths- which sometimes becomes nothing short of a necessity.

Here are two views of a rather lazy fifth, at an angle where it is collapsing flaccidly onto its side:

and here are two of a supportive fifth finger, the activity of which acts almost perfectly within a single plane:

I think it's pretty clear which one looks like a real pianist's hand and which one looks like that of an amateur! However, if you tend towards a lazier fifth finger- please don't suddenly go pulling the hell out of the key just yet! It's important to be gradual and patient about making such adjustments- especially if the muscles have scarcely done anything before. Bear this principle in mind, certainly, but I'd advise you to wait until I've covered the nature of what makes for healthy finger action, before you go for any drastic adjustments.

Anyway, within the plane of activity, the pencil basically rotates around the point of contact against the key. Although I don't want to get too carried away with analogies, notice the very obvious relation to a see-saw. The more you feel the end that you are holding onto is going upwards and forwards, the more the other end is felt to pull down and backwards at the point where it meets the key. This introduces a danger of slipping, of course- so you have to be careful to feel that the point at which the pencil meets the key remains stable. Initially, it's not a bad idea to rest the pencil lightly against one spot and simply rotate it around that single point, without moving the key at all. Feel the circular path around the point of contact:

If you do find it hard to avoid skids, this is a very good way of sensing how to keep the contact stable, as you begin to apply bigger forces. When the end stays in one spot, you should find that the pull on the key is extremely productive and that there is very little thud, no matter how strongly you pull. If you feel a thud, are you sure you didn't start aiming the force right down and only switch to levering AFTER the key landed? Note how there is no feel of changing the movement either during the moment at which the key lands or immediately after. The follow through is not felt differently to the act of pulling the key down to the bed. You just want to keep smoothly drifting through and beyond the time when the key has landed, before you even think of stopping. If the circular motion around the end of pencil has to progress as smoothly as possible, you cannot 'dig in' with any impact. Sometime, just concentrate on the smooth path of the pencil above all and see if you can deliberately take all focus away from the idea of the moving the key down. Strange as it may sound, this may improve the action. Forget the idea of "down" altogether and just let that part happen. Notice the circle that is initiated as a forward and up movement. As described in the last post, however, practise changing your perspective back and forth. Sometimes return to thinking about the down and back action at the other end of the pencil. See if you can gradually combine both perspectives into a single, consistent motion.

Notice how this is NOT perceived as a "tension and then release" style of movement! Basically, if you feel you have endured enough of an effort that you need to willfully release something afterwards, the movement really wasn't anywhere near good enough. It should have felt effortless all the way. So, relax by all means. BUT THEN GO BACK AND IMPROVE IT!!!! You have to be patient but, in the long run, no other intent will do- assuming that you hope to progress. Virtually all healthy base movements are felt to be continuous and all good pianists are certainly capable of doing them whenever required- even if they don't use them for every single thing. If you can't get something continuous, go more slowly until you feel that it is slow enough to be executed entirely without any bumps. This literally applies to even a single note, whether it be sounded with a finger or a pencil. Comfort must be maintained at all times- not habitually lost and then reinstated! If you think that's fine as your fundamental basis for moving a key, you might as well say its fine to routinely walk headfirst into a wall when you meant to pass through a door- as long as you wipe up all the blood from your nose and take an aspirin straight after. It's not fine at all to repeat errors. If you want to learn anything from mistakes, you have to understand that you have indeed made them. "And then relax" is far too forgiving of excess effort- even if it seems to promote relaxation on the surface. It can lead to a perpetual cycle of error- correction -error etc. rather than error- correction- correct movement.


So, did you find a comfortable movement that produces a sizable sound without impact yet? If not, I wouldn't be too put off, but hopefully that should have led to at least an improved understanding and feel for the gradual nature of high quality movements? We don't want any stops, starts or prods in the foundation level of movement. Incidentally, the exact angle may not be the same for everybody- although it should most certainly involve levering the pencil in the general manner described. If not, keep working at it! The point was not to find a single absolute angle- so you might tell all your friends that the "correct" angle at which to aim the finger into a piano key is precisely 10.2453 degrees off the vertical, or whatever else. Far from it. In fact, the exact angle of force should slowly and smoothly be changing, as you move around the circle and depress the key. Even with the pencil, it may well be dependent on such issues as the mass of your arm, the height of your stool and many other variables. This is why advanced mechanics is futile- it's just too precise to translate. Looking at things from more basic principles can actually be a lot more revealing.

If you were expecting geeky calculations or simplistic, hard and fast answers, you've misunderstood the purpose of what I'm doing here. The idea was firstly to challenge the tendency towards downward assumptions about the movement- but above all to help you to FEEL your way to a more productive path. As, I've said, this is not about cold exploration of theory but rather the practical applications that derive from it. Theory does not provide absolute answers, but a basis upon which to have a clearer idea of what you are trying to SENSE within your own feedback loop! I really do advise being thorough with these exercises and taking care to follow the detail in my descriptions. There is really very little to learned from the theoretical description if you do not use it as basis from which to improve your perceptions, so please don't waste your time reading this without doing the exercises! 

One reader told me that he felt the exercise was "worthless" because I didn't state the conclusions straight after and because I didn't explain why you should avoid what is "obviously (...) the easiest way". Well- if you don't even follow the description of the exercise thoroughly enough to realise the fact that aiming the pencil straight down is NOT the easiest way of moving the key, it certainly is "worthless"!!! Try it for yourself now. Just how stiffly do you have to hold the end of the pencil when aiming it straight down, without the end that contacts the key being greatly repelled? It is far more valuable to discover things through experience, than be told them. I cannot provide anything useful to anyone who doesn't put a great deal of effort into bringing their own perceptions to the practical elements.

Anyway, let's look more at the nature of levers, with reference to the arm as a whole. Imagine a series of hinges that connect  a series of levers. Let's say that one free hinge is fixed to an immovable point on a wall but that the others are all entirely free. Of course, everything collapses downwards:

Let's say we need them all outstretched. what if we fix the first hinge in place? The rest still collapses:

Very little benefit came. We can now add an extra internal force to stop the next hinge next from collapsing:

But the rest still collapses etc. Eventually if EVERY joint is fixed into place it all balances- as a single fixed structure, with very limited movability:

Now let's say that we start from the far end now. You pick the end up and walks away from the wall. It can momentarily 'hang' between the fixed point and the supported point. Walk far enough and you get to a point where it is fully supported in every joint without any internal forces having to be generated to stabilise the hinges. The hinges are tightened solely by the pull from the far end, coupled with the stable point of attachment at the wall. Alternately, you could leave just a slight trace of slack and EVERY joint would still be freely moveable, rather than tightened stiff. In this state, everything is "hanging" freely between two points- not being stiffly held together with internal restrictions.

(From another perspective, you could also imagine taking a long heavy sword and holding it horizontally, without any support beyond your grip. It is far easier if you rest the end even very lightly on something- giving support via two points.)

Let's now translate this idea of spreading support into a two-sided balance into the rather similar situation of an arm at a piano.

It really is quite similar. If we only supported at one end here, the elbow could only be stabilised in space via muscular effort, to prevent the gravity pulling it through the marked circular path. But then if the elbow joint were to release the forearm, the wrist would still plummet. It's a similar case, where if we start only from the shoulder end, EVERY successive joint must become be supported by an additional internally created effort, one after the other. Joint after joint is held up by effort, unless the finger is able to create a point of support. However, the moment the finger starts supporting something, the elbow and wrist can become truly free hinges- with zero internal effort! It's like a chain that hangs between two points of contact. The moment the finger plays- the arm can theoretically become wholly supported without internal efforts to fix the joints. ( although, we're likely going to want to reduce the workload upon the finger by taking some extra support at the shoulder) If the finger sets up a point of stable contact between itself and the key, it can pull in a way that would draw a loose arm forwards. This means that the upper arm can release a little more. If we take the component of force that pulls the elbow backwards and match it to the one from the finger that pulls forwards- the whole mechanism is supported. It's also VERY simple as we only have two inherent variables to balance- how much the finger is acting and how much the shoulder is supporting/releasing to balance that via the elbow.

To put that in the simplest way, basically the finger tries to pull them arm lightly forwards and upwards (via the same kind of path we see from the pencil experiment) and the elbow is released enough to pull lightly backwards in response, via gravity's action. Rather than cause the arm to actually move,  this 'tightens' up all the other joints, so they can remain still despite hanging freely (rather than be held immovably via muscular efforts). If this sounds like hard work, let me stress a few things- firstly, it really isn't! The shoulder can still support plenty of the arm's weight. We don't have to rely solely on the fact that the arm will not detach at the shoulder and let it hang completely. It can take on as much or  as little support as you like. Also, this is totally different from the manner in which traditional arm weight technique is based on downward thinking. The down forces supported by the finger are actually rather slight. The finger really doesn't have to bear that much weight for this to balance. It just has to match to the feeling for how gravity is pulling lightly backwards upon the elbow. With regard to this backwards and forwards element of the matching forces- it's really not equivalent to the whole cast of "The Expendables" getting together and having a tug-of-war using a  steel rope. The amount of pull required from the finger (in order to keep the wrist absolutely free of internal tensions) is very slight. It's not so much tightening the free joints, but ALMOST tightening them- so there's a feeling of "hanging" with a touch of remaining slack. Despite no muscular holding, the wrist cannot sag into a collapse. It is held up by forces elsewhere which are just enough for it to be supported. I'll be giving a practical exercise to show exactly to perceive this free state in my next post.  

The notion that the fingers should not contribute to support (but might be better off 'relaxing') after having struck a key is often expressed. But lose that support and you lose the two-sided balance! Even if relax means 'and then be comfortable' why were you ever uncomfortable??? Too much weight to support? Too much willful arm pressure? Whatever it was, none of these things should ever get in the way, if the goals are clear. Once more, what use is a poor quality of motion followed by a vaguely focused attempt at general release supposed to be? The real question is- why did the intention of both starting and finishing with a low effort balance go wrong? To explore that is the simplest and most likely solution. To look at it in terms of generally hoping to relax without even paying attention to the means of low-effort balance seems truly ridiculous, when viewed in this light. Why not focus on creating a comfortable two-sided balance between the a smooth low-effort finger action and a feeling for how gravity pulls the elbow backwards to balance? It's vastly simpler than just thinking "relax" without any specific positive intention. Relax carelessly enough to remove the most useful forces and you simply direct a need for effort into something altogether less constructive. That can actually cause MORE tension than if you start from a natural low effort movement with a clear goal in mind.

Also, note that I have yet to introduce the reaction forces that are generated by movement of the keys.When these are introduced, I'll go on to illustrate why the one-ended model requires rapid and complex changes in state, if it is to avoid heavy impacts. Conversely the two-ended support system is able to absorb reaction forces with minimal changes of state. 

Anyway, that is the basis for this model. In my next post, I'll be giving a series of extremely specific practical exercises to prepare key elements of the arm's role- so as to permit the a very low effort means of perceiving and controlling the release/witholding of  weight.

Improving movement by understanding duality of forces, plus issues of momentum

Before I come on to the second part of the post about feeling movements within one plane, in this post I'm going to illustrate how qualities of movement can be informed and better understood with regard to some very basic scientific principles. Firstly, I'd like to talk about the idea of equal and opposite reactions- with regard to acquiring a dual perspective from which to better perceive movement, rather than the one-sided view that typically evolves. I believe that this concept can be a tremendous aid to building efficiency and comfort in movement in general. Although this post will read more as an introduction to a global concept of movement (rather than contain anything immediately specific to piano playing), bear in mind that the principle will recur in a number of especially specific descriptions of the end product.  

"Every action has an equal and opposite reaction", is the slightly simplified version of Newton's law that is usually quoted. As an example, by jumping in the air a person displaces not only themself, but also the planet. There's no need to be alarmed, however. Being rather substantial in mass, the planet is affected really rather slightly (its acceleration being equal to the small force divided by the planet's huge mass). So there's no immediate need to fear that the earth might begin spiraling rapidly into the sun, should too many people take up aerobics. In fact, it's also true that when falling back down, a person's gravity draws the earth faintly towards them- basically cancelling out the effect of the jump. Anyway, forces occur in opposite pairs- which is why a gun recoils backwards upon firing, when a bullet is propelled forwards. While, in everyday life, we think of opposites as being incompatible and mutually exclusive, in mechanics opposites are part of a single logical reality. The sheer significance of this (where opposites are actually perfectly compatible, as viewed within a whole) should hopefully become increasingly clear as I continue. But basically:

Opposite explanations are not necessarily contradictory!

In virtually all movements, our natural instinct is to focus on only one side of the picture. In many cases some people might choose one of the possible perspectives and some may choose the other. However, there are countless cases where virtually everybody is guaranteed to look at one particular side of the equation, while completely overlooking the other. I'll talk more in future about how moving a finger into a key really ought to be felt equally in terms of the finger pulling at the arm (otherwise we end up stiffening, in a futile bid to stop the inevitable fact that the arm as a whole receives a force, not just the key). For now I want to show how the attempt to appreciate both "action" and "reaction" can make general movement a lot more efficient and free. 

Let's start with something as basic as walking or running. With each push off, you need to ask yourself- am I focussing on trying to use my foot to pull my body forwards across the ground, or am I trying to propel the ground backwards and behind me? Do I focus on the action or the reaction? This image shows the angle of the force, at the end of a stride. 

The force can be analysed in two components within different axes, as described in my previous post (strictly speaking a small element of force runs into a third axis- but this should be of very low significance, compared to the very large components within the backward/forward axis and the upwards/downwards axis). The action is backward from the runner's perspective (to the left from ours) and downwards. The reaction is forward from the runner's perspective (to the right from ours) and upwards. When thinking about these, we might usefully concentrate solely on the forwards/backwards aspects or the upwards/downwards aspects for a time. If we look at each axis separately for a while, it can make it easier to develop that particular element. Then we can start thinking more about the action or reaction as a whole, once again.

Let's start with the backwards/forwards forces first. It really does not matter whether you typically perceive it more from the backward action or the forward reaction. The goal is simply to acquire a balanced perception- so now try the one you are not used to. If that feels like it's a bigger effort, that's fine at first. Switch back to your normal one for a time, but then switch again. Keep switching over between the backward and forward perspectives- trying to notice as acutely as possible what feels different between the two. Both versions ought to become progressively informed by something about the quality of the other. It should feel more and more effortless until you get to the point where, upon switching, there is scarcely any difference to be found in the quality of either. After all, they are supposed to be viewpoints of the same thing- not two different things! Action and reaction BOTH occur, regardless of which you focus on! Hopefully you are now left with a product that is based on a more integrated dual understanding of forces rather than single-sided thinking. However, that might perhaps be a little ambitious, after having only just started to think this way! Most likely, there will already have been improvement to the ease, but it can be a gradual process of development. 

Now let's try it for the up and down, as you walk. Most people will probably think more of the down here. Obviously, your foot naturally exerts a pressure down into the ground. But what if you walk by looking more at the upward nature of the reaction, rather than the action? If you feel how your whole body is lifted over the top (rather than dwell on the downward action at the foot), the whole thing may feel like less effort at once. But again, switch back and forth between the up and down feels. There's not a right way and a wrong way. We want to integrate both elements for a single understanding. Sometimes feel how your foot has to press down into the ground. This will likely feel like more effort. So simply switch to the upward feel for a while. It likely tends to make you feel less digging in, even though that upward force occurs because of the down force. See if you can capture more of that ease when you return to the active perception of the down element. Again, keep alternating until the two (previously conflicting) mindsets converge to the point of causing almost no differences at all.

Arguably this is at least of much an issue of psychology as one of mechanics- although the relation to the nature of forces means that it has foundations in something that is very much real. Psychological as the process of improvement may be, it is constructed around a clear-cut  rational foundation. I believe that this is a lot stronger and a lot more conducive to sustainable improvements than purer psychological strategies such as a mere "remember to relax more" etc. The psychological aspects are focused around a verifiable mechanical factor that can serve to guide the process. It is very different from wishful thinking that exists in a complete vacuum (not that I wish to write off the power of positive thinking outright, by any means).

This kind of dualistic thinking is something that I will come back to in various situations. I believe that one of the big problems in piano teaching has always been polarisation i.e. forcing it to A or B rather than a combination of A and B. Some teachers boldly proclaim the absolute truth of one side whereas others shout as loudly about the other one. However, it's very much down to the student's individual needs as to which side they might draw the most benefit from, with regard to the two-sided reality. What aids one student, might provide an active hindrance to another. In theory, if a lot more movements could be understood from dual perspectives, teachers might be in a position to solve problems with far greater consistency- regardless of which side the student might have strayed on. Although it runs a little deeper than the nature of action and reaction, in a future post I'll be going on to illustrate why the arm-weight approach and the finger based approach are basically polarisations of something that ought to be understood from a similarly dualistic perspective.

Anyway, I also need to introduce the idea of momentum, with regard to to movement. It's well established in the field of resistance training that it tends to be better if you are careful to move relatively slowly. This trains the muscles in a much more rounded way and makes errors in technique far less likely. There can be benefits from more explosive movements, but these are to be done with caution- especially if you are hoping to build sensitivity as well as strength. Anyone who's ever been to a gym will doubtless have seen the type of young, enthusiastic would-be Hercules who likes to illustrate his masculinity by attempting stacks that are far heavier than he is comfortable with. Rather than controlled movements, you see explosive actions that rely on a big initial force- rather than a consistent interaction between the muscles and the resistance. Often, much of the impetus doesn't even come from the muscles that the action is intended to train.

Scientifically speaking, this type of movement relates to the concept of momentum. I'm certainly not seeking to specifically compare piano playing to bench pressing 100kg, say. However, I'd like to illustrate how the difference between such qualities of movement has considerable relevance to both understanding the best ways to achieve control over a piano and to be able to move healthily whilst doing so. According to Newton, an object that is in motion continues to move at constant velocity, unless a resultant force acts upon it. So, if you apply enough force to something, it continues to move for a time, whether you continue pushing it or not. However, if you move something very gradually, you have to exert a more continuous force, in order to keep it moving.  When an object does not already have a large momentum, its motion is dependent upon ongoing forces- for such forces as friction would otherwise have caused a rapid stop. Conversely, a briefly large force might allow something to travel a similar overall distance, without further input of any driving force at all, necessarily. Basically think of the difference between moving around a supermarket trolley, while constantly feeling a small push- compared to if you give it a good old kick and then let it continue on its own steam, until it drops into the canal (don't really do that, obviously). 

(At this point, pure physicists may want to complain that all hammer motions are dependent on momentum- after the hammer is let free from the key. However, regardless of that, the difference between the qualities of movement is very much an issue regarding the fine detail of what happens when the key hits the key bed- in terms of how impact is absorbed and in terms of the balance that follows. When rolling out as many as 16 notes per second, the quality of balance that goes on before, during and after each note is far from a trivial issue. I believe that there is extremely good cause to understand the difference between an initially rapid impetus followed by coasting, compared with a more consistently applied force. The belief that such qualities of movement are a mere psychological illusion is tremendously open to dispute- although I do wish to acknowledge that such beliefs exists, for the sake of accuracy)

To introduce the difference between momentum based movements and more steadily controlled ones, I'd like to refer to a very useful exercise that can be performed away from the piano. In addition to providing a first hand feel for the sheer difference between such qualities of motion, it also happens to be a very good way of better sensing the upper body. Awareness will automatically be raised of many muscles that contribute greatly to the ability to balance at the shoulder (which, when trained to become more sensitive, are less likely to become heavily fixed).

Anyway, this is a very standard exercise- basically that of the press-up. However, we're going to do a very low effort version against the wall and with a very particular type of focus. It doesn't demand any great strength, but rather attention to balance. Standard press-ups against the floor are frequently done with a lot of initial momentum that serves to quickly 'bounce' the body upwards. The return to the ground often follows on as a near free-fall collapse back down- often without so much as a pause at the top. The problem with this is that it works certain muscles rather heavily and others scarcely at all. There is very little room for discrimination as to what goes into it. Severely lopsided training can easily ensue, where one half of the body operates extremely differently to the other. Even if you have the strength to do a large number of repetitions in the bouncing manner, there is reasonable question as to whether some of the relevant muscles are necessarily getting ANY training or contributing anything to the action whatsoever. If you simply move slower (looking out for any jerks, collapses or jolts), many muscles must get involved with the continuation of motion and contribute to balance. However, this can be surprisingly demanding. A standard press up is very difficult to do both slowly and with perfect form. That's why we're just going use the wall for this.

To do the "press-up", stand a couple of feet away from the wall and lean against it, with the hands at shoulder width. Obviously be careful not to strain yourself and stop if you feel any pain or excess stretching (although, seeing as it's nothing more than an enormously easier version of something so standard as a press-up, this barely seems to call for much of a legal disclaimer). Anyway, lean your body in and then control it back and forth in similar form to a regular press-up- trying to keep a single straight line from the toes right up the whole of the body. Try not to bend your back at all. So, how does that feel? Easy to do it ultra slow, with no holes in the movement?

You may well find that, while it's easy to do it fairly quickly or with the odd stop/start in the movement, it's really rather hard to do it slowly and consistently.  If so, this is where the idea of dual perception makes a reappearance. However, if you didn't end up in a position where you were clearly doing it too quickly and with too much momentum, I'd advise you not to try anything in the next paragraph before you've checked the one after. 

In this case, I believe that most people will typically have thought of the away movement in terms of the "reaction" force that generates the motion away from the wall, not the inward "action" that continues towards the wall (notice how this is actually the reverse compared to walking- where I believe that most people will tend to dig down too much into the "action", rather than concentrate on lifting themselves up via the "reaction"). So, as you go away from the wall, in order to improve you're going to want to focus on how you are still leaning into it, rather than too much on the away movement. As you go inwards, you're also going to want to feel how the wall is pushing you away still. This reversal of perspective helps to cure the excessive reliance on momentum, and enables far clearer perception of the stabilising muscles that enable a slow movement to be executed smoothly.

Basically, in order to change your perception you're probably going to want to think of the forces in terms of the opposite direction to that in which you are moving in. However, at this point it would be all too easy to slip into careless polarisation! So, I have to emphasise that not everyone will necessarily be the same. Was excessive momentum actually the problem? If not, you might have looking at totally the wrong solution! Remember that we have to look at both sides- not merely one or the other. If you found that you were actually digging in too heavily (which some may have done), we need to reverse the whole thing! Anyone going with a feeling that resembles ancient machinery grinding together needs to lighten the action.As they go away from the wall, they need to stop thinking of leaning inwards and think away from the wall. As they go into the wall, they need to feel gravity is allowed to ease them inwards- rather than be in a position of resisting it quite so much. Remember though, regardless of the initial fault you still need to switch back and forth from time to time though. Otherwise, the individual cure might just leave you doing it wrong on the other side- instead of converging on what you actually want. Both perspectives are valuable. Neither is inherently more correct or incorrect- except with regard to the current nature of the issue (note that 'current' is a key word).

I hope that this helps to establish some issues of movement with some clarity as well as the danger of polarised one-size-fits-all thinking. Although none of this post is specific to the piano whatsoever, I hope that people will have considered taking the time to think about it. I believe that this is a major issue in terms of what we ought to be understanding, when trying to make corrections to movements. By understanding that superficially opposed mindsets can be one-sided descriptions of a single whole, you can converge on (the seeming contradiction of ) being able to view it from BOTH sides at once! One-sided thinking may be important in the short term, in order to progress closer to the correction. However, two-way understanding is always the end goal. Do we want the person who went too quick to start digging in? Do we want the person who was digging in to start bouncing up and then collapsing in? After a certain point, sometimes you basically have to go back to WHAT HAD BEEN THE PROBLEM!!! If I'd started with that, if might well have sounded pretty ridiculous. But I hope that what I've written will have established the sheer danger that lies within sticking to just one view of a two-sided whole. Looking at just half of the picture without ever referencing it back to the other is rarely wise.