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.

The "Single Plane" Theory part i (plus issues of understanding gravity)

(Sorry, if you were hoping for the latest 9/11 conspiracy theory- I'm afraid you've just landed in rather the wrong place.) 

In this first specifically aimed post, I'm going to begin to introduce both the concept and relevance of axes (plural of the singular axis) or planes of movement. An axis is basically a line of motion- similar to the concept of dimensions, of which there are of course three (well, according to wikipedia we seem to have managed to extend that to one extra these days, but I couldn't personally tell you where the fourth one might be. Rest assured that I'll be omitting the mysterious "w" axis and sticking to the more traditional three). Obviously we are all aware of the upward/downward axis in which keys (basically) move- although it's worth remembering that a key is technically the end of a very long lever, so even this is not strictly a perfect description. We also know that gravity acts along this path. However, here I'll be illustrating some of the benefit to movement and efficiency, that comes from adding greater focus to what also occurs within the forward/backward axis (i.e. directly forwards towards the piano or backwards and away from the piano, from a regular seated position). Obviously there is also the third axis of motion- the sideways line that runs from left to right (or vice versa). This too will prove to be of major importance- although it will not be brought so much into the picture until I have fully established the role of the first two.

Anyway, "That's all very boring" I hear you saying. "What's this got to do with playing the piano- Steven bloody Hawking? I suppose you'll be harping on about black holes and parallel universes next?" Well, as I'll show you how to feel for yourself, the widely held intention to move the key in a perfectly downward path of motion can be HUGELY problematic- causing physical tensions, low efficiency of energy transfer, potentially damaging shock waves through sensitive joints and rather lumpy tone (the last two notably due to the thud that comes with landing the key so directly into the path of the key bed). At this point, to be entirely clear, let me stress that I'm NOT advocating slipping across the surface of the key. Quite the opposite. However, if you grab yourself a pencil (ready for a little experiment), later on I'll show you how to discover what level of significance actually lies within the backwards/forwards axis. If you can totally free yourself from the seemingly obvious assumption that you necessarily ought to aim a key straight down, that change to the rationale alone may very well cause you to experience improvements in the comfort of your playing and help to increment the depth of your tone (even though this is very much a preliminary element).

Anyway, before we get to any of the practical experiments, I'd like to establish a little more of the explanation as to why this is so important. Of course, the key itself goes (almost) directly downward. The problem lies in the fact that the body, the arm and rarely so much as the finger will ever be aligned anywhere near to being straight over the top of the keyboard! With optimal alignment, the sideways axis can virtually cease to be much of a practical issue (incidentally in the future I will go more into the precise nature of what actually defines the often mysterious nature of good alignment- for when you fail to find good alignment, forces within the sideways axis DO tend to arise as major cause of compensatory muscular tensions or unpredictable movements). Anyway, conventional seated postures demand that we use forces that exist very significantly in the backwards/forwards axis. However,  Mitchell Zeidwig (when not too busy balancing a double bass on his chin whilst playing Liszt) found a rather interesting way to partially resolve this problem, if not necessarily the most practical one: 

See the actual performance here on youtube. Pretty remarkable stuff.

Anyway, we cannot afford to simplify to the point of supposing that moving the key is only about up/down forces and actions (be this specifically in the forefront of the conscious, or an underlying assumption that stems merely from casual observation). It just isn't possible to restrict everything to up/down forces alone. If you pretend it is, then the brain's mechanism of trying to simulate such a scenario is liable to turn free joints into fixed points in space- by using muscular efforts to FORCE them to stay still, as if locked in a vice. Without getting to the heart of this flawed mindset, some pianists cannot even tell that they are holding anything still! Rather than fix joints in place, we need to find a more sophisticated way to free them up- i.e. we need to embrace the reality of the backwards/forwards axis and cultivate better understanding of it. This is far more productive than willing yourself to relax, if you persist with a model for movements that mechanically NEEDS fixations to operate. Until you deal with it, the underlying mindset is inherently at odds with the possibility of achieving relaxation- in a contradiction that the subconscious is simply not likely to be up to resolving. Those who are sensitive to movement may (very rarely) be lucky enough to acquire the feel for the backward/forward axis entirely unconsciously- but it's far easier to make improvements when you can consciously steer away from erroneous simplifications in the very foundations of the intent.  

Anyway! The first exercise. I mentioned in the introduction that gravity is widely misunderstood. The misunderstanding is based upon these very same principles. Gravity is perfectly downward, yes. But we must understand that THE RESULT OF GRAVITY on a series of levers (e.g. A human arm) frequently is not! As soon as you talk about gravity causing sideways forces, some people will immediately give you a funny look. But think of the basic mechanics that go into in a gym machine such as this:

Just two pulleys translate the vertical force of gravity into an almost perfectly horizontal pull. Once the weights have been lifted, not only is the gravity trying to pull the weights back down, but it is trying to pull the handle on which the lifter has pulled back along the sideways path. So what REALLY happens when you have quite so many free joints as in a human arm? Well, let's see. Place your hand on the keys as if it to play but then collapse your palm flat onto a cluster of keys and relax your whole arm as much as possible, until it slides right off the keyboard.

"Great! Thanks for wasting my time, you frickin' schmuck!" you're probably thinking. Well, yes, this is a very standard exercise that has been used for years. I didn't claim otherwise. BUT!!!- now try again and this time seek to perceive what really goes on here. Feel your elbow this time. Which direction did gravity move it in? Straight down? Certainly not (assuming that you started with your shoulder nicely at ease). It primarily pulls your elbow backwards (yes, this is slightly simplified, before any pure physicists should protest, but the primary issue here is that the resultant PATH of the elbow is vastly more backwards than downward- the slightly more complex details being of no importance to the practical issue). Gravity seemingly acted sideways! Consider now- if you release weight in your arm, this backward pull is always present, not just the downward aspect! That is, unless you find a corresponding force to balance the backward element, by pulling you forwards.

Anyway, that's getting a little far ahead, so let's come back to the issue of  the elbow actually going backwards, without yet worrying about bringing in the notion of a force to prevent that. Without this practical observation, it is all too easy to fall into the trap of dwelling too heavily on the fact that gravity is a "downward force". Yes, it technically is, but because the resultant effects of gravity are not that simple, the association is deeply problematic. It means that the subconscious is highly liable to "correct" the movement- by using potentially unnecessary muscular contractions or fixations. If inaccurate surface assumptions are lodged in the mind (no matter how deeply in the unconscious parts) they really need to be corrected via the conscious. Then you can put yourself in a position to start feeling what truly goes on- and start to function without the underlying impediment. In order to have a chance of freeing yourself from the excess tensions that such seemingly minor misunderstandings can cause, to hope to will specific muscles into relaxation just isn't adequate. Long-term treatment begins with the source of the problem, not the immediate symptoms. First you must adjust the global overview that introduces the effort. So, the moral is thus:

Forget all preconceptions based around gravity being a downward force and start a clean slate. Downward motions and gravity are not inherently the same thing! Gravity's action is to be understood from that which you can OBSERVE and FEEL through awareness of what results from muscular release. Only by understanding gravity via acutely sensitive personal observations about its truest resultant effects (rather than via preconceived assumptions) can you even begin to truly understand its role.

It's all too easy to falsely think that the results of gravity are necessarily equatable to exact downward motions (despite the fact that it is channeled through so many joints that will greatly redirect it, unless fixations occur) . Drastically worse still, you might even end up thinking the reverse- that actively exerting a downwards force equals using gravity. This evidently occurs in the demonstration within the Taubmann octave film about supposed "free fall" into octaves. In such cases, what is supposed to result from release of effort results in added effort (frequently while simultaneously wasting some of this effort to offset the ongoing action of opposing muscles that simply needed to let go)! You have to start from releases and observe the movement that results- ideally with at least as much attention on the less obvious backwards/forwards as on the up/down. Only then can you be in any position to integrate gravitational effects with sensitivity, instead of by fighting with generic seizures. In the near future, I'll also be introducing the forces that the key sends back at you with regard to Newton's 2nd law. When you move in a directly downward path, the tensions that you are likely to be involving (simply to achieve such a path) don't make terribly good cushions against the massive force that the single axis of motion will cause you to contact head on!

Anyway, while this is all very important to consider, it's still very much preliminary. If you're thinking "that was just a big psychological dung heap- where's the meat, Pedro?" then I'd urge you to wait until I get onto the more specific applications that will rapidly start to follow on. Right now, it's about time we put this thinking into practice at an actual piano! So, have you got that pencil ready? Yep, that's right- we're still easing in at the shallow end, I'm afraid. You're going to use the pencil to play for now, not your fingers- but this should actually give a clearer illustration. Before looking at bringing in the hands and arms, I want to illustrate (or rather, prod you into figuring out for yourself) what an exceedingly direct application the forward/backward issue really has to even a single note. Anyway, here goes:

Grab yourself a long pencil and hold it horizontally across a key (just touching the key with the end of the pencil) like so:

and depress- looking for efficiency and quality of contact. Can you make a big sound with ease and comfort (after all, even here, there's a lot of "technique" to how you move)? You're looking for maximum tone and maximum feeling of "connecting" throughout the whole path- but also for an effortless sense of absorbing the spare energy, upon reaching the key bed.

So, which direction did you aim it in? What? You aimed it straight down? What the hell do think you are playing at? Did you pay attention at all- or have you been too busy picking your nose and scratching your bum? Anyway, to be serious again- it really doesn't matter too greatly what you did, the first time around. Let's try a whole variety of different ways of moving. Even deliberately include the straight down approach as one of them. You need to feel for yourself how the different paths effect different possibilities.

Did you aim the whole pencil in a single path? Or did you find it more efficient to lower/raise the end of the pencil you are holding? As in:

or:

Did you aim a single, consistently directed force, or did it change direction at all? What happens if the pencil slides along the key? Conversely can you make sure that it contacts the same spot, while applying notable levels of forward pushes, or backwards pulls? Experiment to see how just much of a backward or forward feel  you can do without slipping and glancing along the key. Then experiment with reducing it again, to see how much or how little seems to help the most. Remember though above all- no coming down straight over the top like this:

Even Zeidwig comes at the keys with a large horizontal element to his fingers. We have to look at coming from a place that involves at least some kind of horizontal element for this to be relevant to normal playing. As long as you do so, feel free to aim the force in any direction you wish.

So, which direction did you actually have to exert the force in, for the most efficient transfer of energy? Oh, and once you feel that you've found the efficient way, why not try some of the alternatives, purely for observational purposes? Actually, go ahead and start with the vertical pencil now, even, to see what a very pure single axis motion is like. Try all angles. Even introduce some sideways forces, if you wish. You can go into all three axes.

Anyway, I'm going to leave it there for now, but hopefully that will already have provided plenty to think about- if you've done some decent experimenting. If you didn't bother with the experiment, then just what the heck did you hope to learn- from plowing through all of those words but then not engaging in any kind of explorations? The idea of this is for you to teach yourself something. That can't come through the rational element alone- if you don't work at channeling the understanding directly into something that relates to the nature of movement.

In my next post, I'll continue a little more about the idea of axes and introduce planes (which are 2 dimensional versions, based on two axes), as well as the idea of levers- particularly with reference to the results of the pencil experiment. I'll also be looking more into some of the mechanical reasons as to why some types of movements will have been felt to be highly efficient, whereas some others are inherently wasteful of energy- all of which will soon start to lead into the specific implications for regular playing.