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Saturday, 20 November 2010

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. What the hell did you go and do that for, you bloody vandal? I suppose you're going to dump an old fridge in there while you're at it?

(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 spaced out rather widely. Ideally, the elbows should be aligned right behind your hands when you're at the inward point- so there's basically an angle of 90 degrees between your forearms and your upper arm. Feel plenty of space between the upper arm and the armpit as well- so you're very much coming at it from a wide angle. 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 problem (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.


  1. Thank you for the time you took to write this, the detail, and the readable style. I'm resigned to my puils staring at me as if I had 2 heads when I talk about this (they come to play the piano not learn biological mechanics...) so please be assured there is at least one person out here who appreciates your insight. Richard Thomas.

  2. It works. I just tried it. Thinking about both sides of the movement (pushing the wall vs being pushed away) makes a difference, the movement becomes smoother. So nice. Thank you very much for this, it's amazing. Works with a finger as well - when I notice that it BOTH pushes a surface and pushes my arm away - it becomes smoother. Wow!

  3. "Tactile feedback and timing accuracy in piano performance",
    Werner Goebl & Caroline Palmer, Exp Brain Res (2008) 186:471–479

    1. Thanks, looks like an interesting article. What particular points are you posting it in relation to though?