## Saturday, May 11, 2013

### the nature of chi and the value of imagination

Just glancing at the title above, you might think that I am about to take the position that chi is imaginary. Nothing could be further from the truth. In my view, chi is very real, but at a level of abstraction that would be intangible, were it not for the immense computational power of the cerebellum.

Understand that I'm not talking about symbolic computation, but something more comparable to what an analog computer does, performing accumulations and other transformations on combinations of inputs (usually either current or voltage levels) to produce outputs in a useful form. In the cerebellum, the inputs and outputs are patterns of neural activity, and the available transformations include rates of change.

In calculus, a rate of change is referred to as a derivative. An example commonly used in conveying the concept is the sequence: position, motion, and acceleration. Motion, being a rate of change in position, is its first derivative. Acceleration, being a rate of change in motion, is its first derivative, and the second derivative of position. The next step in this sequence is variously termed jerk, jolt, surge, or lurch. Jerk is the rate of change in acceleration, and therefore its first derivative. It is also the second derivative of motion and the third derivative of position.

Before getting into how this relates to the cerebellum and the subjective experience of chi, I need to introduce another set of concepts: mass, force, impulse, and momentum. Mass is like weight, and is in fact proportional to weight if gravity is held constant. Weight is the force exerted on a mass due to gravity, and in fact varies slightly from one location to another across Earth's surface, despite being measured using a constant mass. But force isn't limited to gravity. Electrical and magnetic fields can also exert force. So can flowing air or water, or the skin of one's fingertips when throwing a ball.

Momentum is the multiplicative product of mass and velocity (motion or rate of change in position). Velocities are produced by accelerations. Mechanical force is commonly defined as the multiplicative product of mass and acceleration, and impulse is the multiplicative product of force and time. If mass is held constant, force is proportional to the rate of change in velocity, which is to say that it is proportional to acceleration, and impulse (force x time) is proportional to the accumulation of change in velocity. With variable mass, force is the rate of change in momentum, and impulse is an accumulation of change in momentum.

The thing about impulse is that it is agnostic with respect to time. Time is factored out. A given impulse can represent a small force over a longish time or it can represent a strong force over a very short time. To fold this back into the above discussion of motion and its first and second derivatives, an impulse delivered as a small force over a longish time has a low jerk factor, whereas an equivalent impulse delivered as a high force over a short time has a high jerk factor – a sudden, sharp change in acceleration.

Jerk can result from a hard body part, like the skull, coming into contact with an unyielding surface, like a brick wall, or it can result from a coordinated explosion of neuro-muscular activity. Either way there is some potential for injury, and part of what the cerebellum does is to avoid dangerous extremes.

Now, to come full circle, I believe chi to be the subjective experience of momentum, force, and (most notably) impulse. Imagination figures in because the cerebellum will just as happily estimate these quantities for imaginary objects and fanciful circumstances as for real objects and circumstances – whatever is presented to it, so long as that presentation is vivid and convincing. Imagine yourself doing some difficult movement and your cerebellum will issue the instructions to perform it, the danger being that if you lack either the strength or the range of motion you may end up on the ground in a heap.

Imagination is seldom as convincing as reality, but it can still produce an effect on the cerebellum's output. Moreover, in some cases, as with the square root of minus one, the imaginary nature of what's presented to the cerebellum can factor out. For example, if you imagine passing a ball back and forth between your hands, the additional impulse needed to accelerate the imaginary ball results in your arms moving faster than they otherwise would, but by the time those forces are transmitted to your legs, there is no discernible difference between an imaginary ball and a real one. Another example, if you want to build strength for faster side-stepping, imagine that you are standing over the pivot of a teeter-tooter, having to push yourself up as well as sideways with every sideways step.

I rather like the effect of imagining the handling of a ball, about the size and mass of a volleyball, sometimes incorporating this into my practice, and, because I spent so much time doing so, it's relatively easy for me to imagine the handling of an end-weighted staff convincingly enough that I can practically feel its weight in my hands. I expect this is similar to arts, like Escrima, in which one starts out using sticks and then progresses to empty-hand.

Caveat: I have attributed neural activity which is distributed through other parts of the brain to the cerebellum as a simplification. It's true that the cerebellum plays a pivotal role in coordinating movement. That it does so in close cooperation with the brain stem and midbrain seems beyond the scope of the present purpose, although the reader may be interested in pursuing greater detail.

## Sunday, May 5, 2013

### on symmetry and long lines

Whether recirculating or reciprocating, exercises may be bilaterally (left/right) symmetrical, but aren't necessarily so. Exercises that are not bilaterally symmetrical should be performed on both sides (both mirror-image versions) to approximately the same degree.

There are other symmetries, which can usually be described in terms of rotation, either circular movements or the twisting of a hand, foot, shoulder, or hip to its limit. Circular movements are generally reversible and should usually be performed in both directions. Twisting may also be reversed, although doing so usually causes the original motion to become awkward and in need of other modifications if it is to continue to flow smoothly.

Gently oscillating between opposite twists is a fine, and a good way to familiarize yourself with the limits of movement, but doing so can quickly become boring. It helps to combine joints, for instance rotating one hand as far as you can, twisting shoulder, forearm, and wrist all in the same direction, perhaps twisting the other hand at the same time, either in the same direction or in the opposite direction.

By combining arm/hand and leg/foot twisting together, you will discover that there are stress lines, like rubber bands pulled tight, which you could trace through muscles and tendons, extending continuously from toe to fingertip. These are not the meridians of Chinese medicine, but a chain of tissues that are all being stretched at the same time. You'll also find that the second step in reversing the twisting motion (after relaxing the muscles that put you into a twist in the first place) is to contract all of the muscles along that chain, and that if you continue to do so the result will be an approximately opposite twist.

These long lines, composed of chains of muscle and tendon, when uniformly stretched and developed, are capable of generating movement that is both graceful and powerful, because it involves the entire body.

## Thursday, May 2, 2013

### walls and the cerebellum

A wall is something that stops you, anything that stops you.

If you overdo exercise, exhaustion and soreness can become a wall.

If you do your exercises mechanically, the same way every time, boredom can become a wall.

In the context of the martial arts, if you concern yourself overmuch with application – how effectively a sequence of movements might be applied in combat – or with precise form and maximal dynamism, you may find that you've walled yourself off from all of the various possibilities that can be present at each step, in a more playful approach. And, too, there's legitimate reason for concern that practicing in a violent manner can make one more likely to participate in or even initiate violence, and less apt to take the opportunity to avoid a needless fight.

Similarly, I'm finding that the effort to accurately describe something that is never exactly the same, should never be exactly the same from one moment to the next, can become a wall, both to the work of description and to the practice.

On the other hand, there are still a few ideas that I have yet to touch on, the theory that I mentioned in the original post on this blog.

You already have the basics, stances (with particular attention to positioning of the knee) and recirculating arm motions supported by subtle alterations of those stances (reciprocating motions when exploring cusps), and a small collection of principles to act as a guidebook. While I prefer not to constrain your imagination with respect to what motions you might wish to include in your repertoire, I hope and intend to fill out that guidebook.

Reach to the back of your head and find the little bump at the top of your neck. On the inside of your skull, most of the tissue within a couple inches of that point is contained in the cerebellum. The cerebellum is fundamentally an integration machine. (Integration, along with differentiation, form the basis of calculus. Integration is essentially the accumulation of an effect as the factors creating that effect also change.) The cerebellum measures the effect of various and varying forces upon momentum, your momentum or that of something you handle, throw, or sense remotely. It also makes predictions about the effects of forces that haven't yet occurred. And it does all this incredibly fast, but it needs experience upon which to base what it does.

Along with stretching, strengthening, and mild cardiovascular exercise, the main point of practice is to provide the cerebellum with some experience upon which to base its predictions. The more varied that experience, the better able it will be to handle something totally novel, something it has never had to deal with before. Also, the more diverse the range of situations with which it has learned to cope, the more gracefully it will be able to guide your motion under ordinary circumstances.

The upshot of this is that it is better to ferret out the essence of what your body wants to do today than to stress over whether you are performing some movement correctly. Protect your knees, find something soft to land on if you're doing something that may cause you to lose your balance, and otherwise allow your cerebellum sufficient license to explore variations on motions, even beyond the point of their becoming unrecognizable. Thus liberated, it will guide you well.

## Sunday, February 17, 2013

### incremental variations & escalation, and cusps

To illustrate the concept of incremental variations, let's also introduce a new exercise.

Beginning with your feet positioned about 1.5 shoulder-widths apart, toes pointed just to the outside of straight ahead (about 15°) and knees slightly bent, upper arms hanging loosely at your sides, elbows bent so that your forearms extend in front of you, parallel to the ground, palms facing towards each other, and hands level but otherwise limp, rotate your left forearm so that your left palm points down, even slightly outward if you can do so without pain, and move your right hand across in front of you until it is above your left hand.

Rotate your body slightly to the left, also shifting your weight slightly to the left, and allow your right heel to move slightly outward (to the right) while you slowly push another inch or two to the left with both hands, right above left.

Now, in one motion, pull your right hand towards your body and then down, brushing the inside of your left elbow with you right fingertips, begin to rotate your left hand back towards the palm-inward position, pull your right heel back to its original position, and turn your body back towards facing straight ahead, re-centering your weight.

Now to the right, sweeping your right hand slowly to the right, rotating it down and outward, and move your left hand to the right a little faster, so that it catches up with the right hand, left over right, turning your body slightly to the right and shifting your weight to the right, while allowing your left heel to move slightly outward (to the left). Push both hands an inch or two past your right elbow.

Pull your left hand towards your body and down, brushing the inside of your right elbow and then rotating down and outwards as it moves in front of your body to the left, with the right hand rotating back to the palm-inward position as it also moves in front of your body, rising above the left hand as it catches up with it. Meanwhile, pull your left heel back in, rotate your body and shift your weight to the left, and allow your right heel to move slightly outward.

Now begin to spread your hands further apart vertically as they reach the outer limits of their movements, so they at first make larger circles, then sweeping arcs, then even larger sweeping arcs. Try to do this stepwise, so that each iteration is slightly more expansive than the last but it takes at least twenty repetitions to move from the petite version of the exercise to the most extensive.

(As you become more accustomed to this, and as you gain strength and flexibility, you'll find yourself reaching further to the outside, bending your knees more deeply, and shifting more of your weight.)

There is a point in the escalation of this exercise beyond which it is impossible to maintain recirculating motion, necessarily reverting to reciprocation, because one hand is reaching so high and the other so low (and/or so far behind your back) that they are both exploring corners (cusps), through which no smooth paths exist in your freedom of movement. Go ahead and explore these cusps, when you reach sufficient flexibility to do so, but don't forget to take your time getting to them by very gradually escalating the extension of the movement up to the limit of recirculation, and also be careful not to throw yourself into those cusps more vigorously than your muscles and tendons can handle. By their very nature, cusps limit your options, so be alert to the possibility that you might lose your balance while in an extreme position from which there is only one direction of retreat and go at it carefully.

Henceforth I will use "reciprocating" to mean movement into and out from a cusp, and "recirculating" to mean a flowing sequence of movements that is free of cusps.

This exercise, rather than the first, is the foundation of my practice, and it has more variations than the one already described. I'll get into those in a future installment.

## Sunday, January 6, 2013

### “reciprocating” vs. “recirculating”

I have, until now, referred to the exercises that constitute my practice as “reciprocating”, but that really only applies to a small subset, those involving motion reversal, as though a short video were being played first forward, then backward, then forward, then backward again. Examined in fine detail, this is almost never the case; there is nearly always something which distinguishes the ‘return’ portion (when there is one) of a sequence of motions from being a true reversal. So, in nearly every case, the word “recirculating” is a better descriptor. Likewise, “cycle” is preferable to “sequence”. I will endeavor to use these more descriptive terms in the future.

To put a finer point on this, you might wish to abort a movement, in practice if you find that you are about to overstrain a joint or the muscles connected to it, or in application if you realize that what you'd begun to do stands little chance of working out as you'd hoped and is likely to get you into further trouble. But even aborting and backing out of a movement is not the same as reversing it. The impulse (force X time) that brings the initial motion to a stop and that which launches the backing away motion both point in the same direction, back. They are not mirror images of each other. What is actually happening is that you have initiated a new plan that has initial conditions (position and motion) which are very different from the one that came before it.

Exercises which are equally well described as “sequences” and “reciprocating” as “cycles” and “recirculating” are possible, but they tend to be less interesting (and less useful) than those that are better described by the latter terms. Still, they add some variety to the mix.

## Tuesday, January 1, 2013

### chewing gum while walking: involving the hands

First allow me to apologize, for having succumbed to the temptation to idealize form, in the reciprocating exercise described in the previous few posts. The problem is that most of us can't maintain that 45° angle while shifting weight onto a foot, not without putting undue stress on the knee. Maintaining knee alignment being far more important than maintaining any arbitrary foot position, let's start by modifying the angles.

So, starting as before, with your feet spread about 1.5 times the distance between your shoulders, toes turned outward comfortably, but not more than 45°, shift your weight onto one foot (it really doesn't matter which you start with), removing weight from the other foot. When the unweighted foot becomes light enough to pick up or slide, pull the toes in so they are only turned out about 15° from straight ahead.

Now begin to shift weight onto this foot until the other (the one you first place weight on) is light enough to pick up or slide, and point it directly away from the hip joint that connects it to your torso, so that hip, knee, ankle, and the ball of the foot are all aligned in a vertical plane.

Next, begin to move your weight back towards your unweighted foot, and in the same moment rotate that foot so that it is turned out about 15° from straight ahead, unweight the other foot and point it directly away from its hip, with the hip, knee, angle, and ball of the foot aligned in a vertical plane, as above.

Repeat, seeking the foot placement that results in no net movement, neither forward nor backward.

Now add the lead-with-the-eyes aspect back in. As you come to rest with nearly all of your weight on one foot and the other pointing straight away, imagine a soft shuffling noise coming from behind the ear on the side bearing your weight, turn your eyes towards the noise, allow your head to follow, and rotate your unweighted foot as you begin to shift your weight onto it.

Repeat until you are comfortable with this much.

Now, while at the end of a weight-shift, before beginning the next, raise the hand on the unweighted side with the fingers held straight and vertical, until the tops of the fingers are at eye level, palm turned half outward, with your forearm extended at about 30° from vertical, and pull the elbow in so that it's as close to your ribcage as you can comfortably place it. Place the other hand so that its fingertips are lightly touching the inside of your extended elbow, with its palm cupped and turned downward.

Lead with the eyes as before, then, in one motion, begin the rotation of your unweighted foot, begin moving your weight towards it, and move the hand that was touching the other elbow, first behind that elbow, then beneath it, then wiping along the arm towards the wrist, leading with the index finger. While this is happening, your weight is shifting and your arms are crossing in front of you, with the one that had been extended on the inside.

Properly coordinated, your head finishes its rotation and the foot from which you were removing weight becomes light enough to lift or slide at the same moment that the hand wiping along the other arm reaches the wrist, at which point both foot and hand rotate, the foot to pointing directly away from the hip and the hand that was doing the wiping motion into palm half-outward, fingers vertical, forearm partially extended. At the same time the other hand (on the side that your weight has shifted to) sinks to touch the elbow of your extended arm.

Continue to work on this until the two directional shifts (shifting weight left-to-right and right-to-left, while extending the arm opposite the weight-bearing leg) become mirror images of each other. Then begin to think about how to make each flow into the other so that they become a single movement. That is the real nature of a reciprocating exercise.

## Saturday, November 10, 2012

### a firm foundation: involving the torso

Until now I haven't said anything about what to do with your arms. There are a couple of reasons for this. First and foremost, up until now it really hasn't mattered what you did with your arms, other than to have them ready to catch you if you suddenly felt an overwhelming need to escape from a painful position. But there is another reason, which is that once the arms become involved it's all too easy to let them take precedence over the legs, which would be an unfortunate mistake.

However the time has come to move a little higher, involving the hips and shoulders, and everything in between. For now I'm going to suggest that you put your hands on you hips to keep your arms from flopping around and making a general nuisance of themselves.

At the end of the last installment we were rocking back and forth, side-to-side, moving our weight almost but not quite entirely from one foot to the other. Now we're going to add some rotation around a vertical axis, from about 45º to one side to about 45º to the other side, for a total rotation of about 90º. The axis in question is the vertical line passing through the top center of your skull, and also through the center of your tailbone. You are going to pivot your upper body around this axis.