Analytic Martial Arts

Wednesday, October 31, 2007

A Preliminary Proposal For A System of Martial Arts Notation

It's been quiet over here recently, but I'm still around. I'm occupied trying to identify martial arts families as discussed in my previous post. I suspect that's going to take awhile, so to keep you all entertained I'll throw out a related idea I've been mulling over: martial arts notation.

I've been reading through some of the MA books in my collection and realizing that, when they discuss techniques and forms, its oftentimes difficult to figure out exactly what's going on. Its awkward to describe simultaneous action in English in any sort of a concise way, let alone convey the rhythm of a technique. For example, one form I know involves jumping, executing a punch and a kick, then landing in a specific stance while executing another hand strike. That description of a single, fluid movement is long enough, but if I were to add the additional verbiage to let you know what kind of punch, kick, strike, and stance, and their relative timings, the description would quickly become difficult to understand.

A lot of books use pictures to illustrate techniques, which can be an improvement, especially when augmented with text descriptions. But pictures have some inherent limitations:

  • They're not compact: The pictures necessary to illustrate a single technique can take up an entire page; illustrating an entire form can take many pages. Especially in the case of forms it becomes difficult to present a holistic overview.
  • Photos require cameras: If I want to illustrate a particular technique I need to have the forethought to take pictures, get them developed, and then have them easily accessible. Which is fine if you are putting together a book or a magazine article, but complicates ad hoc writing. An obvious alternative is to use drawings instead of photos. You lose some information in the process, but whether that's a substantial concern is up for debate. The bigger challenge is what to do if you have limited artistic talent.
  • Pictures, be they photos or drawings, are captures moments of time. There's an unseen transition between any two pictures; sometimes the transition is important, but underdetermined by the pictures (more on that later). You can always add more pictures in an effort to determine the transition, but then you start running into the "compactness" issue already mentioned.

What I'm searching for is an alternative to words, picture sequences, or both. Such an alternative should be:

  • Compact: The space required to illustrate a technique or form should be minimized.
  • Easy to use: Whatever notation is chosen it should be easy to read and write, even for the artistically challenged.
  • Generic: It should be able to describe a wide variety of practices rather than being tied to a particular art.
Those are the absolute, bare minimum requirements. A truly useful system will also:
  • Capture motion accurately: It should provide some way to describe the transitions between pictures.
  • Provide timing information: It will show not only what happens, but will also give the reader at least a basic sense of the rhythym of the form/technique as well.
  • Provide a "birds eye view": It would be very useful if the reader could, at a glance, get a general sense of what's going on in the technique/form as a whole.
  • Make comparisons easy: Since this is a blog about comparative martial arts, it would be nice to have a medium by which to perform comparisons. I would like to be able to look at the notation for two techniques side-by-side and immediately pick out the similarities and differences between the two.

The martial arts, at least in terms of choreography, resemble both music and computer animation. I unsure if this is an original insight on my part, but I've not run across the analogy elsewhere, so I'll elaborate a bit. A form/technique is a sequence of events which transpires in a pre-determined, chronological order. Anyone who's done computer animation work can see the similarities; computer animations are programmed as events/motions unfolding with respect to time, a lot like a kata. Like music, a form involves multiple instruments (hands, feet, etc.) which operate independently but work together in a common endeavor. These ides pre-date the rest of the material below; the music/animation connection first occurred to me in 2000/2001 when I was trying to design a computer-based instruction system for teaching martial arts. So, if what follows looks like sheet music or keyframe animation, its not a coincidence.

Now I'm going to work through how I derived the basic ideas for this proposed notation systems in the hopes that others will call attention to where I've made a wrong turn or overlooked the obvious. I started by trying to characterize what I know as a "front ball kick", an elementary technique which is found in many arts. Being one of the "artistically challenged" myself I used stick figures to illustrate the motion: After doing so I made the following observations:

  1. The stick figure did a decent job of conveying the basics of the technique, but failed to convey some important nuance.
  2. Interpreting the sequence requires at least a basic understanding of martial arts. For example, figure is a horse stance; that's probably apparent to a casual practitioner, but not evident to the uninitiated.
  3. The stick figure is more comprehensible that an English description, but more compact than full-fledged drawings/photos. It's still probably to "verbose" for forms.
  4. There's a lot of redundancy; only one leg moves, but the position of all limbs is depicted repeatedly.
  5. The positions of the joints (the black dots) completely determine the configuration of each figure.
  6. The transitions between figures 2, 3, and 4 aren't capture well.
  7. Neither the striking surface nor the direction of the applied force are obvious from the figures.
These observations, in turn, merited the following responses:

Item 1: That the stick figures convey at least a general sense of the technique means that this isn't a totally fruitless avenue of exploration.

Item 2: It's OK if the notation is opaque to non-practitioners; the whole idea of an MA notation will only be of interest to people with a pre-existing MA background. At a more fundamental level the difficulties in interpretation are caused by projecting events occurring in 3D space onto a 2D surface. If it becomes necessary to disambiguate such a sequence it's always possible to present multiple elevations simultaneously: Such disambiguation will often be unnecessary; the action in the hidden dimension will be obvious. As a general rule, though, finding a way to concisely render 3D motion in 2D is going to be important.

Item 3: It may be necessary to have a couple different type of notation: a "detailed" notation for demonstrating specific techniques and a "concise" notation for sequencing techniques.

Item 4: The stick figures should be reduced in some way; the notation should focus on changes in position. This will eliminate the redundancy and (hopefully) contribute to compactness, readability, and ease of use.

Item 5: In conjunction with Item 4, if the figures are going to be reduced in some fashion then what's left should focus on joint positioning.

Item 6: This is a biggie. For example, the sequence 2,3,4 makes it look like the kick delivery and return are symmetric, but in the version of the kick with which I am familiar such is not the case. Remember what I said earlier about transitions being important but underdetermined? Some transitions are essentially path independent; it doesn't matter how you go from A → B as long as you get there. The 3 → 4 transition is an example of such independence; if you make the transition efficiently then the minutia of how you get there is not terribly important. But the 2 → 3 transition is different; there is a very specific way to deliver the kick. Deviate from the prescribed motion and your kick is going to be, at best, ineffective.

Per Item 4 you can characterize a transition by describing how a joint moves in time. We'll concern ourselves with such descriptions shortly.

Item 7: A simple annotation can show striking surface, direction, and even magnitude of the force if we so desire:

Now we come to the point where I just started tinkering. The first thing I realized was that using the positions of the joints in space to describe a transition wasn't the best approach. Absolute positions aren't invariant under scaling and, more importantly, aren't terribly intuitive. Relative positions, at least in terms of Cartesian space, aren't much better, since it's still important ot know how the limb in question relates to the rest of the scene.

I realized that I shouldn't focus on Cartesian coordinates, but rather on joint angles. Angles are invariant under scaling and rotation, so the same description applies regardless of size or orientation. Once I came to this conclusion is was a matter of finding a clean notation to describe the joint angles. I tried a few approaches:

In this figure I've added an interim step and some arrows to indicate how things move. It's too cluttered; it's difficult to read the arrows overlying the joints. So I thought about removing the middle stick figure entirely: Still not particularly descriptive, but I feel like we're moving in the right direction. The use of the arrows to indicate the transition seems like it might have potential, but I'm not sure it tells us anything we don't know. We can tell that the joints must bend in a certain way just by looking at the before and after; what we need is relative timing information. So how about:

So what to make of this? This shows the relative timing of how the three joints should bend; everything starts at the same time, but you need to have your foot bent before impact or else you break your toes. To interpret this you need to assume that the top line represents the hip, the middle line represents the knee, and the bottom line represents the ankle. You also have to assume that we're talking about a leg. I believe that the above figure contains most of the information needed to correctly describe the kick, given the constraints of the figures preceding and following. But, for the sake of readability, I'd also like to add information detailing the direction and magnitude of the joint movement.

Most joints only hae one degree of freedom; they can either bend or straighten. Both motions are meaningful independent of the orientation of the joint/limb, so they're suited to our purpose. As far as magnitude, it seems simple enough to just use degrees. Combining these yields the following:

That seems readable enough. The top says "bend 90 degrees" while the bottom says "straighten 180 degrees". But I realized that a further refinement is possible if we can make assumptions about the default "bend" and the default "straighten". If we assume that "bends" are 90 degrees and "straightens" are 180 degrees (both measures absolute), then we can omit the angle descriptions entirely in these cases. Going back to our motivating example, a front ball kick can now be rendered as:

This figure describes the following:

  1. Start in horse stance.
  2. Make a standard transition from horse stance to crane stance.
  3. Deliver the kick. Drop the knee slightly and straighten the leg to 180 degrees. Bend the ankle to 90 degrees; this should be completed before the knee is completely straightened. The striking surface is the ball of the foot and the force of the blow should be directed straight forward.
  4. Make a standard transition to crane stance.
  5. Make a standard transition to horse stance.
The stick figure diagram is no worse, and quite possibly better, than the English description. It also has some advantages over a sequence of pictures in that its compact and describes the transition between 2 and 3 better.

Recall that we said earlier that we'd like the notation to focus on change; since the configuration of the upper body doesn't change it's only necessary to draw it once. We assume that if there's no notation indicating change then a given configuration remains the same throughout. In order to clarify which limbs are changing we'll divide our notation into an upper portion (above the waist) and a lower portion (below the waist). To disambiguate which leg is doing what we'll further subdivide the lower portion into left and right sections; ditto with the arms. So we end up with something which looks like a musical staff:

But how, then, do we use this to show a "horse stance"?

This is the point where we commit to developing a generic framework rather than a notation for a specific system. A horse stance is a known, static configuration, but the specifics of the stance will vary from system to system. So we need some way to define what we mean when we say "horse stance". This takes us back to stick figures:

We say that a "horse stance", alternatively represented by the glyph "H", is given by the above body configuration. This would be an example of the "detailed notation" I speculated about above. We can then render a horse stance as follows:

Since the horse stance involves both arms simultaneously we represent this fact by positioning the appropriate glyph on the midline dividing the left and right arm regions, an approach we also follow with the legs. Since both the upper and lower body are involved simultaneously we represent this fact by placing the horse stance glyph on the midline dividing the upper body and lower body regions. Assuming that we've defined crane stance by a glyph "C" we can now render the front ball kick as follows:

This is where I'm going to leave it for the time being; this is obviously a work in progress. Some areas for improvement are as follows:

  • Glyph placement: I like placing glyphs on a line to indicate that multiple limbs are involved in a motion, but doing so makes the glyph hard to read.
  • Detailed notation: Drawing the disembodied stick figure leg seems like an ugly hack.
  • Robustness: I know forms that would break this scheme easily. It will have to be expanded to include things like changes in direction, jumping and ducking, attacks delivered off the center line, etc.
I'll continue to tinker with notation as I write more on various topics.

1 comment:

Anonymous said...

There is an interesting discussion over at which might spur some ideas. I googled "fencing notation" and it was the first result. Also, the word "disambiguate" needs some disambiguation.