Flights of Fancy

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[R.A. Robertson]

The legendary Taoist sage Chuang Tsu once famously observed a school of fish swimming in a pool. His remark, "They are happy" led to a discourse about the nature of knowing and identity. I wonder though, if he might have seen something revelatory about the dynamic of their swirling, schooling action. Perhaps his statement was less of an anthropomorphic projection than an insight into a complex harmony of being.

Twenty three centuries later, a man named Craig Reynolds looked at a flock of birds and began to speculate on the driving force behind the amorphous yet oddly cohesive congregation. Was there a leader, some sort of centralized steering mechanism, or were decisions somehow distributed?

In 1986, Reynolds produced a computer simulation of birds flocking and presented a paper on the subject the following year. The goal was not to discover what goes on in the brains of real birds, but to find out if a small set of rules could accurately model flocking behavior.

He called his result "boids" (as in "android," only "bird-oid"). He formulated three simple rules which would account for not only flocking behaviors, but also herding, schooling, swarming, and human crowding. A couple of updated variations on this idea can be seen here <http://www.youtube.com/watch?v=xM9DHHBqBCk&feature=related> and here <http://www.youtube.com/watch?v=rLBrK0K-Ny8&feature=related>.

The three rules internal to flocking simulation are defined by Reynolds as:

Cohesion
Separation
Alignment

Additional rules can be added to simulate environmental factors such as terrain, obstacles, predators, and attractor points; as well as resting (roosting) behavior, and so on. But for our purposes it suffices in the beginning to concentrate on the fundamental three rules. (Note that it is assumed that each agent is in motion.)

Cohesionrefers to an individual agent's tendency to move toward an average location with nearby flock-mates. In other words, a boid will not stray too far from at least a few of its companions.

Separationis the boid's way of steering so as not to collide with or crowd the other boids. Each agent tries to maintain a "body space," and to respect that of others.

Alignmentmeans that each boid monitors the trajectory of those around it, and generally steers towards the averaged vectors.

The first two rules comprise what I like to term a "Goldilocks Zone." In this case, "not too far, not too close." A programmer can set thresholds to determine how spacious that zone can be.

The third rule suggests that it's necessary to "go with the flow." That may be the case, but if the other two rules allow for a wide zone, there can be ample freedom to explore many directions. It could just as well be said "don't go against the flow." This is a subtle but important difference.

To repeat, we cannot know if this is the algorithm that real animals follow. The significance of this work is to show that an extremely small rule set is sufficient to result in complex, rich systems. No central intelligence is necessary to govern the collective, nor do individuals need to follow complicated laws.

Without a doubt, each rule does require a certain amount of programming -- levels of complexity are abstracted and encapsulated. Awareness of surroundings must be built in, multiple headings must be monitored, and decisions must be updated continuously as the system evolves. Even so, the computational requirement for each individual agent is not large. This is true whether the subject is an ant or a pixel on a screen.

Flocking behavior is directly relevant to aikido and can be an interesting thing to explore in the dojo. It works best if there is a sufficiently large group, but as few as eight people in a medium-sized space can work. Instruct the participants to do their best to keep moving at all times, but not to come within an arm's length of any other person (or obstacle or boundary). They should feel free to go anywhere they like, but should not venture further than say. three arm-lengths from their nearest neighbors. To work well, everyone should agree not to attempt to steer the whole group.

This is a fun thing to do in a children's class, and is a great way to discover a lot about the different personalities within the group. A few may try to sabotage the rest, and a few may try to dictate. There are lessons to be gained even here.

But if everyone follows the rules, at least most of the time, the results are instructive. Rules must be obeyed for the system to work. But these rules are hardly Draconian, and when they work, they work as well for the individuals as well as the group. Everyone has tremendous freedom. No one gets hurt.

Note that with larger populations in more spacious settings, it's perfectly natural for some groups to split off from the larger group. As long as every individual agent has a few other agents nearby (or maybe even just one), then no rules are broken. As the total system continues to unfold, the separate groups may reintegrate at any time, even as new sub-groups are formed. Merry meet, merry part, and merry meet again!

Exploring crowd-flocking this way is certainly good self-defense, and the implications are many. But leave it at that, and you've missed the real fun.

The most interesting application of flocking behavior is revealed when we apply it to just two people. How can this be? Two people cannot make up a flock... or can they? If we let our various anatomical parts behave as boids, then we have a whole new approach to aikido.

Hands, elbows, shoulders, hips, knees, feet, and head. Depending on how you count, that's up to 26 boids in a two-person system.

Let's see how it can work. Begin by stipulating that any body part can move freely toward any open space. Now let's apply our three rules.

Cohesion
Some of our boids are stuck together and there's nothing they can do about it. Your right hand will always (we hope!) stay the same distance from your right elbow. Notwithstanding, all boids can move in such a way as to potentially connect or collide with other boids. So what rule should we specify for our aiki-cohesion? Hold that thought, because we're going to answer it with another rule in just a minute. For now, let's just say that at least one boid must stay within a few inches of at least one of the other person's boids, or else we have no game on (although from the larger perspective it's perfectly fine for the two "flocks" to go their own separate ways).

Separation
This one is simple in concept, challenging in execution. All boids must make room for all other boids. How much room? A few inches may suffice, but it's crucial to always avoid collision.

Alignment
Alignment is the key to the other two. Here we get to be sophisticated programmers, and let the parameters of our Goldilocks Zone be a function of alignment. Boids must align their headings to approximate that of their neighbors. If a potential collision is detected, increase separation while continuing to adjust alignment. If alignment is sufficient, then cohesion may be increased even to the point of touching, so long as touch does not become colliding.

At this point, what we have is a really delightful improvisatory dance. There's nothing wrong with that, and I'd encourage you not to skip too quickly over this part of your training. Learn to move with your partner even as your partner moves with you.

But I mentioned earlier that we can add interest to our program by simulating other environmental factors. Let's do so now. Let one person's boids serve as predators, obstacles, hazards, and boundaries. In other words, turn off all or some of their collision-avoidance protocols. Now the remaining individual must continue their regular flocking behavior, but with the addition of an evasion protocol.

In theory this shouldn't require much to change, because avoidance is just a special instance of separation and alignment routines. In practice, the presence of hostile or immovable boids signifies a few degrees loss of freedom. Further, since our human-boid system has kinematic constraints (viz. our skeletal system) we cannot behave as cloud-like as a flock, a swarm, a school, or a herd.

Nonetheless, the closer we can come to it, the better our aikido will be.

What all this implies is that our body, acting alone, is not wholly unlike a flock. The various moving parts have their own degrees of freedom and range of motion.. All is well as long as they generally tend to stay within that range, and do not collide with their neighbor boids. We walk without tripping on our own two feet. We sit, hopefully, without mashing one vertebra into another. (The difference, of course, is that the body is largely centrally governed.)

When it comes to our relationship with our environment, we must extend the coherence of our body-flock with the world around us. Separation keeps us from running into things. Cohesion keeps us connected and informed. Alignment facilitates efficient action and informs optimal proximity.

Further, because we can communicate, we can enhance awareness within ourselves and with others:

You're crowding me ("Squawk!")
You're too far from me ("Squawk!)
Why are you going that way when I'm going this way? (Squawk squawk!!)

There is danger in this additional layer of complexity in that it can lead to attempts at control over neighboring boids, if not the whole flock. The temptation is to say, "I'm going wherever I want, you'd better get out of my way or line up behind me!"

Probably simulations could be coded to show how that can work also. And lest you think this is turning into a Libertarian manifesto, let me assert that I think that kind of pecking hierarchyshould be modeled. (In fact, see <http://www.red3d.com/cwr/steer/LeaderFollow.html >.)Without some centralized coordination of effort, humans so far have not demonstrated great aptitude when it comes to things like putting out a house fire, or responding to an earthquake. We need skilled leaders and skilled followers, and aikidomust include this as an integral part of its discipline.

Still, the topic at hand is to show that flocking behaviors may suffice for the vast majority of daily living, and can go a long way even toward personal self-defense. In most situations, we have far more freedom than we imagine. Unfortunately it can be very difficult to intuit how rules, which by definition are agents of constraint, can liberate.

Yet there it is. A very few simple rules, when followed freely and voluntarily, can establish greater latitude and promote general welfare for all individualsand the social groups they inhabit.

So, I have strayed far. It's time for me to return toward the center... When Chuang Tsu remarked on the happiness of fish, he may have meant something different than the interpretation of traditional commentaries.

He may have been saying "Happiness is so simple it can be described in the most elegant of terms. Happiness is so pervasive that it can even be learned in the schools of the fishes."

10/27/10
Ross Robertson
Still Point Aikido Systems
Honmatsu Aikido
Austin TX, USA
www.stillpointaikido.com (http://www.stillpointaikido.com/)

[Abasan]

Nice... its given me a good idea for 3 games suitable for children and adults too.

[graham christian]

Interesting. The three rules sound like maintaining Ma-ai to me.

Thanks.G..

[dps]

What you have described is Harmony.
Going with the flow is less stressful than going it alone.
There is less decision making, less worry about the decisions made.
Chuang Tsu knew the fish were happy because they were swimming in harmony.

dps

[R.A. Robertson]

Interesting. The three rules sound like maintaining Ma-ai to me.


Nice insight. I hadn't thought of it that way, but it's obvious now that you point it out.

Ma-ai is frequently taught as the proper space between the players in the system, but the more sophisticated view is to look at how all the parts fit together. All elements in the system have to fit together in their proper space. There is much more freedom than this description makes it sound, as the only restriction is not to collide.

If we can learn to prevent our own body parts from colliding with each other, that's a good basis for learning not to allow collisions with others.

In turn, this provides a nice model for avoiding collisions of thought and emotion.

[R.A. Robertson]

What you have described is Harmony.
Going with the flow is less stressful than going it alone.
There is less decision making, less worry about the decisions made.
Chuang Tsu knew the fish were happy because they were swimming in harmony.

The risk, of course, is "groupthink," passivity, and lack of individual responsibility.

Real world examples of herds and schools and flocks sometimes do have more complex behaviors, like circling around the weak, sick, slow, or aged to protect against predators.

Basic flocking dynamics show how utterly simple are the essential requirements for coherent action within a group. But for more evolved systems, I think we'd like to build in some parameters for compassion and altruism, while still keeping the decision-tree as elegant as possible.