Attractor Stability in Game-Based Learning

Imagine you’re teaching your club about ways to get to the other side of the opponent’s blade. You start with a simple constraint based exercise – one person extends, the other person takes the blade with a nice overbind out to one side, then the first person has to find a way to hit. Then you do a variety of games based on going under and around to the other side, like Falling Upon. You’ll probably see most people doing quite nice disengages (under the hilt) pretty quickly, so time to move onto and teach the coupé (over the point) as well. But then you run into a problem – you’re doing new games that allow fencers to go under or over the blade, but everyone is still just going under it.

This is an example of the phenomenon I call “attractor stability”, after motor learning research into gait patterns. The classic example is the transition between walking and running1: when you put someone on a treadmill and slowly increase the speed, they will first tend to use a “walking” gait. Then as the speed continues to increase, there will be some critical speed S1 where they transition to “running”. These are the two main attractors for human bipedal locomotion. But when you reduce the speed again after they’ve transitioned to running, there is a second critical speed S2 where they transition back to walking – and S2 is slower than S1. This means that there’s a middle zone of speeds where both gait patterns are viable, and the gait that a person adopts will generally depend on whether they reach that speed by speeding up from comfortable walking, or slowing down from comfortable running.

This phenomenon is seen in many fields: physics calls it “hysteresis” and uses it to refer to systems where there is a lag between input and output2. In the social sciences, a similar concept is “path dependence”, referring to how the way in which a situation was reached can constrain the types of actions people take in that situation. In fencing we can see it when people find an initial movement solution and then continue to use variations of it as they encounter new problems, often pushing beyond the point when a completely new motor pattern would be better. This is a major part of the local maximum problem Nathan outlines in his article When Games Go Wrong.

Having understood the problem, we can look back at the running example to get an idea of a viable solution: instead of creating new problems to which the previous solution is still somewhat possible, we create new problems where the previous solution is entirely impossible. Then they are forced to adapt by finding a new motor pattern. Once you’ve done this, you can move back to the “middle ground” exercises that admit either motor pattern as a solution.

  1. See Magill et al, Motor Learning and Control, 12th ed., p169 ↩︎
  2. Physics also has a related concept of “path dependence” which is more directly analogous to the social sciences example, but hysteresis is the one I’m more familiar with. ↩︎