Invariants as Diagnostics

In traditional coaching, each movement is normally considered to have an ideal or platonic form, which represents the optimal way it should be executed. Deviation from this form is then an error to be corrected, or at best a variation in response to a specific context.

Obviously the ecological approach entirely rejects this framing, but that doesn’t mean there’s no concept of a “good” motor solution. Instead, I use the term “invariant” to describe a common characteristic of effective solutions to a given problem1. For example, two invariants of footwork for attacks are:

  • When lunging, the front heel will lift off the floor before the front toes.2
  • When doing a direct attack with a passing step, the hit will come as the feet cross or before.3

Both of these are near universal features of effective solutions to the problems in question. They will show up in fencers regardless of whether they’re explicitly coached to do them – in fact, modern fencing has inadvertently provided a clear example that they will show up despite coaching to do so, since the majority of fencing coaches instruct that the toes lift first.

Once we’ve identified such an invariant, the obvious temptation is to cue it for your students, perhaps using external cues. Sometimes this can help people come unstuck and get to a good solution much quicker. However, it’s not quite purely a good idea, because there’s always the risk that you’re wrong about a given invariant.

A good example of this is in thrusting attacks. My friend Tuomas from THMS observed some time ago that most thrust attacks follow a characteristic pattern where the point is first lifted well above the target area as the extension begins, and then “dropped” in as the extension finishes to hit. The temptation would be to cue this for every fencer, but he more recently observed while analysing recent footage from Helsinki Longsword Open that Antek Olbrychski does not generally follow this pattern – instead he lifts the left shoulder strongly and rotates more while driving directly to the target.

To solve this dilemma, change how you use invariants: instead of treating one as a coaching cue, treat it as a diagnostic of a potential issue. If you observe someone’s motor solution doesn’t use a feature that you considered an invariant, you can focus further on what they’re doing to try and understand whether it can be improved (perhaps through giving them a new and closely related problem or constraint).

  1. I’m not sure this is actually in common use. Another term which sees use is “attractor” – I avoid that because it can overlap with the idea of attractors as alternative motor patterns which an athlete switches between based on some environmental factor such as speed. ↩︎
  2. This is a matter of some controversy – fencing orthodoxy suggests that the toes lift up first. Sydney Sabre wrote an excellent blog post and accompanying video demonstrating the heel lift. ↩︎
  3. Stephen Cheney christened this the “ballistic passing step” pattern and explains it in more detail in this video. ↩︎