There is a great deal of geometry in sword play (and martial arts in general of course) - How slight changes in range occur from the straight to the angle, how tangential lines intersect circles only once, about the usage of arcs, cusps, half way points, and on and on.
Add human physiology and gravity to the equation, and you get the strong and weak angles, footwork, power, and options at any one moment ... which is really just Physics, and a natural segue into relative movement in time, through the 3 dimensions, momentum, still points and intersections etc etc.
Of course you add Psychology to the whole .... and thus you get your Tactics. Add the environment and the context .... and thus to Strategy.
Few days ago I was invited to a BJJ class.
I have to admit that BJJ, wrestling, and grappling arts in general, are not my thing ... don't know why, swords hold a huge appeal, rolling around on the floor does not. I guess it's like musical taste in that way, it just 'is'..... But it's always good to get out of your comfort zone and occasionally do something that is a 'gap' in your practice, so I went.
I was certainly curious to take this class because the teacher was a woman, a black belt, and with a few major competition wins to her credit. I also heard she was meticulous about accuracy and correct technique, much more concerned with the efficient use of natural body mechanics than winning through luck or size, and with no interest in 'wins' achieved through brute force.
That all seemed right up my alley, and I am very glad I went.
Jessi ran a great class. The students were mostly guys, but there were a couple women too. The warm ups were good, specific for the sport, and great exercise, and the techniques that we worked on were complicated (for me) but logical, and had a natural flow to them that was very satisfying.
I was really happy that all the potential counters were explored, connecting them to the WHY of how you held position (structure), and how you transitioned between positions, and how the 'WHY' translated into the reason the technique worked.
At one point, Rory's comments came to mind, about the idea of "Position before submission" being a 'Winner's strategy', and how the control, the lessening of options, has to increase from move to move, with no gaps, no mistakes. No chance for the chaos to increase.
My favorite part? When we were looking at the relative geometry between the opponents - the strong and the weak angles, the still points, the gravity and the physiology .... and Jessi said: " I call it Math with no numbers".
I can dig it :-)
She teaches Tuesdays and Thursdays at Soja Martial Arts in Oakland CA