My views on the intersection of (chart overlap on the manifold between) the Tao of Jigokuraku and the Action of Hamilton (as filtered through the syllabus taught according to the Fédération Française d’Escrime):
- a swordsman's Dao/chi/posture is an open in phase space. (in particular, the traditional location of the dantien is suspiciously coincident with the centre of gravity[0])
- a duel is a system tensoring the chi of both participants.
- 戦場ではラグランジュ力学はその場で調達する
which together imply:
- the greater the chi, the higher the entropy, the more possible futures
- one should not look for eigenvectors of the participants alone, but the eigenvectors of their symmetric and antisymmetric combinations. in particular, one attempts to rotate in phase space so that one's control vector is greater than one's opponent's over distance/ma/{whatever this is in chinese}.
- "waves" in the Dao are phase evolutions in phase space. Mei says "strong, strong: no way — Tao: strong, weak" because (absent superhuman energy sources and musculoskeletal constraints) strong motions are necessarily low frequency and hence low entropy, while weak motions give access to the high frequency, high entropy[1] domain.
There's also an impedance notion in play, as mentioned in Jigokuraku: if you are too "strong"[2] you won't sense (« le sentiment du fer »[3,4]) your opponent's techniques, only their sword (and definitely not their spirit!). It takes dialing down far towards "weak"[5] to ascertain their spirit[6].
Around eps 9-10 of the anime, the humans in Jigokuraku begin to read the Tensen's Dao, but I think even earlier there's an occasion where Sagiri realises a Tensen is reading hers, and so (as I mentioned to you I've used profitably) she dials down her spirit, her intentions, so her Dao cannot betray her: no intent, no tells, no betrayal.
Similarly, the FFE teaches that you[7] should be surprised by your own attacks, finding yourself in media res with them already launched...
[0] when I was playing kid's football, they always told me to look at an opponent's belt buckle for the same reason: it's easy to throw fakes with arms and legs, but faking with the dantien is hideously energetically expensive.
[1] I was never a seriously competitive fencer, for whom pistol grips are de rigueur, so I tried to learn the french grip, and when it works it's beautiful because you can do things with the hand that you can't with a pistol grip. (this is partly a defense against time: you can have very satisfying bouts with older people by forgoing use of the legs, turning it into a contest of hand vs hand, where they remain very strong)
[2] I believe the former 3-dan All-Japan Champion's problem, in https://www.youtube.com/watch?v=0HPDAFqN74A , at 8-dan is exactly this: he is used to winning by overpowering the opponent, whereas at 8-dan the examiners want to see that you can shape the match: deliberately allowing, not opportunistically forcing, your opponent to make mistakes.
[3] consider also the notion of having a "round heart": too strong, and your heart is very ellipsoidal... (which ties in with controlling the system variables in phase space, not just your own)
[4] sentiment du fer is very interesting, because 24 frames per second fool the eye, and the ear doesn't notice 22+ kHz, but touch has way better temporal resolution
[5] like a good tango lead, a good epeeist should be feline: not snappy but stalking. Bonaparte is quoted as recommending: "while your opponent is making a mistake — don't interrupt them!"
[6] a former olympian once told me he believes that it's after people are on the piste (all in white and masked) that you see their character — instead of perceiving mostly what they portray, when standing around in street clothes. (the TV audience has a very different opinion; does inability of, or disinterest in, perceiving Dao correlate with them being on a couch, watching the bouts?)
[7] compare "me" and "not-me" from Island!