# Control Theory of Taiji

In Chapter 19 of There Are No Secrets author Wolfe Lowenthal comments that T'ai Chi "... is the subduing of the will to achieve understanding of softness, so that a slight, 75-year-old man, completely relaxed, can with a touch send a 250-lb. Judo champion flying." How in the world could such a thing happen, within the laws of physics?

An idea to pursue: model a person as a system, with sensors and actuators and time-delays. The sensors are the nerves and the brain; the actuators are the muscles; the time-delays are set by reflex and reaction lags. What is the simplest "interesting" such model? In "Artificial Wrestling: A Dynamical Formulation of Autonomous Agents Fighting in a Coupled Inverted Pendula Framework" Yoshida, Matsumoto, and Matsue propose what seems to be a far-too-complex system with multiple springs, controllers, actuators, sensors, and time delays.

Perhaps greater insight could come from something more primitive? Consider, for example, a single inverted solid-bar pendulum. A person is rather like a stick standing upright, kept from falling by small muscle movements that are controlled with a short time-delay based on inner-ear and other sensory inputs. If somebody could perturb that simple feedback-loop, maybe by applying a small force but on timescales shorter than the reaction time, could the system be driven into instability so the stick-person would fall down?

If so, what are the order-of-magnitude scales of the perturbing force and time, and how are they related? If, for instance, you react 50% faster than your opponent, do you only need 10% as much force to win a fight? What if you're ten times faster? What if you can only exert 1% of the other person's pressure? And what are the limitations of this approach? Surely a gnat can't derail a locomotive. But on the other hand, if all of the opposition's punches miss you, and you add an appropriate nudge a when a violent swing has just missed ... hmmmmm?!

(cf. The Complex Mathematics of Robot Wrestling" in MIT Technology Review June 2014) - ^z - 2014-07-23