Abstract: "We show that motion with as few as three degrees of freedom (for instance, a particle moving in a three-dimensional potential) can be equivalent to a Turing machine, and so be capable of universal computation. Such systems possess a type of unpredictability qualitatively stronger than that which has been previously discussed in the study of low-dimensional chaos: Even if the initial conditions are known exactly, virtually any question about their long-term dynamics is undecidable."
If you cut a body by a plane through its center of gravity you _do not_ necessarily have equal volumes on either side of the plane.
He didn't say you have equal volumes. He said you have equal masses.
Cutting a body through it's center of mass doesn't still doesn't necessarily leave equal masses on either side of the (hyper-)plane. The center of mass lets you ignore the distribution of mass as a function of position (density) for certain types of problems. This is not one of them. What you are saying is still trivial, still wrong, and still not the ham sandwich theorem.
Torque is cheap.