The vacuum is observed to be f(x) = f(-x) toward massless boson photons but trace f(x) = -f(-x) toward fermionic matter. Empirical failures of SUSY, neutrino-antineutrino reaction channel ratio, matter-antimatter abundance; string/M-theory, quantum gravitation, and dark matter are fundamental. Trace chiral anisotropic vacuum has intrinsic parity “violations.” Noether’s theorems given trace anisotropic vacuum trace violate conservation of angular momentum, originating Milgrom acceleration not dark matter. 45 years of failed physical theory arise from ECKS gravitation being true (defaulting to general relativity in achiral vacuum).

Opposite shoes fit with trace different energies into trace chiral vacuum. They vacuum free fall along trace non-identical minimum action trajectories, violating the Equivalence Principle. Eötvös experiments are 5×10^(-14) difference/average sensitive. Crystallography’s opposite shoes are chemically and macroscopically identical, single crystal test masses in enantiomorphic space groups: P3(1)21 versus P3(2)21 alpha-quartz or P3(1) versus P3(2) gamma-glycine.

http://www.mazepath.com/uncleal/erotor1.jpg

Test spacetime geometry with self-similar opposite geometric parity atomic mass distributions. One observation falsifies 45 years of theory rigorously derived from an elegantly invalid postulate.

The standard model uses CONTINUOUS groups, Lie groups, not finite groups.

]]>After messing about for a while, it dawned on me that all forms of Solitaire are essentially just complicated ways of sorting the cards – some with guaranteed results, some not. I haven’t worked out a no-table Solitaire that is sufficiently interesting yet, but maybe someday.

Going back to your topic, I have also wondered how to maximize the disorder in the shortest number of shuffles. Would alternating between in-faro and out-faro be optimal? Playing Solitaire again, I have noticed that the cards at the top and bottom of the deck have a stronger tendency to stay in that area. It’s easy to see the extreme case – an ace on the bottom is will stay exactly on the bottom if it’s on the correct side of a faro shuffle. So I now shuffle a couple of times, cut the deck 1/4 from the top or bottom, and then shuffle a few more times, cut again, and shuffle a couple more times. Interestingly, if I do that, I seem to win less often!

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