NOTICE
- DO NOT TRUST THE FOLLOWING
OBSERVATIONS
- numerical integration: some computation would never halt
- someone guesses approximate fixed point of above computation
- what is the "probability" whether the guesser is right
- as far as the system is integrable, this would make sense
- automata: cyclic group could be represented as circular state machine
- apply homology to nodes of an automaton: nodes are loops
- John von Neumann: he worked on cellular automata after his (mathematical) effort on ergodic theory and operator ring theory
- John Nash: existence of core of game / Riemannian embedding
- William Thurston: geometrization conjecture and following studies of automata
SPECULATION
- there must be an inclusive viewpoint for understanding them all as one:
- ergodic theory
- probability theory (especially, stochastic process)
- metamathematics, set-theoretic and lattice-theoretic
- model theory
- (non-relativistic) quantum field theory
- general relativity
- automata theory
- thermodynamics
- dynamic macroeconomics
- financial and monetary economics
TURBULENCE/RANDOMNESS/NON-INTEGRABILITY
- what is "mean coordinates" of chaotic orbit?
