John Nash and riemannian embedding (memorandum)

NOTICE

• DO NOT TRUST THE FOLLOING

HISTORICAL FACTS

• John Nash earned his degree with game theory paper
• it largely solved Francis Edgeworth's conjecture on economic competence and its equilibrium (it had been also vaguely stated by Cournot)
• von Neumann had low opinion on his result: "That's trivial, you know. That's just a fixed point theorem."
• Nash turned to differential geometry and studied riemannian embedding
• Then he went mad and could not continue his prominent career

QUESTION

• Do Nash's two principal research areas are not internally related?

SPECULATION

• Economic system could be a (near-) manifold in economic "spacetime"
• Approach to equilibrium (relaxation, or tatonnement) is performed in time, but not in same time
• Economic system as reference frame have time other than wallclock (physical time)
• above all is global view
• local view should be told with incommutable operators
• two players have strategies, some could be commutable (their payoff is independent each other),  but almost all should be incommutable
• farther they apart, less they interact
• amount of their interaction is curvature of the two-person universe
• and it approaches to zero as they get "wealthier"