Uncomputability of phase diagrams

Geochemical Phase Diagrams and Gale Diagrams

The problem of predicting the possible topologies of a geochemical phase diagram, based on the chemical formula of the phases involved, is shown to be intimately connected with and aided by well-studied notions in discrete geometry: Gale diagrams, triangulations, secondary fans, and oriented matroids.

Uncomputability: the problem of induction internalized

I argue that uncomputable formal problems are intuitively, mathematically, and methodologically analogous to empirical problems in which Hume’s problem of induction arises. In particular, I show that a version of Ockham’s razor (a preference for simple answers) is advantageous in both domains when infallible inference is infeasible. A familiar response to the empirical problem of induction is t...

Magnetic phase diagrams of the

Phase diagrams of mesomorphic mixtures

2014 We have combined the Maier Saupe theory [1] of the nematic-isotropic transition and the Flory Huggins theory of mixtures to describe the phase diagrams of two nematogens A + B. The two components can have different order parameters SA, SB in the mixture. We can then predict the morphology of the phase diagrams in term of a relatively small number (4) of interaction parameters. The final nu...

Uncomputability and undecidability in economic theory

Economic theory, game theory and mathematical statistics have all increasingly become algorithmic sciences. Computable Economics, Algorithmic Game Theory [Noam Nisan, Tim Roiughgarden, Éva Tardos, Vijay V. Vazirani (Eds.), Algorithmic Game Theory, Cambridge University Press, Cambridge, 2007] and Algorithmic Statistics [Péter Gács, John T. Tromp, Paul M.B. Vitányi, Algorithmic statistics, IEEE T...