Eva Miranda and Isaac Ramos proved that a point particle bouncing inside a two-dimensional table with fixed walls can simulate a universal Turing machine, resolving a question left open by Cristopher Moore in 1990. This result shows that undecidability, like chaos, obstructs long-term prediction in classical mechanics, with reachability and periodicity becoming algorithmically undecidable problems.
A blog post explores mathematical billiards, an idealized study of ball trajectories in custom-shaped tables without friction or pockets. It introduces inner billiards (trajectories within convex shapes like ellipses) and outer billiards (abstract motion around geometric shapes), using computer experiments and visualization tools to analyze these dynamical systems.