Geometry of Undecidable Systems
Akira Saito, Keiichi Kaneko · Progress of Theoretical Physics · 1998
Geometric properties of undecidable systems are numerically investigated. As an undecidable set, the halting set of the universal Turing machine is chosen, whose geometric representation is shown to have a different structure on an arbitrarily small scale, and is constructed non-uniformly in time. The set's structure has a fractal boundary dimension converging to the spatial dimension, which gives a geometric characterization of the undecidability.