Gödel's undecidability results showed the incompleteness of formal axiomatic systems. A more concrete demonstration of incompleteness is predicated on Turing's work on uncomputability. Perhaps the most illuminating reason for incompleteness can be seen through algorithmic information theory where Chaitin used incompressibility. Rather remarkably, incompressibilty highlights that incompleteness can be treated to be pervasive phenomenon throughout pure mathematics. Using this work, Chaitin has pointed out that compression can be generalized to a universal concept. In align with this, we argue to embrace compression as a primary method in physics akin to the geometrization of physics in the 20th century. To warrant such a direction, we examine how compression already exists at a foundational level in current information theories associated to physical systems (both classical and quantum). We proceed to argue that applying the concept of compression to the structure of spacetime provides us with a novel path forward in fundamental physics, which includes addressing the conceptual problems in quantum physics where "God plays dice." We provide speculative mathematical ideas for how such a spacetime-information theory could be developed. This alludes to the notion that time itself is intrinsically random.
Del Rajan