Dual-Projection Informational Ontology: Projection Symmetry Between Physics and Mathematics

This paper develops a dual–projection informational ontology according to which what we usually call the “physical world” and the “mathematical world” are not two independent realms, but two projections of a single informational ground. Building on earlier work that models existence as a closed informational manifold and physical reality as the image of an irreversible projection [9, 10, 12], I argue that a second, structurally oriented projection yields the domain of mathematics. The physical projection generates a time–bound, entropic history by hiding information in ways that cannot be undone by any physically admissible process. The mathematical projection, by contrast, quotients out representational redundancies and isolates structural invariants without introducing an intrinsic arrow of time. Within this framework, the deep fit between physics and mathematics is no longer mysterious: both read the same informational manifold under different projection rules. I formulate a Projection Symmetry Principle, according to which laws of nature are structures that are invariant under both projections. I contrast this view with traditional Platonism, nominalism, structural realism, Tegmark’s mathematical universe hypothesis, and Floridi’s informational realism, and I address several objections. A toy example is used to illustrate the two projections in a simple setting. The aim is not to provide a complete theory, but to motivate a research program in which physical reality and mathematical structure are seen as two faces of one informational being.