A Periodic Table of Physical Descriptions I - Mapping Degree-of-Freedom Bases of the Same Universe

Physics uses many mutually consistent descriptions of the same world—quantum fields, particles, hadrons, quasiparticles, continua, geometry, and information/entropy—each with its own natural degrees of freedom (DOF). These are usually taught as layered approximations or as separate subfields. This paper argues instead that they form a structured atlas: a connected family of DOF bases related by a small set of recurring transformation types. We propose four generic transformations that repeatedly appear across physics: Renormalization / scale navigation (how effective descriptions change with scale) Coarse-graining (many-to-one projection that discards microstate detail) Symmetry and gauge factoring (redundancy removal by quotienting) Phase transitions / emergence (creation of new effective DOF such as quasiparticles or order parameters) Using these primitives, the paper models theory space as a mixed graph: nodes are DOF bases and edges are transformations. Most edges are directed projections (information-losing maps). A smaller set are special equivalences—restricted, bidirectional “dictionary” relationships (duality-style correspondences) that exist only under particular conditions. This distinction prevents the atlas from implying a single terminal endpoint (for example, “information”) while still accommodating known two-way correspondences where they genuinely apply. Two complementary visual maps are developed: (i) an atlas diagram grouped by the “carrier” of description (material, geometric, informational), and (ii) a tetrahedral and cubic-lattice representation that makes the taxonomy operational by organizing descriptions along axes of coarse-graining, redundancy/constraints, and descriptive carrier. The “periodic table” analogy becomes predictive in a specific sense: unoccupied regions of the cube represent structured gaps—plausible but underdeveloped descriptive regimes where new formulations or connections may naturally arise. Beyond conceptual clarity, the framework provides practical guidance: when faced with a complex system, a core task is not only to write equations, but to choose the DOF basis in which prediction becomes natural under the available access constraints. Keywords: degrees of freedom, effective theory, renormalization group, coarse-graining, gauge symmetry, emergence, quasiparticles, hydrodynamics, general relativity, entropy, information theory, duality, theory space, descriptive frameworks, foundations of physics