Abstract
Modeling reality is a zoom-in/out process best implemented as a resolution of finite type, in the mathematical sense. This means that at each level of details a finite number of independent degrees of freedom are introduced: dimensions, “digits”, graphs etc. The local corresponding properties (“particle” aspects) are complemented by global properties/correlations (“wave” aspects), providing the framework for the classical-quantum duality. Explicit examples are discussed: real numbers, Haar wavelets and Feynman graphs. The conclusion is: reality is discrete, hierarchic of finite type, well modeled by a duality of the type homology-cohomology. The development of physics, experimental and theoretical, ample supports this claims.
Lucian Miti Ionescu