Abstract: We describe a recent evolution of Harmonic Analysis to generate analytic tools for the joint organization of the geometry of subsets of R n and the analysis of functions and operators on the subsets. In this analysis we establish a duality between the geometry of functions and the geometry of the space. The methods are used to automate various analytic organizations, as well as to enable informative data analysis. These tools extend to higher order tensors, to combine dynamic analysis of changing structures. In particular we view these tools as necessary to enable automated empirical modeling, in which the goal is to model dynamics in nature, ab initio, through observations alone. We will illustrate recent developments in which physical models can be discovered and modelled directly from observations, in which the conventional Newtonian differential equations, are replaced by observed geometric data constraints. This work represents an extended global collaboration including, recently, A. Averbuch, A. Singer, Y. Kevrekidis, R. Talmon, M. Gavish, W. Leeb, J. Ankenman, G. Mishne and many more.