Geometry of numbers and dimensionality

The paper presents an observer-centric analysis of optimal representation that helps define certain relationship between geometry of numbers and corresponding dimensionality. The motivation for this research is the complementarity that exists in looking at numerical data by itself as compared to its description within a pre-supposed structural framework. Specifically, we consider estimates based on intrinsic dimensionality of data and compare these to those where an a priori order is imposed on the data. We show that this approach helps solve the long-standing problem of different values of the Hubble constant obtained using two different methods.