An interdisciplinary program, dealing with statistics within basic geometry, is presented and discussed across some modern physics. Its fundamentals are of general interest in physical chemistry, but specially suit investigating conformational statistics and universal scaling of polymer chains in solution. We pointed out an equivalence principle for shape and statistics that can straightforwardly link probability distributions to geometrical quantities at smaller length scales. The average polymer size is thus expected following analytically from the energy surface of its dimeric unit. This would finally suggest extending molecular mechanics to a geometrical setting that reaches the limit of vanishing scales.