ABSTRACT Recently proposed scaling concepts for geometry are used to deal with conformational properties of macro-molecules. A chain configuration is conceived as a geometrical state, for coil extension and shape, indetermined by its end-to-end dimension. The polymer length distribution is modeled by Lobachevskij waves, solving an ondulatory equation in a quantum like Non-Euclidean space. Chain statistics descends from the geometrical uncertainty, arising from measuring at the polymer size scale, independently of the number of macromolecular configurations (N). Measuring would actually involve three dispersion values (i.e., measure, extension and shape) that degenerate into an unique statistics (measure). When the observation scale is infinitely small, end-to-end distance and characteristic ratio follow from the parallelism angle scaling. In real systems, asymptotic polymer size and monomer energy map are related directly by means of rotation maps. It is lastly suggested to consider either the starting energy surface or the final chain conformation as distorsion profiles of some inner shape, defined at vanishing scales and affected by the observation length. Measuring itself would so represent the uncertainty source intrinsically undetermining the physical observables into statistical processes and length scale-dependent dualities (monomer-polymer, atom-molecules, etc).
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