Pragmatic Association of the Two Evaluation Concepts of Operational Observation and Mathematical Modeling

Recent developments in several theoretical and industrial concepts are closely associated to the relation of operational observation to mathematical modeling. The present work investigates first the interdependence of these two evaluation notions. An assessment of these notions is performed involving different analyses based on philosophical aspects as phenomenology and structural research. These analyses are also supported by illustrations from physics and quantum science. These analyses examine the autonomy limits of each of both concepts and their interdependence. The associate resulting from such interdependence is therefore studied. This involves different aspects characterizing such associate (couple) as its managing in time and its rulings. The immersion of the couple "observation-theory" is subsequently considered through the exploration of different representing cases showing the nature of the interdependence in this couple. The corroborating interdependence is illuminated in the case of coupled amended models. The matching interdependence is illustrated in the cases of the industrial digital twins concept and Bayesian brain theory in neuroscience. Finally, the imitating interdependence is pointed out in quantum and neuromorphic computing technologies. The conclusion of the paper underlines that mathematical modeling needs operational observation simply to be credible and that the second needs the first for deeper research. Additionally, the interdependence of this associate is valuable to the ideas of several research and industrial innovative concepts. Keywords: observation-modeling associate, phenomenology, structural research, Bayesian concepts, quantum science, matching, imitating, corroborating.