Forcing optimality and Brandt's principle

Domenico Napoletani (1) , Marco Panza (2) , Daniele C Struppa (3)

1 Institute for Quantum Studies
2 IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques
3 Schmid College of Science and Technology

We argue that many optimization methods can be viewed as representatives of " forcing " , a methodological approach that attempts to bridge the gap between data and mathematics on the basis of an a priori trust in the power of a mathematical technique, even when detailed, credible models of a phenomenon are lacking or do not justify the use of this technique. In particular, we show that forcing is implied in particle swarms optimization methods, and in modeling image processing problems through optimization. From these considerations, we extrapolate a principle for general data analysis methods, what we call 'Brandt's principle', namely the assumption that an algorithm that approaches a steady state in its output has found a solution to a problem, or needs to be replaced. We finally propose that biological systems, and other phenomena that respect general rules of morphogene-sis, are a natural setting for the application of this principle.

Mots clés: Data Analysis; Optimality; Forcing; Brandt's principle

Domaines: Histoire, Philosophie et Sociologie des sciences

Domenico Napoletani, Marco Panza, Daniele C Struppa. Forcing optimality and Brandt's principle. J. Lenhard and M. Carrier. Mathematics as a Tool, Boston Studies in the Philosophy and History of Science 327, Springer, 2017, ⟨10.1007/978-3-319-54469-4_13⟩. ⟨halshs-01474531⟩