Forcing Optimality and Brandt's Principle
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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 morphogenesis, are a natural setting for the application of this principle
Applied Mathematics | Databases and Information Systems | Mathematics
Domenico Napoletani, Marco Panza, Daniele 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>.
This is a pre-copy-editing, author-produced PDF of a chapter accepted for publication in Johannes Lenhard and Martin Carrier (Eds.), Mathematics as a Tool: Tracing New Roles of Mathematics in the Sciences (Boston Studies in the Philosophy and History of Science).