Munich Center for Mathematical Philosophy (MCMP)

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Talk: Philippos Papayannopoulos (CNRS)

Location: Ludwigstr. 31, ground floor, room 021.

21.12.2022 16:00  – 18:00 


Algorithms and Computations as Dynamical Systems. A Formal Approach to Restoring an Old Peace


How are the concepts of “computation” and “algorithm” related? The classical view is that both terms denote virtually the same thing. “Computation” refers to a mechanical, step-by-step, deterministic process for obtaining a mathematical value, and “algorithm” refers either to the same process or to the set of instructions that specify this process. While this is a well-entrenched view in logic and computer science, I argue that it stands in contrast with how algorithms are used in numerical analysis and other areas of math. Thus, I propose a distinction between two different conceptions of “algorithms” and discuss some features that I think make the two conceptions genuinely irreducible to each other. I also propose that by drawing upon the theory of discrete dynamical systems (DDS) we can treat both conceptions in a new and unified way. This is because at the heart of both notions of algorithms lies the idea of iteration, which is also central in DDS. Finally, I briefly explore the prospects of extending this approach to the case of continuous dynamical systems and continuous computations.