Computation in Mind 1 C OMPUTATION IN

Like Philosophy, Mathematics deals with abstract ideas, i.e. immaterial objects which inhabit and work in the Mind. The chapter “Computation in Mind” proposes to use the power of computational mathematics to explore some of the universal ways by which each human mind builds its “imago mundi”, its image of the world. The primary focus is put on epistemology and the use of mathematics is minimal, relegating the necessary technical details to an appendix. The Chapter develops the viewpoint that Science and Mind are mirror images for each other which use specific calculations over three kinds of numbers. It presents some epistemological consequences of the lack of associativity or commutativity for the two basic operations which are × and + when the calculations are performed over vectors or over matrices. The evolutive nature of the scientific logic is illustrated on several examples. In particular induction in computation suggests that any matrix ring can be usefully considered as a structure of macro-scalars.