Dimension Calculus and Anticipatory Systems

Dimensional analysis permits us the rigorous comprehension of physical quantities by its reduction in terms of mass M, length L, time T, electric charge Q, and temperature Θ. E.g., speed is LT^-1, force is MLT^-2 and so on. However, Saumont has observed that it is no rational to give dimensions to constant quantity and not to give dimensions to variable quantity. Also, standard dimension analysis implies an evident hyper-cubic topology MⁿL^pT^pQ^rΘ^s that isn't incompatible with (hyper)incursive systems that have hypersphere or torus topology. Finally, Grappone has proven that anticipatory systems, in terms of set inclusive networks, are equivalent to first order theories in mathematical logic, i.e. polyadic or cilindric algebras that haven't a simple hypercubic structure. This paper is an attempt to start the solving of these problems.