Mathematics of Nature
Nature does not compute, but is interaction of autonomously operating organisms. What is the new mathematics, that reflect this natural reality that AI has to be based on?
Nature is society of cells or atoms, that interact with each other.
Chemistry, describes this atomic level interactions very well. Atoms that are of opposite charges interact with each other to form a compound. Atoms that is -ve in charge, gives out a electron to the +vely charged atom to make a new bond. Once the bond between atoms is formed, it cannot be broken, and it exhibits a new emergent property. For example, common salt tastes different from its individual component atoms Sodium and calcium.
This is clearly not computation. It is a process by which two processes (Sodium and Chlorine) of complementary needs create a new process (Common salt) with new properties. Present day mathematical tools do not model this. It is time, for a new mathematics, other than computation, which models processes as a component of interaction of smaller processes.
PI calculus, theory of processes is one such theory.
In PI calculus, everything is a process. These processes, show its uniqueness by exposing actions. Actions, like atoms, have -ve and +ve aspects. -ve action receives data and +ve action, outputs data. Complementary actions bind to move process forward. This similarity of pi calculus, to natural processes, makes it an ideal mathematics to model nature.
Like current computer languages are based on Lambda calculus, PI calculus is the right mathematics to model next generation AI devices.