Chapter 23 - Cognitive Delta

Abstract

The brain is neither classical nor quantum but both; indicating the existence of a whole variety of computational paradigms, not just classical or quantum. The continuous and discrete processes are intrinsically intertwined in cognitive operations. Neither classical logical truth-function alone nor wavefunction alone fully accounts for the thinking processes. This chapter demonstrates that the Dirac delta function provides new insight into this problem. The delta function is not really a function but a distribution. It is defined not through the values of the argument as an ordinary function but by the rules of integration of the product of the delta function with a continuous function. The delta theorem allows one to convert naturally from the quantum to classical domain that is from a many-particle system, such as the brain, to a logical system such as consciousness. It follows that systems,which exhibit consciousness are necessarily many-particle complex systems. A system comprising just few particles cannot realize consciousness. The logical integration is similar to the normalization of the wave function, where the integration is carried out over the complete Hilbert space of the problem.