Chapter 7 - Recasting Logic in Dirac Notation

Abstract

With the matrix operator formulation came the new understanding of the fundamental link between logic and quantum physics. Matrix logic continues to attract growing attention due to its wealth of logical structures and promises to resolve the fundamental question of consciousness scientifically. The matrix principle reveals that the operation of matrix multiplication lies at the foundation of logical thinking. Matrix logic consequently offers a realistic opportunity to unlock the mystery of the intelligence code, exploring the well-developed and powerful apparatus of matrix calculus. This chapter takes on particular significance because fundamental and beautiful connections are known to exist between the theory of matrices and quantum mechanics, and one is naturally motivated to seek the links between logic and quantum theory, where a different kind of intuition exists. The purpose is to outline a relationship between the logical structure of quantum mechanics and the logical structure of thoughts. Bearing in mind that in quantum mechanics the formalism of the expectation value is the basis of all comparison between theoretical prediction and experiment, and that expectations should not depend on particular picture.