Abstract: A simple-minded introduction to the "non-commutative culture" (signifying a transition from commutative to noncommutative algebras in geometry, probability theory and physics) will be given. A formalism (called Supmech) will be presented which integrates noncommutative probability and noncommutative symplectic geometry in an algebraic setting; it provides the proper framework for an autonomous development of quantum mechanics. A consistent description of interaction between systems in this formalism is possible only if the systems with noncommutative algebra of observables have the traditional quantum symplectic structure. The treatment of measurements on quantum systems in this formalism provides a straightforward explanation of the von Neumann reduction (which is usually postulated) thereby providing a solution of the measurement problem.