Innovation management from fractal infinite paths integral point of view

Abstract

While a mastery of management innovation is crucial for the future of the economy, to date, there is no theory able to base with objectivity the management of creativity and entrepreneurship. This absence is not due to the lack of methods but to ignorance of mathematical foundations which justify the paradigmatic transgression. These foundations exist nevertheless. It can be mentioned the fractal geometry and the role played by the singularities and correlations over long distances. In the set theory, let us mention Cohen's forcing methods and its engineering consequences through CK theory. In the categories theory, we can mention the principles of Kan extension herein applied by the mean of holomorphic analysis and the analytical extensions. All these methods are based on the recognition of the incompleteness of any structure axiomatically closed (Goedel). At the junction between the physics and the economy, the goal of the present work is to show that the lack of recognition of the role of singularities in this science must be searched in mental biases and the paradigms that affect our concept of equilibrium. We show that this concept must be generalized. If the criticism of the concept of equilibrium in economics is already known, it does not lead, quite as much, to a theory of innovation. We would like to address the issue of creativity by backing the reasoning by the questioning of the concept of equilibrium, using an analogy coming from the physics in fractal structures. The idea is to consider the equilibrium as some steady state limit of a fractional dynamics. The fractional dynamics is a dynamics controlled by non integer fractional equation. These equations will be considered in the Fourier space and by the means of their hyperbolic geodesics. Due to the intrinsic incompleteness of the fractality and of its cardinality, the thickening of the infinite will be used to show that there is no even physical balance but only pseudo-equilibria. The practical use of this observation leads to the design of a dynamic model of creativity, named DQPl (Dual Quality Planning), giving a topologic content to the innovation process. New principles of management of innovation emerge in naturally.