1. Management in complexity The exploration of a new paradigm Complexity theory and the Quantum Interpretation Walter Baets, PhD, HDR Associate Dean for Innovation and Social Responsibility Professor Complexity, Knowledge and Innovation Euromed Marseille – Ecole de Management

2. Sometimes small differences in the initial conditions generate very large differences in the final phenomena. A slight error in the former could produce a tremendous error in the latter. Prediction becomes impossible; we have accidental phenomena. Poincaré in 1903

3. Mathematical complexity

4. Sensitivity to initial conditions (Lorenz) X n+1 = a * X n * (1 - X n ) 0.294 1.4 0.3 0.7

5. Cobweb Diagrams (Attractors/Period Doubling) X n+1 =  * X n * (1 - X n ) (stepfunction) dX / dt =  X (1 - X) (continuous function) On the diagrams one gets: Parabolic curve Diagonal line X n+1 = X n Line connecting iterations

6. Lorenz curve (Butterfly effect) Lorenz (1964) was finally able to materialize Poincaré’s claim Lorenz weather forecasting model dX / dt = B ( Y - X ) dY / dt = - XZ + rX - Y dZ / dt = XY - bZ

7. Fractals (Mandelbrot set) Julia set: Z  Z 2 + C (C is constant; Z is complex) Self-similarity on different levels of detail Coastline Cody Flower Branches of a tree Those forms cannot be reduced to any geometrical figure (Mandelbrot) It is a set of attractors (gingerbread-man) for a set of different equations Dependence on starting values of z Mandelbrot set is a fractal (needs a computer)

8. Why can chaos not be avoided ? Social systems are always dynamic and non-linear Measurement can never be correct Management is always a discontinuous approximation of a continuous phenomenon