Complex beyond words

This paper addresses the fundamental question of whether mathematics is necessary for the science of complex systems or whether a verbal approach is sufficient. The science of complex systems is presented as interdisciplinary, in which case mathematics is essential. In case this interdisciplinary approach is rejected, classes of systems are identified that are inherently mathematical for which research cannot be conducted in words alone. This includes almost all systems involving human beings! By definition it includes all social-technical systems, and it includes all aspects of systems that involve mathematics, the statistical analysis of data, time series or power laws, chaos, flows, have large umbers of heterogeneous elements, have many heterogeneous relationships, have top-down and bottom-up dynamics, have complicated entailments with positive and negative feedback loops, have stochastic dynamics, or involve infinitesimals. Thus a certain level of mathematical knowledge is essential to be a competent complex systems scientist. This is because complex systems research requires teams of scientists with complementary knowledge, and it is essential that they can communicate using the core ideas of the science. In order to make mathematics and other essential scientific concepts available to the whole complex systems community, the Complex Systems Society is coordinating the definition of a core curriculum and is providing free web-based education and certification through the Paris-based Open University for Complex Systems.