ABSTRACT
Up to this point we have seen that linear science, by which we mean the science of phenomena that have been described by linear equations of motion, can describe a wide range of complicated behavior. If this were not the case the industrial society of the last two centuries would not have been possible since the engineering on which it was built was predominantly linear. However such analyses are no longer adequate for controlling complex phenomena in the physical, social and life sciences of today’s information society. Modernity requires us to think about the mathematics we use to describe complexity in large measure because it is mathematical reasoning that enables scientists and engineers to untangle the knots of the real world. We explore the more obvious reasons why the traditional calculus including differential equations are not sufficient to capture the full range of dynamics found in natural and artificially constructed processes and events.
