The broad challenges for the next century are much the same as in the past - war, terrorism, poverty, health care, education, global warming, biodiversity, energy, pollution and many others. Underlying many of these issues are complex systems involving networks of nonlinear interacting agents with chaotic dynamics. Thus, on the scientific level, the challenge is to understand the architecture and dynamics of political, social and environmental issues. Fortunately, computers are now sufficiently powerful to model the complex systems underlying political, social and environmental issues and rapid progress can be expected.
Such studies are inherently interdisciplinary and are best approached using simple mathematical models. It is already clear that very simple models are capable of exhibiting a wide variety of realistic behaviours, including pattern formation, spontaneous symmetry breaking, self-organisation and chaos. With better understanding, it might be possible to improve prediction, achieve advance warning of failures, and to engineer systems that are more immune to adverse behaviour. It may be possible to deduce sweeping fundamental principles or laws of nature that govern such systems and constrain their behaviour much as the laws of physics do in the physical world.
Julien Clinton Sprott is author of books including Chaos and Time-Series Analysis (buy this book from Amazon (UK) or Amazon (USA)), and Physics Demonstrations: A Sourcebook for Teachers of Physics (buy this book from Amazon (UK) or Amazon (USA)). See his website.