Complex systems Complex systems present problems both in mathematical modelling and philosophical foundations. The study of complex systems represents a new approach to science that investigates how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment. Such systems are used to model processes in computer science, biology, economics, physics, chemistry, and many other fields.
Chaos theory A double rod pendulum animation showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions. Chaos: When the present determines the future, but the approximate present does not approximately determine the future.
Panarchy Panarchy is a conceptual term first coined by the Belgian philosopher, economist, and botanist Paul Emile de Puydt in 1860, referring to a specific form of governance (-archy) that would encompass (pan-) all others. The Oxford English Dictionary lists the noun as "chiefly poetic" with the meaning "a universal realm," citing an 1848 attestation by Philip James Bailey, "the starry panarchy of space". The adjective panarchic "all-ruling" has earlier attestations. In the twentieth century the term was re-coined separately by scholars in international relations to describe the notion of global governance and then by systems theorists to describe non-hierarchical organizing theories. Freely choosing government In his 1860 article "Panarchy" de Puydt, who also expressed support for laissez-faire economics, applied the concept to the individual's right to choose any form of government without being forced to move from their current locale. Le Grand E.
Order Out of Chaos" Let's return to the world of weather forecasts for a moment, as well as the world of butterflies and hurricanes. You've probably heard of chaos theory, the mathematical field concerned with the seemingly disorganized behavior of highly dynamic systems. The term originates in 1961 with meteorologist Edward N. Lorenz and his fascination with how the smallest of atmospheric variables can result in drastically different weather models. Chaos Theory: A Brief Introduction What exactly is chaos? The name "chaos theory" comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data. When was chaos first discovered? The first true experimenter in chaos was a meteorologist, named Edward Lorenz. In 1960, he was working on the problem of weather prediction.
Mixing (mathematics) Mixing in a ball of colored putty after consecutive iterations of "Smale horseshoe map" (i.e. squashing and folding in two) Let be a sequence of random variables. Category:Panarchy The discussion of panarchy herein will be embryonic in nature. I will begin with the complete shape, but only in the simplest of forms. As I add more material, the overall structure will become more developed and clarified, but all of the essentials will have been laid out in the beginning. Panarchy is a transdisciplinary investigation into the political and cultural philosophy of "network culture."
John Holland, Emergence The Bactra Review: Occasional and eclectic book reviews by Cosma Shalizi From Chaos to Order John Holland