Some recent advances in scientific thought cannot be ignored by anyone interested in understanding the world. At the start of the 20th century Kandinsky felt a cultural shock in response to Rutherford's splitting of the atom. Are we responding similarly to the equally far-reaching consequences developing from the science and ideas at the start of the 21st?
The title might be a bit grandiose, but these areas of thinking inform my own work and research, so an 'in a nutshell' approach seems like a useful exercise. Each section attempts to cover the basic concepts as far as I understand them.
NOTE: article in progress; references and links incomplete.
Chaos theory has become so embedded in popular culture that it is easy to overlook the remarkable impact it has had on our thinking. The principal tenets state that small initial changes produce large end results and, at a point where things do not tend too much toward either order or disorder, they dance around in a state of 'chaos', following endless permutations within the limits of their boundaries, yet retaining a kind of fluid organisation which echoes many processes in the natural world, and enables some of them to be modelled. Chaos explains how clouds or trees, although never identical, remain recognisable. It explores how dynamic systems, such as those seen in turbulence or the weather, are sustained. Underpinning this are non-linear equations - seemingly simple yet insoluble mathematical equations that, with the right input, generate an infinite and ever-changing series rather than a fixed result. Chaos theory also includes the fractal notion of self-similarity - that (for instance) the surface of a small broken rock resembles the face of a mountain, or zooming in on the Mandelbrot set again and again simply reveals endless permutations of similar patterns. James Gleick's book Chaos is a sound overview.
One of the principal tenets of complexity theory is - to be trite - that the whole is greater than the sum of its parts. Another, that the most interesting stuff (in biology, economics, physics, etc.) happens - as with chaos theory - at the point where there is neither too much nor too little order or disorder. A third, that things tend to organise themsleves into dynamic patterns that retain their structure while remaining in a constant state of change. Complexity theory, while embracing the specifics of chaos theory, examines the broader picture - how collections of differing systems can interact to produce a dynamically stable state, which emerges spontaneously from their interactions without any external management. The most well-known keywords are emergent behaviour and self-organisation; and systems contain basins of attraction. The guru of complexity is Murray Gell-Mann (discovered the Quark), and the place to be when it all happened was the Santa Fe Institute. Gell-Mann's The Quark and the Jaguar is an essential read, and M. Mitchell Waldrop's overview Complexity: The Emerging Science at the Edge of Order and Chaos (in similar style to Gleick's Chaos) is a stimulating journey though the key ideas and origins of this most important of interdisciplinary sciences; there is a detailed outline here.
Postmodern thought might have atempted to do away with the grand narratives of modernism, but they linger on in popular views of science at a time when science itself has developed its own postmodern perspectives. See three modernist myths, here I've attempted to outline how modernists ideas are challenged. [to develop: key concepts - no grand narratives, relativism (web-like, rather than methodological, thinking), deconstruction, linearity, etc. Write a 'that's all you need to know' summary - don't read Foucault, Lyotard etc., or applications of 'pomo' to art used to lend intellectual weight to 'seriously playful' activity, but garner an overview of postmodernism in a postmodern way by inference and websites, dipping in. Also see Alan Sokal's hoax.]
Tolerance of uncertainty is a crucial part of current thinking. Everyone has heard of Schröedinger's cat, but Kurt Gödel's incompleteness theorems dashed Hilbert's hope that all mathematics could be proved true from a complete and consistent set of axioms; a radical concept in a field where - intuitively - it might seem possible to indulge the hope of complete certainty. Yet alongside this acceptance of uncertainty, new all-embracing theories of everything seem tantalisingly close.
The idea that consciousness is a product of the brain, and is inseparable from it, has a 21st century rival. Roger Penrose and Stuart Hameroff are conducting research that explores the possibility of consciousness existing independently from the physical structure of the brain. The associated Horizon Research Fellowship has also been set up to monitor hospital patients who are able to witness events at times when there is no sign of brain activity, under lab conditions (what have become known as 'out-of-body' experiences or 'OOBs'). Some criticisms of this view are centred around the fact that consciousness must be an emergent property of our physical makeup, and there are competing theories that attempt to explain OOBs.
see Roger Penrose - beyond algorithms and this review of Penrose's Shadows of the Mind.