Chaotic systems present unique challenges to the Newtonian Ideal of the reducible universe. With chaos theory we see systems that are deterministic, but which still generate unpredictable outcomes. One feature of chaotic, dynamical systems is their sensitive dependence on initial conditions (sometimes called the butterfly effect), meaning that miniscule changes to the initial conditions of the system can result in vastly different outcomes. We can see this in many places in the world around us; most notably in the weather.
Complex, adaptive systems are agent based and are capable of expressing behaviors that seem highly ordered despite lacking a central, controlling authority. Such systems commonly operate far from equilibrium, yet still manage to regulate themselves, or self-organize. One of the most interesting features of such systems is Emergence.
Through emergence, independent agents, interacting with each other based upon a few simple rules, can cause new levels of complexity to arise spontaneously within a system. This is often seen with social insects, who, working together, create architecturally complex hives and engage in startlingly complicated behaviors. Such behaviors often give the appearance of these creatures being subject to an overarching intelligence, but, in fact, we are seeing new levels of organization emerge through spontaneous interaction; organization that, in turn, exerts control over the agents that created it in the first place. Unlike self-organization, in which new levels of organization may be reduced into the behavior of individual agents, emergence is irreducible. That is to say, it results from the interactions of the agents under a variety of changing circumstances rather than through predictable behaviors by individual agents themselves. This makes emergent phenomena very difficult to understand and basically impossible to predict outside of simulation. This important and fascinating facet of the Complexity Sciences is a subject of great interest to Artificial Intelligence and Robotics research, as a greater understanding of emergence has allowed for synthetic creations to mimic patterns found in nature. It is believed by many that higher intelligence itself is an emergent phenomena that takes place within biological neural networks.
Modern information is still largely subject to an obsolete model . . . that is to say, people directly controlling a limited amount of information. However, the proportion of information to people has made this an unmanageable paradigm, and this ratio only grows more extreme each day. We need to find ways to make our information do more of this work by itself. All modern information systems employ metadata. Metadata is information about information and information about how information is packaged. Think of it like this: if the information is a book, the metadata could be its entry in Amazon. Metadata serves as a proxy for a unit of information. We use metadata to search for and organize information in modern information systems every day. Our metadata, however, is still primitive in some ways. Like the card in an old card catalog, it normally requires a person to edit in changes. Such metadata is highly limiting in our modern, information age. I propose that, by using a combination of browser initiated activity and off-site metadata indexes acting in concert, metadata can be cross-pollinated to allow it to exhibit adaptive, self-organizational behaviors. This metadata will be able to adapt dynamically to changes in knowledge, changes to ontologies, and even correct accidental shortcomings in an original metadata record. On a more powerful level, however, these proposed schemata elements will, I hope, exhibit emergent properties by doing more than simply exchanging tags. These metadata units will also be altered based on the structure of the taxonomy that they exchange tags within, and will have new tags generated reflecting references, URIs, and even the search terms used to find a record. Depending on how these tags are utilized, spontaneous new information pathways could emerge, new, implicit ontologies could take shape, and new ways to manage information could be discovered. This approach differs significantly from approaches, such as purpose-built ontologies, which rely on "borrowed" human intelligence to do their work. I presented my paper Imagining Emergent Metadata, Realizing the Emergent Web at the LibTech 2012 conference, and it was later published in the Journal of Library Metadata.