Modern research in sociology, psychology, neuroscience, and anthropology is showing that our world does not revolve around ourselves as individuals—contrary to Enlightenment and later claims that we are inherently self-centered creatures. Instead, what we are like as individuals critically depends on how we are linked socially and emotionally with others in relational networks reaching far and wide.
Why? We have evolved as a species to be quintessentially social creatures.
oogle’s Pagerank algorithm has become one of the most famous in computer science. It was originally designed to rank websites according to their importance by assuming that a site is important if it is linked to by other important sites.
The algorithm works by counting the links to a website and the importance of the sites these come from. It then uses this to work out the importance of the original site. Through a process of iteration, the algorithm comes up with a ranking.
Since Google’s founders, Larry Page and Sergei Brin, developed the algorithm in the mid-1990s, researchers have begun using it to rank nodes in other networks. One idea has been to use it to rank scientific papers using the network of links in the references they contain. Another is to use it for elections in which everyone is a candidate and can vote for anybody else.
If we’re to have any hope of managing complex systems and keeping them from collapse or crisis, we need a new approach. Whether or not the quote is apocryphal, what Einstein allegedly says holds true here: "We cannot solve our problems with the same kind of thinking that created them." What other options do we have? The answer is perhaps surprising: we have to step back from centralized top-down control, which often ends in failed brute-force attempts to impose a certain behavior. However, as I will now explain, we can find new ways of letting the system work for us.
This means that we should implement principles such as distributed bottom-up control and guided self-organization. What are these principles about and how do they work? Self-organization means that the interactions between the components of the system spontaneously lead to a collective, organized and orderly mode of behavior. That does not, however, guarantee that the state of the system is one we might find desirable, and that's why self-organization may need some "guidance."
The Santa Fe Institute (SFI) has launched a web-based educational platform, Complexity Explorer. SFI is a private research institute well known for its cross-disciplinary approach to complex systems such as ant colonies, biological cells, economies, and social systems. The stated mission of the institute is to “discover, comprehend, and communicate the common fundamental principles in complex physical, computational, biological, and social systems that underlie many of the most profound problems facing science and society today.”
As part of the institute’s outreach mission, SFI’s Complexity Explorer offers free open online courses (“MOOCs”) as well as searchable repositories of education-related resources. Past SFI MOOCs have attracted over 20,000 enrollees from nearly 100 countries.
This Fall SFI is offering three free MOOCS for people at different levels of expertise to learn about complex systems
In The new science of cities (Amazon US| Amazon UK), Michael Batty argues that a more productive approach is to think of cities in terms of flows, connections and relationships – in other words, as a network. Places like Times Square or the Champs Elysée are not big, famous or busy because of their inherent qualities, but rather because they sit at the intersections of movements of people, wealth, information, or power.
As we move to a model where learners have options in terms of how they learn, there is a new role for assessment in diagnosing how best to support an individual learner. This new role should not be confused with computerized adaptive testing, which has been used for years to give examinees different assessment items depending on their responses to previous items on the test in order to get more precise estimates of ability using fewer test items.
Adaptive assessment has a different goal. It is designed to identify the next kind of learning experience that will most benefit the particular learner. The School of One demonstration project used adaptive assessment to differentiate learning by combining information from inventories that students completed on how they like to learn with information on students’ actual learning gains after different types of experiences (working with a tutor, small-group instruction, learning online, learning through games). This information was used to generate individual “playlists” of customized learning activities for every student.
This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. Strogatz's book, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering." The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the course is its emphasis on applications. These include airplane wing vibrations, biological rhythms, insect outbreaks, chemical oscillators, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory. The theoretical work is enlivened by frequent use of computer graphics, simulations, and videotaped demonstrations of nonlinear phenomena. The essential prerequisite is single-variable calculus, including curve sketching, Taylor series, and separable differential equations. In a few places, multivariable calculus (partial derivatives, Jacobian matrix, divergence theorem) and linear algebra (eigenvalues and eigenvectors) are used. Fourier analysis is not assumed, and is developed where needed. Introductory physics is used throughout. Other scientific prerequisites would depend on the applications considered, but in all cases, a first course should be adequate preparation
Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University
Among the properties that are common to complex systems, the presence of critical thresholds in the dynamics of the system is one of the most important. Recently, there has been interest in the universalities that occur in the behavior of systems near critical points. These universal properties make it possible to estimate how far a system is from a critical threshold. Several early-warning signals have been reported in time series representing systems near catastrophic shifts. The proper understanding of these early-warnings may allow the prediction and perhaps control of these dramatic shifts in a wide variety of systems. In this paper we analyze this universal behavior for a system that is a paradigm of phase transitions, the Ising model. We study the behavior of the early-warning signals and the way the temporal correlations of the system increase when the system is near the critical point.
Behavior of early warnings near the critical temperature in the two-dimensional Ising model Irving O. Morales, Emmanuel Landa, Carlos Calderon Angeles, Juan C. Toledo, Ana Leonor Rivera, Joel Mendoza-Temis, Alejandro Frank
We have seen that self-organizing systems can be very effective and efficient, but their macro-level behavior crucially depends on the interaction rules, interaction strength, and institutional settings. To get things right, it's important to understand the factors that drive the dynamics of the system.
Proceedings from the 2014 Complex Systems Summer School are now posted, complete with a network map of the students’ collaborations. The students welcome comments and feedback.
Included in the proceedings are an exemplary set of more than two dozen papers -- more than half of which are being considered for publication.
Some of the topics: Can simple models reproduce complex transportation networks? What are the non-linear effects of pesticides on food dynamics? What role do fractals and scaling play in finance models?
It’s a good thing some words have many meanings -- ambiguous words actually make communication easier and may be an inevitable consequence of a language’s evolution, according to a new SFI working paper by External Professor Ricard Sole and Pompeu Fabra University physicist Luis Seoane.
“Ambiguity is, against our intuitions, a major player in making human language so powerful,” says Sole.
Words with multiple meanings are a universal feature of language -- think “ticket,” which could get you into a movie or make you pay a fine, depending on context. The distribution of meanings per word is thought to follow a power law, an observation linguist George Zipf attributed to a “least effort” principle: speaking clearly takes effort, but so does understanding ambiguous speech. The compromise is that some words have multiple meanings, while most don’t.
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