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Hyperreal numbers: infinities and infinitesimals - "In 1976, Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers. Now it's free, with a Creative Commons copyright!" (pdf—25mb :) [more inside]

Network Theory Overview - "The idea: nature and the world of human technology are full of networks! People like to draw diagrams of networks. Mathematical physicists know that in principle these diagrams can be understood using category theory. But why should physicists have all the fun? This is the century of *understanding living systems and adapting to life on a finite planet*. Math isn't the main thing we need, but it's got to be part of the solution... so one thing we should do is develop a unified and powerful theory of networks." (via ;)

Estimated US Energy Use in 2012: 95.1 Quads - "Energy flow charts show the relative size of primary energy resources and end uses in the United States, with fuels compared on a common energy unit basis." (via) [more inside]

Is Psychometric *g* a Myth? - "As an online discussion about IQ or general intelligence grows longer, the probability of someone linking to statistician Cosma Shalizi's essay *g, a Statistical Myth* approaches 1. Usually the link is accompanied by an assertion to the effect that Shalizi offers a definitive refutation of the concept of general mental ability, or psychometric *g*." [more inside]

The Nature of Computation - Intellects Vast and Warm and Sympathetic: "I hand you a network or graph, and ask whether there is a path through the network that crosses each edge exactly once, returning to its starting point. (That is, I ask whether there is a 'Eulerian' cycle.) Then I hand you another network, and ask whether there is a path which visits each node exactly once. (That is, I ask whether there is a 'Hamiltonian' cycle.) How hard is it to answer me?" (via) [more inside]

Professors' global model forecasts civil unrest against governments - With protests spreading in the Middle East (now Yemen - not on the list) I thought this article and blog on a forecast model predicting "which countries will likely experience an escalation in domestic political violence [within the next five years]" was rather interesting. [more inside]

The Logic of Diversity "A new book, *The Wisdom of Crowds* [..:] by The New Yorker columnist James Surowiecki, has recently popularized the idea that groups can, in some ways, be smarter than their members, which is superficially similar to Page's results. While Surowiecki gives many examples of what one might call collective cognition, where groups out-perform isolated individuals, he really has only one explanation for this phenomenon, based on one of his examples: jelly beans [...] averaging together many independent, unbiased guesses gives a result that is probably closer to the truth than any one guess. While true — it's the central limit theorem of statistics — it's far from being the only way in which diversity can be beneficial in problem solving." (Three-Toed Sloth)

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