These are my links for March 15th through March 18th:
- Book Review – The Information – By James Gleick – NYTimes.com – The universe, the 18th-century mathematician and philosopher Jean Le Rond dâ€™Alembert said, â€œwould only be one fact and one great truth for whoever knew how to embrace it from a single point of view.â€ James Gleick has such a perspective, and signals it in the first word of the title of his new book, â€œThe Information,â€ using the definite article we usually reserve for totalities like the universe, the ether â€” and the Internet. Information, he argues, is more than just the contents of our overflowing libraries and Web servers. It is â€œthe blood and the fuel, the vital principleâ€ of the world. Human consciousness, society, life on earth, the cosmos â€” itâ€™s bits all the way down.
- www.andrew.cmu.edu/user/awodey/preprints/fold.pdf – In the present work, we generalize the entire arrangement from propositional to ï¬rst-order logic. Boolean algebras are replaced by Boolean categories presented by theories in ï¬rst-order logic, and spacesof models are replaced by topological groupoids of models and their isomorphisms. A duality between the resulting categories of syntaxand semantics, expressed ï¬rst in the form of a contravariant adjunction, is established by homming into a common dualizing object, nowSets, regarded once as a boolean category, and once as a groupoid equipped with an intrinsic topology.
- First-Order Logical Duality.pdf – “â€¦an extension of Stone Duality for Boolean Algebras from classical propositional logic to classical first-order logic. The leading idea is, in broad strokes, to take the traditional logical distinction between syntax and semantics and analyze it in terms of the classical mathematical distinction between algebra and geometry, with syntax corresponding to algebra and semantics to geometry.”
- Tim Berners-Lee on the next Web | Video on TED.com – 20 years ago, Tim Berners-Lee invented the World Wide Web. For his next project, he’s building a web for open, linked data that could do for numbers what the Web did for words, pictures, video: unlock our data and reframe the way we use it together.