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To give shape to this blog, I’ve been jumping around quite a lot through the fields of mathematics, physics, and the neurological and cognitive sciences. I decided today to let more of my weight drop into philosophy. It’s not unusual when reading about 19th century developments in mathematics (the ones that lay the groundwork for […] A recent Radiolab episode brought some interesting things together by exploring loops, repetitions, and self-referencing phenomena. Among other things, they told the story of Melanie Thernstrom (The Pain Chronicles) who, in trying to manage her pain, investigated the self-inflicted pain of religious rites. She later did some work with neuroscientist Sean Mackey. Mackey had seen […] I feel like I was pulled into a little whirlpool of interesting bits of info this morning. I was attracted to the title of David Castelvecchi’s blog: Archimedes and Euclid? Like String Theory versus Freshman Calculus. The blog reports the opening of an exhibition at the Walters Art Museum in Baltimore, showcasing one of three […] David Castelvecchi, at the Scientific American blog network, wrote about a Comment article that appeared in the July 13 issue of the journal Nature. The author, Peter Rowlett, takes note of what could happen when the mathematician “pushes ideas far into the abstract, well beyond where others would stop.” He does this with a collection […] I recently listened to a radiolab podcast (from this past November!) that featured two authors: Steven Johnson (author of Where Good Ideas Come From) and Kevin Kelly (author of What Technology Wants). The thrust of the argument, that both authors defended, was that the things we make (from tools to gadgets to computers) are an […] Today, I was working on a piece I’m writing about 19th century developments in mathematics and I saw something interesting. In the piece, I draw particular attention to a few things. One of these is the precision Weierstrass brought to the concept of a limit, removing all references to motion or geometry, and giving it […] I was reading up on some nineteenth century philosophy and science for a book project of mine and I found an essay by Timothy Lenoir called The Eye as Mathematician. It is a discussion of the construction of Helmholtz’s theory of vision. The title suggests that the eye is acting like a mathematician. My disposition […] There are countless ways to explore what may be called the two faces of mathematics – algebra and geometry. Modern mathematical systems have their roots in both algebraic and geometric thinking. Like the organs of the body which are built on the redirected sameness of cells, algebra and geometry live in all manner of relationship […] Some of George Berkeley’s fame comes from his vehement critique of Newton’s calculus. His criticism was harsh and inspired a number of responses from contemporaries who accepted the vanishing quantities Newton used to formulate his notion of fluxions or, in modern terms, his understanding of instantaneous rates of change. The discussion that followed Berkeley’s 1734 […] I have spent some time pointing to milestones in the history of modern mathematics where a conceptual shift produces provocative new thought – as when Riemann gave a new foundation to geometry, or when Cantor brought precision to the notion of countability. Modern mathematics, partnered with physics, increasingly refines what the human mind can perceive. […] |
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