I found myself tied a bit to the theme of last week’s blog when my attention was brought to a very recent article in PLoS Biology called Darwin in Mind: New Opportunities for Evolutionary Psychology. In it a team of biologists, psychologists and philosophers from the Netherlands, the United States and Scotland, suggest that the […]
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NPR recently hosted an interview with Dean Buonomano, neuroscientist and author of the book Brain Bugs: How The Brain’s Flaws Shape Our Lives. I usually like evolutionary perspectives, and enjoy thoughts on how our experience, however abstract and complex it may seem, is somehow built on the biological stuff of our world. But the best […] In a recent post, I referred to a study at MIT that suggested that infants reason by mentally simulating possible scenarios in a given configuration (like different colored objects bouncing around in a container). They then figure out which outcome is most likely based on just a few physical principles (like whether the object nearest […] 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 […] I happened upon an article in Plus about the vector analysis that ants seem to be using to find their way home. Studies exploring insect navigation tools are relevant, not only to building robot navigation tools, but also to understanding the extent to which cognitive structures exist in other living things (and, perhaps, how they […] My last post caused me to survey some things related to Bayesian statistics as they relate to mathematics and cognition. First, I want to say that despite the fact that I have been looking more closely at 19th century developments in mathematics, I didn’t know until today that Laplace, in 1814, described a system of […] It happens many times in class that I say, “in mathematics when you see something you don’t know, you try to figure it out using something you do know. And, recently, in the context of thinking about the generalizations that blossomed in late 19th and early 20th century mathematics, I’ve also wondered how it is […] 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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