Familiar mathematical structure is found in the neural activity that governs how the body orients itself and navigates its environment. Grid cells are neurons, found in areas neighboring the hippocampus, whose individual firings line up in a coordinate-like pattern according to an animal’s movement across the full extent of its environment. Their grid pattern acts […]
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The idea that geometry in Gothic architecture was used to structure ideas, rather than the edifice itself, has come up before here at Mathematics Rising. But I would like to focus a bit more on this today because it illustrates something about mathematics, and mathematics’ potential, that the modern proliferation of information may be obscuring. […] Not too long ago I wrote about entropy, and what has come to be known as Maxwell’s demon – a hypothetical creature, invented in 1871 by James Clark Maxwell. The creature was the product of a thought experiment meant to explore the possibility of violating the second law of thermodynamics using information to impede entropy […] When I read the subheading in a recent Scientific American article, it brought me back to some 18th century thoughts which I recently reviewed. The subheading of a piece by Clara Moskowitz’s that describes a new effort in theoretical physics reads: Hundreds of researchers in a collaborative project called “It from Qubit” say space and […] A recent issue of New Scientist featured an article by Kate Douglas with the provocative title Nature’s brain: A radical new view of evolution. The limits of our current understanding of evolution, and the alternative view discussed in the article, are summarized in this excerpt: Any process built purely on random changes has a lot […] Each year, Edge.org asks contributors to respond to their annual question. In 2014, the question was: What scientific idea is ready for retirement? There were 174 interesting responses, but one that got my attention was written by Scott Sampson (author, Dinosaur Odyssey: Fossil Threads in the Web of Life). The idea that Sampson would like […] Recently, I became intrigued with the discussions of topology that I found among architects and historians of architecture. I saw a few familiar threads running through these discussions – like the emergence and self-organizing principles of biology, together with the view that mathematics was not, primarily, a tool but more a point of view. I […] This is something of a follow-up to my last post. I checked out a series of links related to Max Tegmark in the last few days, having heard about the release of his first book Our Mathematical Universe. But I was also motivated by having observed that the latest conference organized by the Foundational Questions […] Much of the research done in cognitive science is designed to study the development of concepts – internal representations that define the idea-driven nature of modern human experience. And, in our experience, it’s difficult to mend the rift that’s been created between what we call thought and what we call reality. But a number of […] The Atlantic Monthly just did an interesting piece on Douglas Hofstadter, Pulitzer Prize-winning author of Gödel, Bach and Escher. Hofstadter’s 1979 book investigates the nature of human thought processes by looking at common themes in the work of the mathematician Gödel, the musician Bach and the artist Escher. In particular, it addresses the question of […] |
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