As I talked about in a recent post, string theories, and the multiverse models they imply, have been widely criticized for their lack of testability. Some physicists argue that the problem is that the theory is more mathematics than it is physics. Is the distinction becoming fuzzier? And why isn’t that discussed? Why not bring […]
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Back in July, David Castelvechhi blogged about a conversation between John Horgan and George Musser. I missed it when it was new, but I’m glad I didn’t miss it completely. Most of their discussion focuses on the value or viability of what has come to be known as string theory. It was a thoughtful debate […] I have often said that I get particular pleasure from mathematics that defies common sense expectations. A simple example would be the observation that two things can be the same size even though one of them is contained in the other – like the set of natural numbers and the set of positive even integers. […] 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 […] 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 […] I’m a little pressed for time this week so I thought I would try to provide some fun links. Steven Strogatz, mathematician and writer, speaks on a radiolab broadcast about an early insight. It was in a high school math class where he says he was being taught how to use graph paper. The teacher […] Mathematics today can seem an isolated discipline, removed from the questions of life and questions of meaning. But even a brief look at some of the writing of individuals like Leibniz, Weyl, and Poincare demonstrates substantial interest on the part of the mathematician to reconcile mathematics with common human experience. I remember one of my […] When I looked recently at Riemann’s famous lecture On the Hypotheses which lie at the Bases of Geometry, I gave some attention to this remark: besides some very short hints on the matter given by Privy Councillor Gauss in his second memoir on Biquadratic Residues, in the Göttingen Gelehrte Anzeige, and in his Jubilee-book, and […] I’ve been spending a lot of time reading about the significance of Riemann’s Habilitation Dissertation and, today, a little bit of looking into the pervasive human desire to generalize led me yet again to Plato. I keep thinking that a closer look at what Plato actually said is consistent with even the most brain-based thoughts […] |
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