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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Here is an excerpt from a piece by Alain Connes in The Princeton Companion to Mathematics: It might be tempting at first to regard mathematics as a collection of separate branches, such as geometry, algebra, analysis, number theory, etc., where the first is dominated by the attempt to understand the concept of “space,” the second […] I had the opportunity to listen to Paul Churchland when he gave a talk last Friday, on Cognitive Enhancement, at the University of Texas at Dallas. He used the time to address, not enhancement drugs or exercises, but the enhancement effects of language and symbol. I poked around today to find more more on the […] I’ve thought that one of the reasons it’s difficult to resolve questions about the nature of mathematical reality is that we’re not exactly clear on what it means to ‘perceive’ something. Trying to establish whether or not even the data of our senses is somehow independently ‘real,’ has fueled centuries of philosophical debate. I found […] I just flipped back and forth between reading about 18th and 19th century developments in mathematics (analysis in particular) and 18th and 19th century transitions in art. The language of art history and the language of math history is very different. It does feel a little like going from color to black and white, or […] It’s easy to neglect the detail of one person’s, now historic, philosophical discussion of math and science. But there is a moment, in Henri Poincare’s well known text Science and Hypothesis, that I would like to shine a light on today. The first English translation of the book was published in 1905. Chapter IV is […] The first page of text in Morris Kline’s Mathematics and Western Culture quotes Descartes: …..I was not surprised that many people, even of talent and scholarship, after glancing at these sciences, have either given them up as being empty and childish or, taking them to be very difficult and intricate, been deterred at the very […] I like the word plasticity, the idea that something would be capable of being shaped or formed. It’s an optimistic word, pointing to the promise of change, or transformation (another word I like). Today I happened upon some of the work of Nancy Nersessian, Professor of Cognitive Science at the Georgia Institute of Technology. She’s […] I wrote not too long ago about the recording of the aftermath of particle collisions in ongoing high energy physics experiments. The post took note of the imaginative management of uncertainties (quantum mechanical uncertainties, measurement uncertainties and statistical errors). This hotbed of uncertainties is disentangled with the mathematics of probability. Mathematics here is being used […] |
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