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 […]
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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 […] New Scientist published an article by Amanda Gefter in their August 15 issue which describes how and why the notion of infinity has come into question again. The distinction between a potential infinity (the process of something happening without end), and an actual infinity (represented, for example, by the set of real numbers) was disputed […] One of the reasons that the nature of mathematics has been such an enigma, is that we associate it with thought, and we tend to distinguish thought from the physical world. We do find mathematics in natural structures – some of these beautifully represented in a film you may have seen called Nature by the […] As I read more discussions of the relationship between mathematics and physics, I find that what mathematics might reveal about how physical science progresses becomes an increasingly interesting question. I recently found the text of a lecture given by Paul Dirac in 1939. It was reproduced on the occasion of the Dirac Centennial Celebration organized […] In the August issue of Scientific American, Meinard Kuhlmann addresses, yet again, the conceptual difficulties inherent in the interpretations of experimental data of modern physics. …the particle interpretation of quantum physics, as well as the field interpretation, stretches our conventional notions of “particle” and “field” to such an extent that ever more people think the […] I’ve referred to category theory on more than one occasion (particularly with respect to physicist Bob Coecke’s graphical language). Not too long ago, Ronald Brown, at Bangor University, brought my attention to the work that he and colleagues have been doing to investigate the kind of mathematics that could be used to model the complexity […] My piece on Riemann and cognition was published this week in +Plus. Here’s the link. A preview of a paper to be published in the journal eLife was provided by phys.org on June 23. Plants do sums to get through the night researchers show, was the title given their report. New research shows that to prevent starvation at night, plants perform accurate arithmetic division. The calculation allows them to use […] There was once what many call a ‘foundational crisis in mathematics’ – disputes among mathematicians about both their ideas and their methods. But while one needn’t now address the relationship between mathematics and reality in order to pursue a successful career in mathematics, the conceptual and experimental puzzles of modern physics likely reflect a similar […] |
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