I did some following up on the work of Vladimir Voevodsky and for anyone who might ask, “what’s actually going on in mathematics,” Voevodsky’s work adds, perhaps, even more to the mystery. Not that I mind. The mystery emerges from the limitless depths (or heights) of thought that are revealed in mathematical ideas or objects. […]
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An article in a recent issue of New Scientist highlights the potential partnership between computers and mathematicians. It begins with an account of the use of computers in a proof that would do little, it seems, to provide greater understanding, or greater insight into the content of the idea the proof explores. The computer program […] 
Can the presence of intelligent behavior in other creatures (creatures that don’t have a nervous system comparable to ours) tell us something about what ideas are, or how thought fits into nature’s actions? It has always seemed to us humans that our ideas are one of the fruits of what we call our ‘intelligence.’ And […] In a recent Scientific American article, the late physicist Victor Stenger, along with authors James A. Lindsay and Peter Boghossian argue that, while not acknowledged as such, some interpretations of quantum mechanics are implicitly platonic (with a lower-case p). We will use platonism with a lower-case “p” here to refer to the belief that the […] A recent post on Mind Hacks challenged the perspective outlined in a NY Times op-ed by psychologist Gary Marcus with the title Face It, Your Brain Is a Computer. The title of Marcus’ piece may be misleading. The brain/computer analogy that he proposes is more a strategy than a theory. But the rejection of brain/computer […] 
The Amazing World of MC Escher is a new exhibit at the Scottish National Gallery of Modern Art in Edinburgh. It will be there from June 27 to September 27. The exhibit prompted a nice piece on Escher in The Guardian. Author Steven Poole mentions, but does not much explore, the relationship between Escher’s work […] The analysis of collective behavior is quickly becoming cross-disciplinary. I wrote a few years ago about a study that analyzed the coordination of starling flocks. That post was based on the work of Thierry Mora and William Bialek, presented in their paper Are Biological Systems Poised at Criticality. The paper was published in the Journal […] Studies and insights into the nature of consciousness always get my attention. Inevitably I see mathematics in the discussion, tangentially or directly (as with Giulio Tononi’s qualia space). I’d like to outline, here, a particular train of thought that emerged after reading a couple of articles and a few papers. The first of these, written […] I read a short article on scientificamerican.com reporting on a recent advance in the investigation of the neural systems that support navigation, or our sense of direction. When I did some follow-up on the individual who led the study, I was surprised to find another interesting collaboration between scientists and artists. While the collaboration was […] A short article in the April 16 issue of New Scientist reported on an applied soft computing paper that proposes an improvement on what’s known as ‘particle swarm optimization (PSO). Particle swarm optimization (PSO) is an optimization technique inspired by the social behavior of birds. Described as a simple and powerful algorithm, it can be […] |
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