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. […]
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 […]
A paper by Virginia Chaitin was recently brought to my attention. She is currently a Post-Doc at the Univeridade Federal do Rio de Janeiro, with research interests that include, among others, the history and philosophy of science, epistemology, and interdisciplinarity. The paper I just read, Metabiology, Interdisciplinarity and the Human Self-Image, focuses on the kind […]
Today, I involved myself in a debate that hasn’t gotten very loud yet and, perhaps for that reason, I felt like I was going around in circles a bit. The questions I began trying to answer were sparked by a Mind Hacks post entitled Radical embodied cognition: an interview with Andrew Wilson. Wilson’s ideas challenge […]
Flipping through some New Scientist issues from this past year, I was reminded of an article in their July 19 issue that brought together a discussion of the brain and mathematics with particular emphasis on the effectiveness of employing the sometimes counter-intuitive notion of the infinity of the real numbers. The content of the article, […]
I’ve become fascinated with Gregory Chaitin’s exploration of randomness in computing and his impulse to bring these observations to bear on physical, mathematical, and biological theories. His work inevitably addresses epistemological questions – what it means to know, to comprehend – and leads him to move (as he says in a recent paper) in the […]
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 will be joining a few colleagues for a symposium at CogSci2014 and I’ve been gathering some notes for my talk. The talk will focus on the impact of embodiment theories on a philosophy of mathematics. As I looked again at some of the things I’ve chosen to highlight in my blogs, I came upon […]
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 did an article in their February 6 issue called Mind Maths: Five laws that rule the brain.
As is usually the case, the article’s allure is the suggestion that new research may hold the promise of capturing the brain’s complexity in just a few mathematical models. And, as is usually the case, I […]