Orientation through words and notation

I thought recently, again, about the relationship between the written word and mathematical notation, both being systems of marks that carry meaning. Both systems grow with usage, and both provide some steady refinement of what we are able to see. I’m not so much interested, here, in the relationship between mathematical proficiency and language proficiency, […]

The mathematics of common sense

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 […]

Beauty, Passion and Computation

I listened to a couple of interviews with Gregory Chaitin on the Closer to Truth website. They may have been part of TV episodes that I haven’t seen but I was actually invigorated by some of the things he said, and it made me want to share them.

One of the interviews (in two parts) […]

What does our experience have to do with mathematics?

This is something of a follow-up to my last post. I checked out a series of links related to Max Tegmark in the last few days, having heard about the release of his first book Our Mathematical Universe. But I was also motivated by having observed that the latest conference organized by the Foundational Questions […]

Thinking as a churning, swarming activity

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 […]

Embodied and dis-embodied meaning

I found a short paper today by Mark Andrews, Stefan Frank and Gabriella Vigliocco focused on reconciling two trends in the study of meaning in cognitive science. These two trends are represented by embodied cognition theories (which treat meaning as a simulation of perceptual and motor states) and by computational or distributional accounts of meaning […]

Daniel Tammet and imagination

I recently got a copy of Daniel Tammet’s latest book, Thinking in Numbers. As you may know, Daniel Tammet has been described as a high functioning autistic savant. He gained some notoriety in 2004, when he recited the decimal expansion of pi to 22,514 places in just over 5 hours. You can see him do […]

Birds and the number 0

I’ve been working on an article that has me thinking about neuroscientifc studies on the cerebral representations of magnitude and it happened to be brought to my attention today that Irene Pepperberg spoke at the 2012 Francis Crick Memorial Conference on Consciousness in Animals.

Pepperberg is famous for having worked for many years with […]

Anosognosia, Consciousness and Mathematics

In last weeks post, I reported on the work of a computer scientist (Jürgen Schmidhuber’s artificial curiosity) and neuroscientist Gerald Edelman. I would like to follow-up a bit with more about Edelman’s work and perspective, in part because I was captivated by a story he told (in more than one venue) to illustrate the fact […]

Mathematics, movement, music and Leonardo

I’ve always been intrigued by the sensation of movement in music. And it is fair to say that it was my first calculus class that led me to graduate study in mathematics because, for the first time, I saw movement in mathematics. My fascination with each of these was nudged again by an interview with […]