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 […]

A Look Back at Where Mathematics Comes From (reconciling the internal and the external)

I wanted to take a closer look at the Lakoff/Nuñez book Where Mathematics Comes From and its relationship to what has come to be called the embodied mind.  It seems to me that the biologists who pioneered embodiment had a more radical view of cognition than many of the cognitive scientists who use the paradigm.  […]

Cognition and Will

I see mathematics as associated with a searching, instinctual will, whose direction is shaped by our biology.   I find some of its roots in the way our visual system constructs what we see, or in the way grid cells (neurons lit by location) tell a rat where it is, or the way ants can find […]

Embodied Minds, Surfing and Mathematics

Mark Turner, cognitive scientist at Case Western Reserve, wrote an article that was recently posted on the Social Science Research Network entitled  The Embodied Mind and the Origins of Human Culture.  He makes the point that our awareness is divorced from “Almost all the heavy lifting in human thought and action,”  which is done “in […]