Computations can be very natural

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 […]

Collective behavior: flocks, magnets, neurons and mathematics

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 […]

The end of science?

Paperback and electronic versions of John Horgan’s 1996 book, The End of Science, have recently been published by Basic Books. Horgan wrote a bit about how the text was received in 1996 on his weekly Scientific American blog. I read the book in 1996 and wrote to Horgan about the impact it had on me. […]

Golden variables

An article on physicsworld.com reported the discovery of variable stars whose periodic dimming and brightening frequencies have a ratio at or very near the golden ratio.

The objects were found in data from the Kepler space telescope by looking for stars with two characteristic pulsation frequencies that have a “golden ratio” of approximately 1.62. The […]

Embodiment and a Philosophy of Mathematics

Yesterday I gave a talk at a symposium at the 36th annual Cognitive Science Conference. The content of the talk was described this way in our symposium proposal:

Mathematics has been the subject of experimental studies in cognitive science that explore the sensory grounding of number and magnitude. But mathematics also provides conceptual schemes that […]

Gravitational waves, cathedrals and mathematics

In their March 22 issue, New Scientist reported on the recent detection of gravitational waves that are predicted by the inflationary theory in physics.  This observation could help reveal details of what the cosmos was like “in the first slivers of a second” following the big bang.  It supports the theory that implies the existence […]

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 […]

Love, Mathematics and the Universe

I just saw The Guardian’s Science Weekly podcast for November 11, 2013 which included a discussion with mathematician Edward Frenkel about his new book Love & Math:  The Heart of Hidden Reality. I then listened to a Huffington Live segment from January 7 where Max Tegmark and Brian Greene talked about the link between mathematics […]

Scientific American Guest Blog Link

I’m planning to post something new this week, but I would also like to share the link to my guest blog for Scientific American that was posted last week.  The title of the piece is:  To What Extent Do We See With Mathematics?

Hope you enjoy it.

New questions about infinity and how mathematics sees things

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 […]