Thinking without a brain

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 […]

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 […]

Bees, art, consciousness and mathematics

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 […]


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 […]

The mathematical nature of self-locating

A 2011 TED talk in London was brought to my attention recently. The speaker, Neil Burgess  from University College London, spoke on the topic, “How your brain tells you where you are.” Burgess investigates the role of the hippocampus in spatial navigation and episodic memory. In the talk he describes the function of what are […]

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 […]

Savants, neurons, and ants

Jason Padgett, author of the book Struck by Genius, appeared on CBS This Morning on April 24.  On May 5, livescience also did a piece on him and his book.  Padgett was assaulted in 2002 and suffered a severe concussion.  But, following this head injury, he acquired an extraordinary facility for seeing mathematics.  He is, […]

Wasps, bees, faces and mathematics

An article in the December issue of Scientific American gave me a new insect behavior to ponder and one that might reveal, in the insect’s biology, a distant cousin to the mathematical idea we call mapping.  It seems that there are insects that have a talent for recognizing faces. Their talent has much in common […]

The thought behind it

The most recent issue of New Scientist has an article called Thoughts: The inside story.  In it, philosopher Tim Bayne begins with a survey of all of the things we mean by the word ‘thought’ – the mental activity that accompanies perceptions, problem solving, the integration of various perceptions, the uncontrolled associative train of connected […]

Pufferfish, bowerbirds and pragmatism

One of the reasons that the nature of mathematics has been such an enigma, is that we associate it with thought, and we tend to distinguish thought from the physical world.   We do find mathematics in natural structures – some of these beautifully represented in a film you may have seen called Nature by the […]