Mathematical behavior without a brain?

I have made the argument on more than one occasion that a refreshed look at mathematics may help illuminate the relationship between our experience of the physical and our experience of the thoughtful. Mathematics is a discipline characterized by complex relations among abstract things but, as has been explored from many directions, the action of […]

The plasticity of grids, in our heads and otherwise

Familiar mathematical structure is found in the neural activity that governs how the body orients itself and navigates its environment. Grid cells are neurons, found in areas neighboring the hippocampus, whose individual firings line up in a coordinate-like pattern according to an animal’s movement across the full extent of its environment. Their grid pattern acts […]

Where does the mind begin?

The slow and steady march toward a more and more precise definition of what we mean by information inevitably begins with Claude Shannon. In 1948 Shannon published The Mathematical Theory of Communication in Bell Labs’ technical journal. Shannon found that transmitted messages could be encoded with just two bursts of voltage – an on burst […]

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 […]

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 […]

Mathematics in the light of Maturana’s biology of cognition

As I have investigated all of the things in science and mathematics that get my attention, I have developed an impression of mathematics that, philosophically, seems most consistent with Humberto Maturana’s biology of language.  Maturana outlines his perspective in great detail in an essay by the same name that appeared in 1978 in the text […]

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 […]

Numerosity, vision, language and mathematics

Understanding the neural functions that contribute to the birth of mathematical structure and meaning is an active subject of research in cognitive science.  A significant amount of work has been done to identify an innate ability we share with other creatures, namely the ability to perceive quantity.  This is sometimes called our approximate number sense.  […]