Plato, graphs, vision and another anchor

I’m not sure what led me to David Mumford’s Why I am a Platonist,  which appeared in a 2008 issue of the European Mathematical Society (EMS) Newsletter, but I’m happy I found it. David Mumford is currently Professor Emeritus at Brown and Harvard Universities. The EMS piece is a clear and straightforward exposition of […]

The continuity of things

I think often about the continuity of things – about the smooth progression of structure, that is the stuff of life, from the microscopic to the macrocosmic.  I was reminded, again, of how often I see things in terms of continuums when I listened online to a lecture given by Gregory Chaitin in 2008.  In […]

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 […]

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 […]

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 […]

Navigation cells, intent, and folded dimensions

I read a short article on reporting on a recent advance in the investigation of the neural systems that support navigation, or our sense of direction.  When I did some follow-up on the individual who led the study, I was surprised to find another interesting collaboration between scientists and artists. While the collaboration was […]

Representation, action, and mathematics

Today, I involved myself in a debate that hasn’t gotten very loud yet and, perhaps for that reason, I felt like I was going around in circles a bit. The questions I began trying to answer were sparked by a Mind Hacks post entitled Radical embodied cognition: an interview with Andrew Wilson. Wilson’s ideas challenge […]

Pattern, language and algebra

I’ve spent a good deal of time exploring how mathematics can be seen in how the body lives – the mental magnitudes that are our experience of time and space, the presence of arithmetic reasoning in pre-verbal humans and nonverbal animals, cells in the brain that abstract visual attributes (like verticality), the algebraic forms in […]

Continuity, randomness and the Oracle

Flipping through some New Scientist issues from this past year, I was reminded of an article in their July 19 issue that brought together a discussion of the brain and mathematics with particular emphasis on the effectiveness of employing the sometimes counter-intuitive notion of the infinity of the real numbers. The content of the article, […]

A mathematical philosophy – a digital view

I’ve become fascinated with Gregory Chaitin’s exploration of randomness in computing and his impulse to bring these observations to bear on physical, mathematical, and biological theories. His work inevitably addresses epistemological questions – what it means to know, to comprehend – and leads him to move (as he says in a recent paper) in the […]