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 […]

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 […]

Orientation through words and notation

I thought recently, again, about the relationship between the written word and mathematical notation, both being systems of marks that carry meaning. Both systems grow with usage, and both provide some steady refinement of what we are able to see. I’m not so much interested, here, in the relationship between mathematical proficiency and language proficiency, […]

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 […]

What we see when….

I recently listened to Krys Boyd’s interview with Peter Mendelsund, author of the new book What We See When We Read,  on North Texas’ public radio. Mendelsund is an award-winning book jacket designer. The interview had the effect of connecting his thoughts about reading to thoughts that I have had about mathematics. It wasn’t immediately […]

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 […]

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 […]

Quantum Mechanical Words and Mathematical Organisms

My post appeared on the Scientific American Guest Blog this morning.  Here’s the link:

Quantum Mechanical Words and Mathematical Organisms