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 […]

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 the experience of mathematical beauty could imply

Back in September, 1992 Semir Zeki wrote an article for what was then a special issue of Scientific American called Mind and Brain. In it he described what was known about how the brain produces visual images.  I have referred back to the article many times because it highlights the philosophical implications of our current […]

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 […]

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 […]

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 […]

Wigner, Persig, Leibniz and the nature of reality

I saw an opinion piece by Stephen Ornes, in the March 16 issue of New Scientist which ties the ongoing debate about the nature of mathematical ideas, to a modern one about money and ownership.  Ornes argues that patentability is one of the most hotly contested issues in software development.  The problem, as many see […]

Computational Linguistics, Matter and Meaning

Not long ago I wrote about the work of Bob Coecke, an Oxford University physicist, who is pioneering an application of category theory to quantum mechanics.  In that post I referred to the work he is also doing with language, using the same kind of graphic structures. I drew attention to the fact that category […]

That something out of nothing problem…

It seems that quite a number of categorical remarks got thrown around by Lawrence Krauss – about philosophers, theologians and physicists – in the discussions surrounding his recent book A Universe From Nothing.

But, as is often the case, these kinds of categorical judgments, that question the value of very different kinds of work, do […]