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 […]

Where does mathematics live?

A Scientific American article brought mathematical knitting to my attention once again, and within the article was a link to Bridges, an organization which oversees the annual Bridges conference that explores the connections between art and mathematics.  Following the link to their 2013 Conference, I found their Short Movie Festival. I’ve watched a number of […]

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 […]

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 […]

Infinities, Tolstoy, dreams and Nabokov

My interest in mathematics is more personal than it is academic. I learned what I know formally, in the usual sequence of undergraduate and graduate math courses. But it has penetrated my personal life, and I have come to see mathematics as deeply rooted in a fundamental human drive to live more, or to live […]

Pollock, fractal expressionism and a mathematical thought

In a blog back in January, I referenced a talk given by David Deutsch in which he made the argument that, while empiricism has been the basis of science, empiricism alone is inadequate because scientific theories explain the seen in terms of the unseen.

What we see, in all these cases, bears no resemblance to […]

Dante, art, vision, and mathematics

We adopted a dog a couple of months ago, and there have been moments when I have watched a change in his attention or a change in his behavior, and wondered how his awareness might be structured.   When we drive with him, he usually sits in front of the back seats of our Honda Element, […]

Mathematics, movement, music and Leonardo

I’ve always been intrigued by the sensation of movement in music.  And it is fair to say that it was my first calculus class that led me to graduate study in mathematics because, for the first time, I saw movement in mathematics.  My fascination with each of these was nudged again by an interview with […]

Finding the quasicrystal

I read a few articles today that brought aesthetic and religious expression, mathematical curiosity, and physical discovery into contact.

A recent Physics World article reported that an architectural researcher found the first examples of perfect quasicrystal patterns in Islamic architecture.  Also known as Penrose tiles, these patterns were described mathematically by Roger Penrose in […]

Babies, sculpture and bowerbirds: A look at structural coupling

I have tried to make the argument, in some of the things I have written, that mathematics experiments with the ways we are able to ‘see.’  But there is a great deal of complexity in what it means ‘to see.’ ‘Seeing’ and ‘reasoning’ are not easily unraveled.  An infant’s ‘intuitive physics,’ the subject of recent […]