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 […]

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.  […]

More on category theory and the brain

I’ve referred to category theory on more than one occasion (particularly with respect to physicist Bob Coecke’s graphical language).  Not too long ago, Ronald Brown, at Bangor University, brought my attention to the work that he and colleagues have been doing to investigate the kind of mathematics that could be used to model the complexity […]

What can’t be sensed

Step by step, our ideas about the nature of our reality have moved far from the sensory constructions of space and time that define our immediate experience. And once fully outside the knowledge brought with sensation, we lose our footing.  It’s difficult to manage ‘what can’t be sensed.’  But our conceptual difficulties with quantum mechanics […]

What’s the tool, what’s the reality, what are we doing?

I am intrigued by the current debate in physics concerning the significance of the wave function in quantum theory.  The nature of the debate opens the door to a host of philosophical issues surrounding both physics and mathematics.  In an article appearing in the June issue of Scientific American, I was introduced to a relatively […]

Structure, structure and more structure

I was expecting to write about a paper I found recently by Oran Magal, a post doc at McGill University, On the mathematical nature of logic. I was attracted to the paper because the title was followed by the phrase Featuring P. Bernays and K. Gödel

I’m often intrigued […]

Embodied and dis-embodied meaning

I found a short paper today by Mark Andrews, Stefan Frank and Gabriella Vigliocco focused on reconciling two trends in the study of meaning in cognitive science.  These two trends are represented by embodied cognition theories (which treat meaning as a simulation of perceptual and motor states) and by computational or distributional accounts of meaning […]

The solstice, archaeoastronomy and mathematics

Given the arrival of the summer solstice and this post on the EarthSky website, I decided to write a little bit about what prehistoric monuments (like Stonehenge) suggest to me about some of the roots of mathematics.

With a photograph to support the claim, the EarthSky post tells us:

If you stood inside the Stonehenge […]

Category Theory and the extraordinary value of abstraction

Bob Coecke has received a grant of over $111,000 from the Foundational Questions Institute to continue his work on a graphical language to describe quantum mechanical processes.  The work is based on category theory, a branch of mathematics that focuses less on the mathematical objects themselves, and more on the maps that transform them. The […]