Finding hidden structure by way of computers

An article in a recent issue of New Scientist highlights the potential partnership between computers and mathematicians. It begins with an account of the use of computers in a proof that would do little, it seems, to provide greater understanding, or greater insight into the content of the idea the proof explores. The computer program […]

Physics, Plato and epistemology

In a recent Scientific American article, the late physicist Victor Stenger, along with authors James A. Lindsay and Peter Boghossian argue that, while not acknowledged as such, some interpretations of quantum mechanics are implicitly platonic (with a lower-case p).

We will use platonism with a lower-case “p” here to refer to the belief that the […]

M.C. Escher’s visual inquiries

The Amazing World of MC Escher is a new exhibit at the Scottish National Gallery of Modern Art in Edinburgh. It will be there from June 27 to September 27. The exhibit prompted a nice piece on Escher in The Guardian. Author Steven Poole mentions, but does not much explore, the relationship between Escher’s work […]

Poe’s cosmology

A post from John Horgan with the title Did Edgar Allan Poe Foresee Modern Physics and Cosmology? quickly got my attention. Horgan writes in response to an essay by Marilynne Robinson in the February 5 New York Review of Books where Poe’s book-length prose poem Eureka was brought to his attention. Eureka was written by […]

Reanimating the living world

Each year, Edge.org asks contributors to respond to their annual question. In 2014, the question was: What scientific idea is ready for retirement? There were 174 interesting responses, but one that got my attention was written by Scott Sampson (author, Dinosaur Odyssey: Fossil Threads in the Web of Life). The idea that Sampson would like […]

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 […]

Architecture, orientation and mathematics

Recently, I became intrigued with the discussions of topology that I found among architects and historians of architecture. I saw a few familiar threads running through these discussions – like the emergence and self-organizing principles of biology, together with the view that mathematics was not, primarily, a tool but more a point of view.

I […]

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 […]

Embodiment and a Philosophy of Mathematics

Yesterday I gave a talk at a symposium at the 36th annual Cognitive Science Conference. The content of the talk was described this way in our symposium proposal:

Mathematics has been the subject of experimental studies in cognitive science that explore the sensory grounding of number and magnitude. But mathematics also provides conceptual schemes that […]