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 […]

“…an anchor in the cosmic swirl.”

Looking through some blog sites that I once frequented (but have recently neglected) I saw that John Horgan’s Cross Check had a piece on George Johnson’s book Fire in the Mind: Science, Faith, and the Search for Order. This quickly caught my attention because Horgan and Johnson figured prominently in my mind in the late […]

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 […]

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 […]