The idea that geometry in Gothic architecture was used to structure ideas, rather than the edifice itself, has come up before here at Mathematics Rising. But I would like to focus a bit more on this today because it illustrates something about mathematics, and mathematics’ potential, that the modern proliferation of information may be obscuring. […]
My last post focused on the kinds of problems that can develop when abstract objects, created within mathematics, increase in complexity – like the difficulty of wrapping our heads around them, or of managing them without error. I thought it would be interesting to turn back around and take a look at how the seeds […]
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 […]
I listened to a couple of interviews with Gregory Chaitin on the Closer to Truth website. They may have been part of TV episodes that I haven’t seen but I was actually invigorated by some of the things he said, and it made me want to share them.
One of the interviews (in two parts) […]
I recently considered the role that mathematics plays in bringing meaning, or perhaps even story, to our experience. Mathematics is often used to reveal the structure that can be found in large sets of data, or in any number of physical things that change over time, or in the properties of the abstractions themselves. Mathematics, […]
I followed a lead today that came at the end of Clifford Pickover’s The Math Book.
The last of Pickover’s 250 milestones in mathematics is Max Tegmark’s Mathematical Universe Hypothesis, which Tegmark published in 2007 in both scientific and popular articles. The hypothesis is that “our universe is not just described by mathematics – […]
Some of George Berkeley’s fame comes from his vehement critique of Newton’s calculus. His criticism was harsh and inspired a number of responses from contemporaries who accepted the vanishing quantities Newton used to formulate his notion of fluxions or, in modern terms, his understanding of instantaneous rates of change. The discussion that followed Berkeley’s 1734 […]
Let’s ask again, “What is the nature of the bridge between sense perceptions and concepts? It’s a simple question to ask, but a fairly difficult one to answer.
Raphael Nunez contributed a chapter to the Springer book, Recasting Reality: Wolfgang Pauli’s Philosophical Ideas and Contemporary Science. A pdf of the chapter can be found here. […]
I’ve become a bit preoccupied recently with the world of early 20th century mathematicians, partly because of a book I’m working on, but also because of how late 19th and early 20th century thinking largely defines the mathematics students learn today. In this light I found a book of selected writings of Hermann Weyl, a […]
The hoopla about Hawking’s new book made it frustratingly clear that there’s a real impasse in the centuries-old debate over whether science, and its intrinsic rationality, can or should definitively dispute religious ideas. The impasse is, I believe, a consequence of our not seeing the elephant in the room, namely ourselves. The debate proceeds, as […]