Shared paths to Infinity

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 […]

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 […]

What mathematics can make of our intuition

The CogSci 2014 Proceedings have been posted and there are a number of links to interesting papers.

Here are some math-related investigations:

A neural network model of learning mathematical equivalence The Psychophysics of Algebra Expertise:  Mathematics Perceptual Learning Interventions Produce Durable Encoding Changes

Two Plus Three is Five:  Discovering Efficient Addition Strategies without Metacognition

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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 […]

The mathematics of common sense

I will be joining a few colleagues for a symposium at CogSci2014 and I’ve been gathering some notes for my talk.  The talk will focus on the impact of embodiment theories on a philosophy of mathematics.  As I looked again at some of the things I’ve chosen to highlight in my blogs, I came upon […]

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 […]

The Irrationality of Mathematics?

When I write, I often choose my words very carefully in order to remove any opportunity the reader might have to make a quick judgment about the content of what I am saying.  I’m hoping they will keep thinking about what I am saying.  The unexpected pairing of words often accomplishes this, and in this […]

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 […]

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 […]

Are we living in a mathematical object? And what might that have to do with religion?

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 – […]