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 – […]

The Gift of Steve Jobs

Contrary to the by-line, this post is by Bob not Joselle. She wanted me to post an item that’s been of interest lately.

As a reader of Mac and Apple rumor sites over the years, I was surprised the night of October 5th when I went to to show Joselle a news item which […]

Archimedes, particle accelerators and being visual

I feel like I was pulled into a little whirlpool of interesting bits of info this morning. I was attracted to the title of David Castelvecchi’s blog: Archimedes and Euclid? Like String Theory versus Freshman Calculus. The blog reports the opening of an exhibition at the Walters Art Museum in Baltimore, showcasing one of three […]

Grid cells and time cells in rats, continuity, and the monkey’s mind

I have often said that I get particular pleasure from mathematics that defies common sense expectations. A simple example would be the observation that two things can be the same size even though one of them is contained in the other – like the set of natural numbers and the set of positive even integers. […]

The Expressiveness of Number

For me, one of the more intriguing things that happened in mathematics is what is called the arithmetization of the Calculus. This is not because it contributes to my understanding of fundamental concepts (because it doesn’t). Nor is it because the ideas are exotic (they’re not). I’m captivated, instead, by what it may demonstrate about […]

The Origin of Concepts and Some Thoughts on Watson

Quite a lot of work is being produced by cognitive scientists about metaphor – what they are -what they do, how they shape thought – and I find it all interesting and provocative. The way in which metaphor shapes the way we see the world is the subject of James Geary’s book I Is an […]

Bernays, Wittgenstein and Imagination

I started today by taking a look at what might be the latest on what cognitive scientists were saying about mathematics. The broad scope of cognitive science includes the investigation of what Mark Turner calls (in the title of one of his books) “the riddle of human creativity.” When exploring the origins of conceptual systems, […]

Pauli, Jung, Matter and Symbol

In the first half of the twentieth century, physicists and mathematicians began to raise questions about what they could say about what they were actually doing. The ‘truth’ of things was beginning to elude the seekers of that truth. Both the validity of mathematical ideas and the objectivity of physics came under scrutiny. Questions about […]

The Imaginary Part: Not By Logic But By Intuition

I decided to write today a little more directly about mathematics. A book I’m working on led me to review a story I like very much, the incubation and birthing of the complex number. The story has been told many times (Dantzig’s Number and Nahin’s An Imaginary Tale to name just two). But most of […]