Number, insight, and the Riemann Hypothesis

The Riemann Hypothesis came to my attention again recently. More specifically I read a bit about the possibility that quantum mechanical measurements may provide a proof of a centuries-old hypothesis and one of mathematics’ most famous enigmas.

Within mathematics itself, without any reference to its physical meaning, the Riemann Hypothesis highlights the kind of […]

Inquiries

A short article in the April 16 issue of New Scientist reported on an applied soft computing paper that proposes an improvement on what’s known as ‘particle swarm optimization (PSO).

Particle swarm optimization (PSO) is an optimization technique inspired by the social behavior of birds. Described as a simple and powerful algorithm, it can be […]

Golden variables

An article on physicsworld.com reported the discovery of variable stars whose periodic dimming and brightening frequencies have a ratio at or very near the golden ratio.

The objects were found in data from the Kepler space telescope by looking for stars with two characteristic pulsation frequencies that have a “golden ratio” of approximately 1.62. The […]

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 […]

Savants, neurons, and ants

Jason Padgett, author of the book Struck by Genius, appeared on CBS This Morning on April 24.  On May 5, livescience also did a piece on him and his book.  Padgett was assaulted in 2002 and suffered a severe concussion.  But, following this head injury, he acquired an extraordinary facility for seeing mathematics.  He is, […]

My article in +Plus Magazine

My piece on Riemann and cognition was published this week in +Plus.  Here’s the link.

Mental Magnitudes

I am increasingly fascinated by the mathematics of fundamental cognitive processes – like creatures finding their way to and from significant locations, or foraging for food, or foraging with the eyes, or comprehending the duration of an event. I’m excited by the fact that there are cognitive neuroscientists that have become focused on the architecture […]

Daniel Tammet and imagination

I recently got a copy of Daniel Tammet’s latest book, Thinking in Numbers. As you may know, Daniel Tammet has been described as a high functioning autistic savant.   He gained some notoriety in 2004, when he recited the decimal expansion of pi to 22,514 places in just over 5 hours.  You can see him do […]

Finger counting, finger gnosia and cerebral structures

In June The Guardian posted an interesting piece on finger counting and numbers.  The main content of the article concerns the work of cognitive scientists Andrea Bender and Sieghard Beller which explores the cultural diversity in finger counting.  It tells us that if asked to use you hands to count to 10, these variations will […]