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, […]

Numerosity, vision, language and mathematics

Understanding the neural functions that contribute to the birth of mathematical structure and meaning is an active subject of research in cognitive science.  A significant amount of work has been done to identify an innate ability we share with other creatures, namely the ability to perceive quantity.  This is sometimes called our approximate number sense.  […]

My article in +Plus Magazine

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

Pigeons, rats, monkeys and real numbers

I’d like today to stay on the topic of mathematics from the cognitive science perspective, and in particular, to make available another set of interesting studies summarized by C. R. Gallistel, Rochel Gelman and Sara Cordes. The studies are described in their contribution to the book Evolution and Culture (edited by Stephen C. Levinson and […]

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 […]

Riemann, angelfish and ants

I have recently spent some time sorting out the points Arkady Plotnitsky makes about the significance of Riemann’s notion of manifold (or manifoldness) in his paper which appeared in the journal Configurations in 2009.  The paper has the title Bernhard Riemann’s Conceptual Mathematics, and the Idea of Space.  It is refreshing in that it considers […]

Birds and the number 0

I’ve been working on an article that has me thinking about neuroscientifc studies on the cerebral representations of magnitude and it happened to be brought to my attention today that Irene Pepperberg spoke at the 2012 Francis Crick Memorial Conference on Consciousness in Animals.

Pepperberg is famous for having worked for many years with […]

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.   […]