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 […]

Mathematics in the light of Maturana’s biology of cognition

As I have investigated all of the things in science and mathematics that get my attention, I have developed an impression of mathematics that, philosophically, seems most consistent with Humberto Maturana’s biology of language.  Maturana outlines his perspective in great detail in an essay by the same name that appeared in 1978 in the text […]

Where does mathematics live?

A Scientific American article brought mathematical knitting to my attention once again, and within the article was a link to Bridges, an organization which oversees the annual Bridges conference that explores the connections between art and mathematics.  Following the link to their 2013 Conference, I found their Short Movie Festival. I’ve watched a number of […]

What does our experience have to do with mathematics?

This is something of a follow-up to my last post.  I checked out a series of links related to Max Tegmark in the last few days, having heard about the release of his first book Our Mathematical Universe.  But I was also motivated by having observed that the latest conference organized by the Foundational Questions […]

Wasps, bees, faces and mathematics

An article in the December issue of Scientific American gave me a new insect behavior to ponder and one that might reveal, in the insect’s biology, a distant cousin to the mathematical idea we call mapping.  It seems that there are insects that have a talent for recognizing faces. Their talent has much in common […]

Sundials and mathematical action

Much of the research done in cognitive science is designed to study the development of concepts – internal representations that define the idea-driven nature of modern human experience.  And, in our experience, it’s difficult to mend the rift that’s been created between what we call thought and what we call reality.  But a number of […]

Embodied and dis-embodied meaning

I found a short paper today by Mark Andrews, Stefan Frank and Gabriella Vigliocco focused on reconciling two trends in the study of meaning in cognitive science.  These two trends are represented by embodied cognition theories (which treat meaning as a simulation of perceptual and motor states) and by computational or distributional accounts of meaning […]

Turing again, illuminating the path to an insight

I was still a graduate student when I first imagined that mathematics was actually outlining our cognitive potential (what we could see and understand).  I considered writing a paper called An Asymptotic Approach to a Theory of All the Things, convinced that as the mind grew it would continue to approach the reality behind perception, […]