Orientation through words and notation

I thought recently, again, about the relationship between the written word and mathematical notation, both being systems of marks that carry meaning. Both systems grow with usage, and both provide some steady refinement of what we are able to see. I’m not so much interested, here, in the relationship between mathematical proficiency and language proficiency, […]

Architecture, orientation and mathematics

Recently, I became intrigued with the discussions of topology that I found among architects and historians of architecture. I saw a few familiar threads running through these discussions – like the emergence and self-organizing principles of biology, together with the view that mathematics was not, primarily, a tool but more a point of view.

I […]

The mathematical nature of self-locating

A 2011 TED talk in London was brought to my attention recently. The speaker, Neil Burgess  from University College London, spoke on the topic, “How your brain tells you where you are.” Burgess investigates the role of the hippocampus in spatial navigation and episodic memory. In the talk he describes the function of what are […]

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 […]

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 […]

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 […]

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 […]