The continuity of things

I think often about the continuity of things – about the smooth progression of structure, that is the stuff of life, from the microscopic to the macrocosmic. I was reminded, again, of how often I see things in terms of continuums when I listened online to a lecture given by Gregory Chaitin in 2008. In […]

Thinking without a brain

Can the presence of intelligent behavior in other creatures (creatures that don’t have a nervous system comparable to ours) tell us something about what ideas are, or how thought fits into nature’s actions? It has always seemed to us humans that our ideas are one of the fruits of what we call our ‘intelligence.’ And […]

Computations can be very natural

A recent post on Mind Hacks challenged the perspective outlined in a NY Times op-ed by psychologist Gary Marcus with the title Face It, Your Brain Is a Computer. The title of Marcus’ piece may be misleading. The brain/computer analogy that he proposes is more a strategy than a theory. But the rejection of brain/computer […]

Representation, action, and mathematics

Today, I involved myself in a debate that hasn’t gotten very loud yet and, perhaps for that reason, I felt like I was going around in circles a bit. The questions I began trying to answer were sparked by a Mind Hacks post entitled Radical embodied cognition: an interview with Andrew Wilson. Wilson’s ideas challenge […]

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 […]

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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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 […]

What the experience of mathematical beauty could imply

Back in September, 1992 Semir Zeki wrote an article for what was then a special issue of Scientific American called Mind and Brain. In it he described what was known about how the brain produces visual images. I have referred back to the article many times because it highlights the philosophical implications of our current […]

A continuum of senses

I was intrigued by a paper that came to my attention in the December 2013 issue of Philosophical Studies by Anna Farennikova in which she argues that we ‘see’ absence. In other words, seeing that something is not there is as much a product of our visual system as seeing an object. The example with […]

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 […]