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On Wilczek and Symmetry (Inside and Out)

I had the opportunity to attend a talk given by Frank Wilczek, Nobel laureate in physics and author of the book The Lightness of Being. During the Q and A after the talk he was asked if our aesthetic judgment of symmetry could be said to prejudice scientific inquiry. Wilczek first pointed to the rich […]

Neuroscience and Riemann

I would like to go back today to Riemann, and the significance of his generalized notions of space and magnitude, but with an eye on what neuroscience may be adding to how mathematics gains its effectiveness.

In a recent post, I pointed to the influence the philosopher Herbart had on Riemann’s 1854 lecture in which […]

The Point of Intersection of Limit and Freedom

Mathematics today can seem an isolated discipline, removed from the questions of life and questions of meaning. But even a brief look at some of the writing of individuals like Leibniz, Weyl, and Poincare demonstrates substantial interest on the part of the mathematician to reconcile mathematics with common human experience. I remember one of my […]

Gauss, Riemann and Einstein: Neurons Reaching Behind Experience

I had the opportunity to listen to Paul Churchland when he gave a talk last Friday, on Cognitive Enhancement, at the University of Texas at Dallas. He used the time to address, not enhancement drugs or exercises, but the enhancement effects of language and symbol. I poked around today to find more more on the […]

Plato And Fish That Count

In a recent post I said that one of the things that dissuades us from accepting the existence of a truly Platonic mathematical world, or believing in the timeless existence of its forms independent of human minds, is the habit we have of distinguishing ourselves from the rest of nature, despite all the evidence we’ve […]

The Biology of Mathematics

The first page of text in Morris Kline’s Mathematics and Western Culture quotes Descartes:

…..I was not surprised that many people, even of talent and scholarship, after glancing at these sciences, have either given them up as being empty and childish or, taking them to be very difficult and intricate, been deterred at the very […]

The Fruits of Plasticity

I like the word plasticity, the idea that something would be capable of being shaped or formed. It’s an optimistic word, pointing to the promise of change, or transformation (another word I like). Today I happened upon some of the work of Nancy Nersessian, Professor of Cognitive Science at the Georgia Institute of Technology. She’s […]

Embodied Cognition

My attention was brought again today to cognitive scientists working in what has come to be called embodied cognition. My initiation into these ideas happened when I read the book Where Mathematics Comes From by George Lakoff and Rafael Núñez. The book explores mathematical ideas from the perspective that our bodies, living in their world, […]

Michelangelo and the Brain

I just read through a series of blogs generated by an article in the journal Neurosurgery, in which two neurosurgery researchers at Johns Hopkins University argue that an anatomically accurate image of the human brain is hidden in God’s neck in one of Michelangelo’s frescos. I was struck by how little the reports and blogs […]