Mathematics Rising

As a brief follow-up to my last post, I reread some pages in Tobias Dantzig’s book Number and, on one of them, he is critical of early 20th century formalists when he says about symbols in mathematics: To me the tremendous importance of this symbolism lies not in these sterile attempts to banish intuition from [...]

I often get stuck in the gap we rarely notice between the word and what the word is meant to signify.   Do we really understand what word and symbol actually do?  Or, even more to the point, can we see what the body is accomplishing in the evolution of these cognitive tools? In a film [...]

Most of us begin drawings with lines.  And even though those lines may not be in the subject of a rendering, they are nonetheless perceived.  Some of the visual information we use to re-present our experience in a drawing is also used in mathematics, geometry in particular.  A difficult question to answer  but an interesting [...]

I just heard Radiolab’s show on words (you can listen here).   The show explores just how much of our experience is born of language.  It begins with experiments which seem to reveal that until we can bridge islands of our experience with phrases, we can’t actually think.  This may be a difficult argument to make [...]

The story of online gamers solving protein structure problems for biochemists has been reported by many, including the New York Times, NPR’s 360, Youtube, and a host of blogs.  The gamers, by using their three-dimensional puzzle solving skills, have made significant contributions to biochemical research. The problem for biochemists is predicting the shape that a [...]

This may not be a timely commentary, but I only recently read the book Naming Infinity (Harvard University Press 2009). It was a gift from my husband who rightly expected that I would be interested in a book purported to be about how mathematicians were supported through a conceptual crisis by the bold work of [...]

It has been understood for some time that metaphor provides a sensory anchor to abstract ideas.  But, more recently, cognitive psychologists have looked at how active the role of metaphor may be in thinking.  In a recent article on Boston.com, experiments are cited which explore the extent to which metaphor shapes thought. The article cites [...]

Now we can identify the number the brain is identifying! An article in Science News reports on how neuroscientists are able to determine the quantity of dots a person is looking at by looking at their brain activity patterns using an MRI. The study also revealed that the patterns that correspond to some number of [...]

Our family lived in France for the last six months and at the end of that time we had the chance to visit family in Florence. Since we drove to Florence we could stop at Pisa along the way.  I found Galileo all around me. Dava Sobel’s book, Galileo’s Daughter, once drew me in and [...]

I hope to use this blog to find new things to see about mathematics.  And this might even have some effect on how we see ourselves. I want to start with something Henri Poincare said. Poincare was an intellectual heavyweight, a mathematician, theoretical physicist, and philosopher. He was the last person to be able to [...]