Mathematics Rising

In last weeks post, I reported on the work of a computer scientist (Jürgen Schmidhuber’s  artificial curiosity) and neuroscientist Gerald Edelman.   I would like to follow-up a bit with more about Edelman’s work and perspective, in part because I was captivated by a story he told (in more than one venue) to illustrate the fact [...]

Leibniz disassociated ‘substance’ from ‘material’ and reasoned that the world was not fundamentally built from material.  His is not simple or familiar reasoning but it was clear to Leibniz that for a substance to be real, it had to be indivisible and since matter was infinitely divisible, the true nature of reality could not be [...]

Yesterday I happened upon a Huffington Post blog from Mario Livio. For anyone who has been following my blog, it will come as no surprise that this piece, about the surprising similarity between spider webs and computer generated cosmic webs, caught my attention.  After showing us a few, Livio says: For an astrophysicist, perhaps the [...]

Given the arrival of the summer solstice and this post on the EarthSky website, I decided to write a little bit about what prehistoric monuments (like Stonehenge) suggest to me about some of the roots of mathematics. With a photograph to support the claim, the EarthSky post tells us: If you stood inside the Stonehenge [...]

Three things I read today converged in a way I had not anticipated and they all had something to do with truth.  First, there was the announcement of the Foundational Questions Institute’s 4th essay contest.  Entrants are invited to address this topic: Which of Our Basic Physical Assumptions Are Wrong?  Scientific American is a cosponsor [...]

The extent to which an idea in mathematics creates an idea in science is largely underappreciated.  It is common to think of mathematics as the tool that one needs to describe the reality explored by physics, as if the mathematics is secondary, or a purely linguistic consideration.  But it should be clear that this is [...]

Bob Coecke has received a grant of over $111,000 from the Foundational Questions Institute to continue his work on a graphical language to describe quantum mechanical processes.  The work is based on category theory, a branch of mathematics that focuses less on the mathematical objects themselves, and more on the maps that transform them. The [...]

I’ve spent a considerable amount of time thinking about how, if mathematics grows out of fundamental cognitive mechanisms, it provides opportunities for seeing more.  It is mathematics that allows for the tremendous expansion of empirical study – what we call science.  I had the opportunity, last week, to listen to a talk given by Craig [...]

On April 16 Scientificamerican.com reported on research that links hunting for words with foraging for food. Our brains may have evolved to forage for some kinds of memories in the same way, shifting our attention from one cluster of stored information to another depending on what each patch has to offer. Recently, Thomas Hills of [...]

Alain Connes is currently a professor at the College de France and Vanderbilt University.  Connes won the Fields Medal in 1982 and Crafoord Prize in 2001.  He has authored a number of books and represented the Platonist point of view in a debate with neuroscientist Jean-Pierre Changeux presented in the Princeton book: Mind, Matter and [...]