Mathematics Rising

Things happen in nature.  Cells socialize and build structure, organisms grow, and move, and interact, and then more things grow – like music, language, and mathematics. Generally, talk about evolution is very pragmatic.  Cell organization, the shaping of roots, leaves, nourishment mechanisms, reproductive drives, are all usually understood as fairly specific purposeful processes.  Perhaps by [...]

One of the points I wanted to make in last week’s post was that studies in animal cognition suggest the presence of mathematics in the behavior of non-human species – the ants, for example, who can be seen to pass on quantitative information to other ants. We don’t see the mathematics they may be doing [...]

I found a short paper today by Mark Andrews, Stefan Frank and Gabriella Vigliocco focused on reconciling two trends in the study of meaning in cognitive science.  These two trends are represented by embodied cognition theories (which treat meaning as a simulation of perceptual and motor states) and by computational or distributional accounts of meaning [...]

Not long ago I wrote about the work of Bob Coecke, an Oxford University physicist, who is pioneering an application of category theory to quantum mechanics.  In that post I referred to the work he is also doing with language, using the same kind of graphic structures. I drew attention to the fact that category [...]

This blog is motivated in part by my conviction that life itself is far more mysterious than we are yet able to ponder.  And it is mathematics that has often redirected my attention back to that mystery as its wealth of conceptual possibilities shows me more of what we don’t understand.  David Deutsch very nicely [...]

The following exchange between M.P. Schutzenberger and A. Connes is lifted from the book Triangle of Thoughts: M. P. S. — …language begins with poetry rather than with grammar; euphony plays a big role here. A. C. — Your point of view coincides with my own, since I sincerely believe that music is at its [...]

The hoopla about Hawking’s new book made it frustratingly clear that there’s a real impasse in the centuries-old debate over whether science, and its intrinsic rationality, can or should definitively dispute religious ideas.  The impasse is, I believe, a consequence of our not seeing the elephant in the room, namely ourselves.  The debate proceeds, as [...]

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 [...]

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 [...]