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 [...]

I have recently spent some time sorting out the points Arkady Plotnitsky makes about the significance of Riemann’s notion of manifold (or manifoldness) in his paper which appeared in the journal Configurations in 2009.  The paper has the title Bernhard Riemann’s Conceptual Mathematics, and the Idea of Space.  It is refreshing in that it considers [...]

In 2011, Science Daily reported on a study done at Queen Mary University of London and published in Biology Letters.  The study examined the foraging strategies of bumblebees and found that “after extensive training (80 foraging bouts and at least 640 flower visits), bees reduced their flight distances and prioritized shortest possible routes.” The bees [...]

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 [...]

Mathematics is usually thought of as a tool that quantifies things in our lives and there is good reason for this.  Early in our experience, it is presented to us as a counting and measuring device, not as a way to see something.   But this characterization of mathematics is misleading.  Quantification alone would not get [...]

In another blogging heads interview (and in a related blog), John Horgan explores with David Rothenberg the significance of beauty in scientific thinking.  Rothenberg’s new book Survival of the Beautiful, is the subject of much of their discussion.  While the conversation centers on questions of beauty (how biology does or does not take it into [...]

I have often said that I get particular pleasure from mathematics that defies common sense expectations.  A simple example would be the observation that two things can be the same size even though one of them is contained in the other – like the set of natural numbers and the set of positive even integers.   [...]

A number of websites have reported on a recent study, that correlated innate number sense with mathematical ability.  A concise report of the study can be found in the Johns Hopkins University Gazette, published by the institution where the study was done.  The study’s results confirm a correlation between the strength of ones number sense [...]

I found myself tied a bit to the theme of last week’s blog when my attention was brought to a very recent article in PLoS Biology called Darwin in Mind: New Opportunities for Evolutionary Psychology.  In it a team of biologists, psychologists and philosophers from the Netherlands, the United States and Scotland, suggest that the [...]

NPR recently hosted an interview with Dean Buonomano, neuroscientist and author of the book Brain Bugs: How The Brain’s Flaws Shape Our Lives. I usually like evolutionary perspectives, and enjoy thoughts on how our experience, however abstract and complex it may seem, is somehow built on the biological stuff of our world. But the best [...]