Self-organizing, art, and mathematical mutants

Deciphering the principles of self-organizing systems is often at the heart of new ideas in biology, including neurobiology. A complex, self-organizing system contains a large

number of elements that have predictable, local interactions with each other, but these local interactions create global properties that cannot be predicted from even the most well-understood local events. This […]

Mathematical behavior without a brain?

I have made the argument on more than one occasion that a refreshed look at mathematics may help illuminate the relationship between our experience of the physical and our experience of the thoughtful. Mathematics is a discipline characterized by complex relations among abstract things but, as has been explored from many directions, the action of […]

The plasticity of grids, in our heads and otherwise

Familiar mathematical structure is found in the neural activity that governs how the body orients itself and navigates its environment. Grid cells are neurons, found in areas neighboring the hippocampus, whose individual firings line up in a coordinate-like pattern according to an animal’s movement across the full extent of its environment. Their grid pattern acts […]

The Mind of Arithmetic

I like finding what I believe are productive generalizations, or some sameness across apparently diverse events.  Often the subject of Mathematics Rising are things like the observation that we seem to search for words in patterns that resemble the trajectories of a rat foraging for food, or the possibility that natural language can be described […]

Number, insight, and the Riemann Hypothesis

The Riemann Hypothesis came to my attention again recently. More specifically I read a bit about the possibility that quantum mechanical measurements may provide a proof of a centuries-old hypothesis and one of mathematics’ most famous enigmas.

Within mathematics itself, without any reference to its physical meaning, the Riemann Hypothesis highlights the kind of […]

The difference between dreaming and being awake

I could go on for quite some time about the difference between dreaming and being awake.  I could see myself picking carefully through every thought I have ever had about the significance of dreams, and I know I would end up with a proliferation of questions, rather than a clarification of anything.  But I think […]

Points of view and a curve

Roger Antonsen came to my attention with a TED talk recorded in 2015 that was posted in November.  Characterized by the statement, “Math is the hidden secret to understanding the world,” it piqued my curiosity. Antonsen is an associate professor in the Department of Informatics at the University of Oslo. Informatics has been […]

Infinity is not the problem

An article published in May in Quanta Magazine had the following remark as its lead:

A surprising new proof is helping to connect the mathematics of infinity to the physical world.

My first thought was that the mathematics of infinity is already connected to the physical world. But Natalie Wolchover’s opening few paragraphs were inviting:


What’s the fuss about entropy?

In 2011 John Horgan posted a piece on his blog, Cross Check (part of the Scientific American blog network), with the title, Why Information can’t be the basis of reality. There Horgan makes the observation that the “everything-is-information meme violates common sense.” As of last December (at least) he hadn’t changed his mind. He referred […]

The promise of uncomputability

I just listened to a talk given by Virginia Chaitin that can be found on   The title of the talk is A philosophical perspective on a metatheory of biological evolution.   In it she outlines Gregory Chaitin’s work on metabiology, which has been the subject of some of my previous posts – here,  here, and […]