Had I not studied mathematics, I would probably never have written the essay that follows. I wrote it 17 years ago but I decided to post it this holiday season. I hope you enjoy it. We were on our way home from daycare on a dark December evening. “Gook, mommy.” my two year old daughter yelled out, startled and excited. She spotted a house, unexpectedly lit around the edges with white Christmas lights. “Wow,” she sighed when we passed the next one. Trees and bushes had a new trick. “Pri-tee,” she finally said with a big smile. “Yes, Aiyanna” I said, “pretty.” Then came the full recognition that ..read more

I began a post in 2013 by recognizing something that David Deutsch said in a TED talk in 2005. I have referred back to it many times since, and here I will do it again.  But this time I would like to present it more completely. It’s a beautiful articulation of something that’s just true: Billions of years ago and billions of light-years away, the material at the center of a galaxy collapsed towards a supermassive black hole. And then intense magnetic fields directed some of the energy of that gravitational collapse, and some of the matter, back out in the form of ..read more

I’ve spent a number of years using this blog to highlight the way that mathematical things seem to operate in very natural occurrences like the way our brains work, the way ants navigate, the way plants calculate an efficient consumption rate of their stored starch, the collective behavior of insect colonies, flocks, schools, and so much more. I do this to counter the view that mathematics is merely a miraculously productive human tool. I believe that if we look at it more carefully, we will see that mathematics itself is part of nature, as are all aspects of our thoughtful and imaginative liv ..read more

I have spent quite a bit of time, using much of the information provided in these posts, to argue that mathematics is in a unique position to show us that our thoughts (the silent language in our heads) that appear to be produced in the privacy of our imagination, have some independent reality. By this I mean that our thoughts are not just ‘in our heads,’ and perhaps the use, and the history of mathematics (which reflects our science-oriented imagination) could help us understand something new, or see something new, about the fundamental nature of thought itself. I have written a yet unpublish ..read more

I came upon an MIT News article about the work of Ila Fiete who studies brain functions, like the neurological processes that govern navigational reasoning about our surroundings. Fiete uses computational and mathematical tools. Her interest in biology, and her respect for the “aesthetic to thinking mathematically,” (as she put it) led her to systems biology, where computational and mathematical analyses and modeling, are applied to the understanding of complex biological systems. She did most of her PhD research at MIT, ….where she studied how the brain uses incoming signals of the velocity ..read more

A New Scientist article began with a now familiar refrain: They call it the “unreasonable effectiveness of mathematics.” Physicist Eugene Wigner coined the phrase in the 1960s to encapsulate the curious fact that merely by manipulating numbers we can describe and predict all manner of natural phenomena with astonishing clarity… The article by Michael Brooks has the title Is the universe conscious? It seems impossible until you do the maths. As I expected, the primary focus of the article is Integrated Information Theory, a way to understand consciousness proposed by neuroscientist Giulio Ton ..read more

Category theory in mathematics is a relatively new and provocative branch of mathematics that has found many faithful followers and some critics. By relatively new I mean that category theory notions were first introduced only as far back as 1945. Criticism of the theory is often related to the level of abstraction it requires. But abstraction is also critically important to its strength. I’ve chosen to highlight things about category theory in these earlier posts: Category Theory and the extraordinary value of abstraction More on category theory and the brain Quantum Mechanical Words and Mat ..read more

A recent column in Quanta Magazine, by theorist Seam Carroll, highlights the far reaching implications of the role played by probability theory in quantum mechanics. Carroll’s intention is to bring into focus the need, which does seem to exist, for us to understand what, exactly, those probabilities are telling us. In quantum mechanics, the partnership of mathematics and physics has the unusual effect of both clarifying and mystifying things. Carroll’s concern is whether the probabilities that seem to contradict long held deterministic views of the physical world, should be thought of as pro ..read more

If you were listening, the season brought the usual surge of Christmas music through all manner of electromagnetic transmission, wired and wireless, causing me to remember again my mild preoccupation with one tune in particular, namely – Do You Hear What I Hear? For the past few years I found myself listening more closely to the lyrics of this piece because, for me, they created an image related to the many things I have written about mathematics and cognition. I decided this year to try to pin down my thoughts more clearly, and share them. The song describes the ‘transfer of informat ..read more

Another article about physics and mathematics by Natalie Wolchover, published in both Wired and Quanta Magazine, got my attention because it began like this: In late August, paleontologists reported finding the fossil of a flattened turtle shell that “was possibly trodden on” by a dinosaur, whose footprints spanned the rock layer directly above. The rare discovery of correlated fossils potentially traces two bygone species to the same time and place. Cosmologist Nima Arkani-Hamed makes the connection: Paleontologists infer the existence of dinosaurs to give a rational accounting of s ..read more