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:

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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 academia.edu.   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 […]

The conceptual plasticity of ancient Babylonian astronomers

A recent discovery in the history of science and mathematics has prompted a number of articles, links to which are provided at the end of this text. Astrophysicist and science historian Mathieu Ossendrijver, of Humboldt University in Berlin, made the observation that ancient Babylonian astronomers calculated Jupiter’s position from the area under a time-velocity graph. […]

Plato, Gödel and quantum mechanics

I’ve been reading Rebecca Goldstein’s Incompleteness: The Proof and Paradox of Kurt Gödel which, together with my finding David Mumford’s Why I am a Platonist, has kept me a bit more preoccupied, of late, with Platonism. This is not an entirely new preoccupation. I remember one of my early philosophy teacher’s periodically blurting out, “See, […]

Plato, graphs, vision and another anchor

I’m not sure what led me to David Mumford’s Why I am a Platonist,  which appeared in a 2008 issue of the European Mathematical Society (EMS) Newsletter, but I’m happy I found it. David Mumford is currently Professor Emeritus at Brown and Harvard Universities. The EMS piece is a clear and straightforward exposition of […]

“…an anchor in the cosmic swirl.”

Looking through some blog sites that I once frequented (but have recently neglected) I saw that John Horgan’s Cross Check had a piece on George Johnson’s book Fire in the Mind: Science, Faith, and the Search for Order. This quickly caught my attention because Horgan and Johnson figured prominently in my mind in the late […]