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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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Random Geometry

Random is often the word chosen to describe something that has no order. But randomness has become an increasingly useful tool in mathematics, a discipline whose meaningfulness relies, primarily, on order.

In statistics, randomness as a measure of uncertainty, makes possible the identification of events, whether sociopolitical or physical, with the use of probability distributions. […]

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 […]

Testable thoughts?

Quanta magazine has a piece on a recent conference in Munich where scientists and philosophers discussed the history and future of scientific inquiry. The meeting seems to have been mostly motivated by two things. The first of these is found in the diminishing prospects for physics experiments – energy levels that can’t be reached by […]

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, […]

“…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 […]

The continuity of things

I think often about the continuity of things – about the smooth progression of structure, that is the stuff of life, from the microscopic to the macrocosmic. I was reminded, again, of how often I see things in terms of continuums when I listened online to a lecture given by Gregory Chaitin in 2008. In […]

Physics, Plato and epistemology

In a recent Scientific American article, the late physicist Victor Stenger, along with authors James A. Lindsay and Peter Boghossian argue that, while not acknowledged as such, some interpretations of quantum mechanics are implicitly platonic (with a lower-case p).

We will use platonism with a lower-case “p” here to refer to the belief that the […]

Computations can be very natural

A recent post on Mind Hacks challenged the perspective outlined in a NY Times op-ed by psychologist Gary Marcus with the title Face It, Your Brain Is a Computer. The title of Marcus’ piece may be misleading. The brain/computer analogy that he proposes is more a strategy than a theory. But the rejection of brain/computer […]

Collective behavior: flocks, magnets, neurons and mathematics

The analysis of collective behavior is quickly becoming cross-disciplinary. I wrote a few years ago about a study that analyzed the coordination of starling flocks. That post was based on the work of Thierry Mora and William Bialek, presented in their paper Are Biological Systems Poised at Criticality. The paper was published in the Journal […]