A mathematical philosophy – a digital view

I’ve become fascinated with Gregory Chaitin’s exploration of randomness in computing and his impulse to bring these observations to bear on physical, mathematical, and biological theories. His work inevitably addresses epistemological questions – what it means to know, to comprehend – and leads him to move (as he says in a recent paper) in the […]

Shakespeare, art, religion and mathematics

I recently considered the role that mathematics plays in bringing meaning, or perhaps even story, to our experience. Mathematics is often used to reveal the structure that can be found in large sets of data, or in any number of physical things that change over time,  or in the properties of the abstractions themselves.  Mathematics, […]

Scientific American Guest Blog Link

I’m planning to post something new this week, but I would also like to share the link to my guest blog for Scientific American that was posted last week.  The title of the piece is:  To What Extent Do We See With Mathematics?

Hope you enjoy it.

Are we finding the mathematical structure of reality?

I’m intrigued by Max Tegmark’s conviction that the universe is, itself, a mathematical structure.  He presented his ideas, again, on February 15 at the recent annual meeting of AAAS, in a symposium called Is Beauty Truth? He said that he has just completed a book on the same topic.  I listened to the entire session […]

Can we see where math begins and science ends?

Galileo is often called the father of modern science because of an insight he had about the relationship between mathematics, and what we are able to see in our world. Two of John Horgan’s recent blog posts (and the writing to which they refer) nicely demonstrate what I think is a remarkable oversight in discussions […]

Pollock, fractal expressionism and a mathematical thought

In a blog back in January, I referenced a talk given by David Deutsch in which he made the argument that, while empiricism has been the basis of science, empiricism alone is inadequate because scientific theories explain the seen in terms of the unseen.

What we see, in all these cases, bears no resemblance to […]

Julian Barbour, from metaphysics to mathematics to us

Julian Barbour is a theoretical physicist with a clear interest in tackling foundational issues and the errors of judgment that can lead physics theories astray.  One of these candidates for a mistaken judgment is time itself, and in 1999  Barbour authored the book The End of Time published by the Oxford University Press. He wrote […]

Leibniz’s Insight? Looking forward and back

Leibniz disassociated ‘substance’ from ‘material’ and reasoned that the world was not fundamentally built from material.  His is not simple or familiar reasoning but it was clear to Leibniz that for a substance to be real, it had to be indivisible and since matter was infinitely divisible, the true nature of reality could not be […]

Mathematics and the Higgs

In general, I tend to resist talking about the thing that everyone is talking about, but I find reason to make an exception today.  I do want to say something about yesterday’s announcement from physicists at the LHC that they saw the Higgs particle.  Frank Wilczek describes the significance of this observation (particularly nicely) in […]

The solstice, archaeoastronomy and mathematics

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 […]