Continuity, randomness and the Oracle

Flipping through some New Scientist issues from this past year, I was reminded of an article in their July 19 issue that brought together a discussion of the brain and mathematics with particular emphasis on the effectiveness of employing the sometimes counter-intuitive notion of the infinity of the real numbers. The content of the article, […]

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 […]

Beauty, Passion and Computation

I listened to a couple of interviews with Gregory Chaitin on the Closer to Truth website. They may have been part of TV episodes that I haven’t seen but I was actually invigorated by some of the things he said, and it made me want to share them.

One of the interviews (in two parts) […]

Networks: The brain, the internet, and the cosmos

I was completely captivated by something David Deutsch said in a TED talk in 2005.  This particular observation was not the theme of his talk.  But I found the language he chose to describe the working model of the universe (that physics and mathematics have provided) to be loaded with implications about human knowledge, even […]

Chaitin, creativity, biology and mathematics

I was looking today, once again, at Gregory Chaitin’s most recent work which is described in his book Proving Darwin.  I realized that much of what has been written about this work (even what I have written) doesn’t give adequate attention to the crucial shifts in perspective that metabiology proposes. Chaitin says concisely:

According to […]

Kurzweil’s How to Create a Mind, and mathematics

I listened last week to Diane Rehm’s interview with Ray Kurzweil, author of the book “How to Create a Mind: The Secret of Human Thought Revealed”  A transcript of the interview can be found here.

Published in mid-November, it is already a New York Times bestseller, and some of the responses to it from prominent […]

Compression, meaning, and mathematics

One of the more interesting applications of algorithmic action can be seen in Jürgen Schmidhuber’s work on artificial curiosity.

Schmidhuber has been building what he calls ‘artificial scientists and artists’ that possess an algorithmic mechanism for motivating invention. He provides a brief and fairly straightforward description of his creative machines in the transcript of a […]

Spider webs and a random walk in software space

Yesterday I happened upon a Huffington Post blog from Mario Livio. For anyone who has been following my blog, it will come as no surprise that this piece, about the surprising similarity between spider webs and computer generated cosmic webs, caught my attention.  After showing us a few, Livio says:

For an astrophysicist, perhaps the […]

Quantum realities, decoding and computing

If one is paying attention, questions about the relationship between mathematics and reality just get more interesting.  Mathematician Alain Connes  is certainly the modern representation of the Platonic view that mathematical reality is a discoverable, fully existent reality.  But there is also the view from MIT cosmologist Max Tegmark that our physical world is not […]

Turing again, illuminating the path to an insight

I was still a graduate student when I first imagined that mathematics was actually outlining our cognitive potential (what we could see and understand).  I considered writing a paper called An Asymptotic Approach to a Theory of All the Things, convinced that as the mind grew it would continue to approach the reality behind perception, […]