Conversations with a Mathematician by Gregory Chaitin

Kolmogorov-Chaitin complexity measures the complexity of a bit string in terms of the length of the theoretical shortest program that could have produced it (actually determining whether a program is the shortest one is undecidable). You could say the entire book is about using this measure to probe whether the real line is actually real.

Watson center, is best known for co-inventing, along with Kolmogorov, a measure of computational complexity called Kolmogorov-Chaitin complexity.

You cannot write about this stuff without saying something about the 600 lb gorilla in the room, namely Stephen Wolfram’s A New Kind of Science and I will make a brief detour through that and the whole cellular automaton apporach in Part II.Ĭhaitin, a rather famous member of the rather famous IBM T. I am not competent to review (let alone summarize) these books, but I’ll lay out what I understand, why I think this direction of development is important, and what the gaps in my own understanding are, that perhaps you can help fill. In part III, for the physics/computation/information theory aspects, we’ll turn to Seth Lloyd’s Programming the Universe and Charles Seife’s Decoding the Universe. In this first part, for the mathematical foundations, I’ll talk about Gregory Chaitin’s Meta Math!: The Quest for Omega. I’ll talk about three books that develop this approach in an accessible manner, and about one formidable one that I think confuses the issues in pointless distracting ways. The debate has relevance even further afield, to questions about the nature of consciousness.

Not only must they reconstruct centuries of physics built on top of calculus (a fundamentally continuous sort of math) but to finish the job at a satisfying level, take on continuum mathematics itself and reconstruct it in discrete terms. Proponents of this view - called digital physics or nearly-equivalently, digital philosophy- take on not one but two terrifying tasks. Among the more radical suggestions for fixing physics is to get away from continuous models altogether and ask if the universe is fundamentally a discrete entity in some way. In a previous article, I reviewed some of the troubles ailing superstring theory, as chronicled by two prominent and articulate discontents.

Conversations with a Mathematician by Gregory Chaitin