Meta Math!: The Quest for Omega

Picked this off the shelf at Dymocks on Sunday never having heard of this guy. Needless to say, I finished it Monday morning and I am now a Chaitin convert. He is dead right that Godel's theorem is hard to follow told in the normal context and it much much clearer told from an information theoretic perspective. Has opened me up to a new vista of how to think about all these things (probability, randomness, completeness, inference, reconstruction, compression, theory, models, etc. etc...).

A very clear introduction to the main ideas of algorithmic complexity and how they connect with epistemology. The basic idea is that there are certain facts that cannot be explained in the sense that any explanation is provably more complex than the facts themselves. A very nice feature of this book is Chaitin's enthusiasm for doing mathematics and the sense of elation, adventure and discovery (as opposed to rule following) that goes with it. The idea that insight comes first and proof later and that insight is hard hard work that, when reached, brings great great joy.

The guru's latest explanation for non-expert readers of his randomness (and algorithmic-information-theory) approach to the incompleteness of mathematics. On computer science, he concludes that "proving correctness of software using formal methods is hopeless" and that software design can't be completed prior to implementation. Edsger Dijkstra may be turning over in his grave.

I want to read this book but I'm put off by the amount of exclamation marks. I do like enthousiasm but this is overdoing it.

Algorithmic complexity can not be reliably determined! Whoa. There goes several attempts at formal software development cycles.