Bill Clementson's Blog

Gregory Chaitin, Math, Philosophy and Lisp

Wednesday, June 16, 2004

A long time ago (several lifetimes in my mind), I majored in Mathematics at university (this was after majoring in Political Science and before majoring in Philosophy and Art History; but, never mind, I was majoring in Mathematics at one stage!). Although I never actually continued my studies in Mathematics, I still have a soft spot for it and will occasionally break open a math book just for kicks. So, when I came across a new book by a mathematician who is also a Lisp enthusiast, I couldn't resist it. Gregory Chaitin has just made available the electronic version of his soon-to-be-released book Meta Math! The Quest for Omega, a book that combines math, philosophy and Lisp. Ostensibly, it's about how he "discovered" the Omega number, but he describes what the book's really about in the Introduction: "It's about reasoning questioning itself, and its limits and the role of creativity and intuition, and the sources of new ideas and of new knowledge." Since this is a Lisp weblog, I'll not go into the math topics he discusses in his book. However, he does discuss Lisp (and it's role in his work) as well - his description of Lisp in the book is very nice: "Unfortunately, as programming languages become increasingly sophisticated, they reflect more and more the complexity of human society and of the immense world of software applications. So they become more and more like giant tool boxes, like garages and attics stuffed with 30 years of belongings! On the contrary, LISP is a programming language with considerable mathematical beauty; it is more like a surgeon's scalpel or a sharp-edged diamond cutting tool than a two-car garage overflowing with possessions and absolutely no room for a car. LISP has a few powerful simple basic concepts, and everything else is built up from that, which is how mathematicians like to work; it's what mathematical theories look like. Mathematical theories, the good ones, consist in defining a few new key concepts, and then the fireworks begin: they reveal new vistas, they open the door to entirely new worlds. LISP is like that too; it's more like pure math than most programming languages are. At least it is if you strip away the 'useful' parts that have been added on, the accretions that have made LISP into a 'practical tool'. What's left if you do that is the original LISP, the conceptual heart of LISP, a core which is a jewel of considerable mathematical beauty, austere intellectual beauty." Some additional interesting Chaitin Lisp facts for those who aren't familiar with his work: Gregory Chaitin has used Lisp in six of his books. He gave a lecture on "Elegant Lisp Programs" in Auckland, New Zealand. Chaitin has a web page with a Lisp interpreter that you can use to try out snippets of Lisp code from his books. (Note: the Java code for the applet is here and here) He explains "What is Lisp? Why do I like it?" in the Introduction to his Exploring Randomness book. In order to keep his software intellectually manageable, Chaitin would re-write all of his Lisp code from scratch each time he advanced in his understanding of a problem. In his book's conclusion, Chaitin talks about where new ideas come from - although his comments are specifically about math ideas, they hold true for innovative ideas in general: "This book is full of amazing case studies of new, unexpected math ideas that reduced the complicated to the obvious. And I've come up with a few of these ideas myself. How does it feel to do that? Well, you can't find them if you don't look for them, if you don't really believe in them. Is there some way to train for it, like a sport?! No, I don't think so! You have to be seized by a demon, and our society doesn't want too many people to be like that!" ... "So you're not going to be surprised to hear that I think that we desperately need new ideas about how human society should be organized, about what it's all for and how to live." Not your typical Math book, eh? But, what would you expect from someone who is a mathematician, a philosopher, and a Lisp enthusiast?