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Genesis of a Historical Novel

Friday, January 05, 2007

the quest for omega

We woke to snowfall. Wet snow has fallen all day. I shoveled the heavy, translucent stuff from the sidewalks in front of our building. Now I hear trickling sounds and a couple of drumbeats of drops falling outside.

Yesterday was sunny and clear, with a chill wind blowing from the west. Kimmie and I walked in the neighborhood called Norgate Park, an anomalously flat district of North Vancouver resting on the apron of land just inland of the industrial foreshore. Small ranch-style houses rest on little lots in a labyrinth of cul-de-sacs.

Then, while Kimmie shopped for ribbon at Fabricland, I got myself two packages of highlighters at Staples and headed into the newly opened Indigo Books store on the lower level of Park Royal's south mall. Kim and I agree that this store is not very good--barely an improvement over the Coles Books store (also owned by Indigo) located nearby and shut down to make way for this new operation, even though this new store is much bigger. For all its size, it has only one small alcove, maybe 10% of the store, containing books of any interest to me (history, science, political science). The rest of the store seems to be filled with children's book, teens' books, notebooks, cookbooks, diet books, self-help books, and of course fiction: long rows of this in the main open area of the store.

Browsing without much interest the science section, a small book caught my eye: Meta Math!: The quest for Omega by Gregory Chaitin. I was drawn by the name of the author, with which I was familiar from reading books by the mathematician Rudy Rucker. I picked up the book and flipped through it. Yeah, some equations, some demonstrations set off in boxes, and a writing style that appeared to make heavy use of exclamation marks and bold type.

"What is this omega anyway?" I thought. The back flap blurb described it as "an exquisitely complex representation of unknowability in mathematics." Hmm, sounded promising.

I thought back to February 1990, when I was laid up at home with pneumonia. I was so weak I could hardly get up off the sofa. But to have variety in my life, I got out of bed in the morning, made my way downstairs to lie on the sofa, and then climbed back up to bed at night. The infection had me running a fever much of the time. If I'd been unable to read, it would have been very boring. But I find that a (mild) fever actually heightens my concentration and alertness, so I was in good condition to read. Even though I was sick, I decided it was a good opportunity to try making it all the way through Rudy Rucker's Infinity and the Mind, which I'd bought back in 1984.

I was completely absorbed, and able to read the book all the way through during my illness. In it he makes mention of Gregory Chaitin along with other important 20th-century mathematicians such as Kurt Gödel and Alan Turing. (He brings in Turing and Chaitin much more in a subsequent book, Mind Tools.) These thinkers have concerned themselves with questions such as how much can be known or discovered in mathematics--finding the limits of formal mathematical systems. It may sound obscure, but it has important implications for digital computers, which are now the primary machine of our world.

As is my custom, I made a point of starting this book (despite 10 or so competitors in my coffee-table reading stack) when I got home. I was surprised and pleased to find this paragraph on the first page of the preface:

Science is an adventure. I don’t believe in spending years studying the work of others, years learning a complicated field before I can contribute a tiny little bit. I prefer to stride off in totally new directions, where imagination is, at least initially, much more important than technique, because the techniques have yet to be developed. It takes all kinds of people to advance knowledge, the pioneers, and those who come afterwards and patiently work a farm. This book is for pioneers!

Embroiled as I am in research (admittedly not mathematical or scientific), "studying the work of others," I felt heartened and stimulated by this. I really liked Chaitin's excited attitude--altogether unexpected from this longtime computing sage who has worked for IBM forever and is the pioneer of the daunting-sounding field of "information mechanics".

Yes, infinity is one of those things I kind of keep tabs on. It's a very important concept, at the very least. The big question is whether it is anything more than a concept--whether infinity denotes something actual. My own hunch is that it does indeed, and that the workers on infinity--all the many different infinities, infinitely many of them, in fact--are studying important properties of the world we live in. I believe, in fact, that the study of infinity is a form of exact theology: where the tools of mathematics are applied to the divine, the numinous.

Hmm. Maybe I'll venture a bit further myself on the quest for Omega...

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