Wednesday, November 24, 2010

Sense and self-indulgent nonsense

I recently referred - perhaps unfairly - to the propensity of many mathematicians and scientists to be naive and uncritical when thinking outside their areas of expertise. Of course, we are all inclined to be naive and uncritical at times, but the phenomenon is more striking in a person who exhibits high levels of critical thinking in a specialist area. My original observation was based in part on having read a lot of autobiographical and other material written by very gifted scientists and mathematicians and wondering why I found myself having to 'make allowances' for them.

The distinguished mathematician Gregory Chaitin is a case in point. Here are a few instances of the strange mix of sense and nonsense that flows from Chaitin's pen when he moves beyond the work which has made him famous. [All the quotations are from his book Meta Math! The quest for omega*.]

On medical care. "[I]n my grandmother's generation in the old country, women would have a dozen children, most of whom would die before puberty. So you were trying a dozen mixes of DNA subroutines from both parents. (In the Middle Ages, babies weren't even named til they were a year old, since so many of them would die the first year.) Now instead of trying to keep women pregnant all the time, we depend on massive amounts of medical care to keep alive one or two children, no matter how unhealthy they are. While such medical care is wonderful for the individual, the quality of the human gene pool inevitably deteriorates to match the amount of medical care that is available. The more medical care there is, the sicker people become! The massive amounts of medical care become part of the ecology, and people come to depend on it to survive ... "

On mathematical prehistory. "[F]undamental questions go back millennia and are never resolved. For example, the tension between the continuous and the discrete, or the tension between the world of ideas (math!) and the real world (physics, biology). You can find all this discussed in ancient Greece. And I suspect we could even trace it back to ancient Sumer, if more remained of Sumerian math than the scrap paper jottings on clay tablets that are all we have, jottings that give hints of surprisingly sophisticated methods and a love for calculation that seems to far outstrip any practical application."

Chaitin cannot resist a footnote: "Did Sumer inherit its mathematics from an even older civilization - one more advanced than the ancient Greeks - that was destroyed by the glaciers, or when the glaciers suddenly melted, or by some other natural catastrophe? There is no way for such sophisticated computational techniques to appear out of nowhere, without antecedents."

On ideas and creativity. "Let me describe what it feels like right now while I'm writing this book ... [T]he ideas I'm discussing seem very concrete, real and tangible to me. Sometimes they even feel more real than the people around me. They certainly feel more real than newspapers, shopping malls and TV programs ... In fact, I only really feel alive when I'm working on a new idea, when I'm making love to a woman (which is also working on a new idea, the child we might conceive), or when I'm going up a mountain! It's intense, very intense."

Chaitin elaborates and reiterates with references to beautiful women, art and food (" ... like an amazing ethnic cuisine I've never tasted before."). He continues:

"And I'm a great believer in the subconscious, in sleeping on it, in going to bed at 3 a.m. or 5 a.m. after working all night, and then getting up the next morning full of new ideas, ideas that come to you in waves while you're taking a bath, or having coffee. Or swimming laps. So mornings are very important to me, and I prefer to spend them at home. Routine typing and e-mail, I do in my office, not at home. And when I get too tired to stay in the office, then I print out the final version of the chapter I'm working on, bring it home - where there is no computer - and lie in bed for hours reading it, thinking about it, making corrections, adding stuff.

"Sometimes the best time is lying in bed in the dark with my eyes closed, in a half dreamy, half awake state that seems to make it easier for new ideas, or new combinations of ideas, to emerge. I think of the subconscious as a chemical soup that's constantly making new combinations, and interesting combinations of ideas stick together, and eventually percolate up into full consciousness. That's not too different from a biological population in which individuals ... combine to produce new individuals. My guess is that all this activity takes place at the molecular level - like DNA and information storage in the immune system - not at the cellular level. That's why the brain is so powerful, because that's where the real information processing is, at the molecular level. The cellular level, that's just the front end ...

"Yes, I believe in ideas, in the power of imagination and new ideas. And I don't believe in money or in majority views or the consensus. Even if all you are interested in is money, I think that new ideas are vital in the long run, which is why a commercial enterprise like IBM has a Research Division and has supported my work for so long. Thank you, IBM!"

It takes your breath away, does it not?

* Vintage Books, 2005