Monday, February 26, 2007

Chaitin Series: *Conversations with a Mathematician*
Chaitin, Gregory J. Conversations with a Mathematician: Math, Art, Science and the Limits of Reason. London: Springer-Verlag, 2002.

I've been reading a lot about Gregory Chaitin lately, for various reasons. I find his mathematical work pretty admirable on its own and algorithmic information theory plays a pretty big part in my developing account of epistemology. The mathematics library around here has basically all of his books, so I figured I'd inaugurate a "Chaitin Series" and get through as many as I could (some of them seem pretty LISP heavy, which isn't much fun for light reading, but I'll try.)

So yesterday I finished Conversations with a Mathematician, which is a collection of interviews with and lectures by Chaitin. It's apparently available on his website, so I've linked to it up top. I found it pretty enjoyable overall. It definitely stays close to the light reading territory and so it doesn't really need a huge review. Chaitin mostly explains his work in mathematics as well as some of the philosophical implications he draws from his results. He certainly seems to be acquainted with philosophy, but most of this is pretty "armchair" in tone. That's not to say it's problem, I don't consider him obligated to be interested in the things I am, to the degree I am. He gestures towards a lot of stuff I'd like to be serious about like a mathematical theory of evolution, and information theoretical epistemology, but this means that I get to be the one who investigates this stuff. He's coming to a philosophy of mathematics that would render it as a quasi-empirical science, which I am tentatively comfortable with. Much of the book is devoted to slightly more personal topics like what being a mathematician is like. Some of his remarks about the nature of insight and the evolution of science are poetically spot-on.

There are a few problems. One is that since for each lecture and interview, he has to cover some basic ground, the book tends to be pretty redundant. It's skimable and short so there's not too big of a problem there. He switches back and forth a couple times between being overly cautious with the mathematics (like providing footnotes that explain what a real number is, as if he had a huge audience outside of the group of people who took algebra in high school) and occasionally blowing through some relatively hard to understand parts without much explanatory detail. Still, it's an entertaining read and it's pretty short, so I'd recommend it if you want a very light introduction to some of Gregory Chaitin's ideas or some thoughtful musings about what it means to do mathematics.

I've been reading a lot about Gregory Chaitin lately, for various reasons. I find his mathematical work pretty admirable on its own and algorithmic information theory plays a pretty big part in my developing account of epistemology. The mathematics library around here has basically all of his books, so I figured I'd inaugurate a "Chaitin Series" and get through as many as I could (some of them seem pretty LISP heavy, which isn't much fun for light reading, but I'll try.)

So yesterday I finished Conversations with a Mathematician, which is a collection of interviews with and lectures by Chaitin. It's apparently available on his website, so I've linked to it up top. I found it pretty enjoyable overall. It definitely stays close to the light reading territory and so it doesn't really need a huge review. Chaitin mostly explains his work in mathematics as well as some of the philosophical implications he draws from his results. He certainly seems to be acquainted with philosophy, but most of this is pretty "armchair" in tone. That's not to say it's problem, I don't consider him obligated to be interested in the things I am, to the degree I am. He gestures towards a lot of stuff I'd like to be serious about like a mathematical theory of evolution, and information theoretical epistemology, but this means that I get to be the one who investigates this stuff. He's coming to a philosophy of mathematics that would render it as a quasi-empirical science, which I am tentatively comfortable with. Much of the book is devoted to slightly more personal topics like what being a mathematician is like. Some of his remarks about the nature of insight and the evolution of science are poetically spot-on.

There are a few problems. One is that since for each lecture and interview, he has to cover some basic ground, the book tends to be pretty redundant. It's skimable and short so there's not too big of a problem there. He switches back and forth a couple times between being overly cautious with the mathematics (like providing footnotes that explain what a real number is, as if he had a huge audience outside of the group of people who took algebra in high school) and occasionally blowing through some relatively hard to understand parts without much explanatory detail. Still, it's an entertaining read and it's pretty short, so I'd recommend it if you want a very light introduction to some of Gregory Chaitin's ideas or some thoughtful musings about what it means to do mathematics.

Labels: book review, gregory chaitin

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