into and beyond logic
This past week, D. Eric Smith, a resident researcher at the Santa Fe Institute, spoke at my university about the beginning of life on Earth. His talk was compelling, and although his talk was directed at a scientifically-literate general audience including undergraduates and faculty, his background and work betray extensive breadth and depth of thought.
I had an opportunity to talk with Eric earlier in the day about my potential interest in developing an introductory undergraduate course on complexity theory or self-organization. He suggested Jaynes’ book on probability theory as a good starting point for the course, a way to efficiently clear up some misconceptions about design, causality, reductionist approaches in science, and statistical mechanics. It’s been awhile since I have really done math; my undergraduate physics degree from Harvey Mudd and my graduate physics coursework at UC Berkeley were relatively math-intensive, but since 1993 my work has been primarily in qualitative-study-leaning subjects such as music (the quadrivium notwithstanding). So I knew I was going to be in for a challenge.
I checked out Jaynes’ book from our library, and it remains to be seen how far I will be able to work my way through it, but to this point, the effort required is certainly worth it. (I’ll probably end up buying my own copy, so I can write in it…)
The book explores logic and probability theory and connects them (or will connect them) to how we as people work with plausibility. In other words, this book seems to be a bridge between core aspects of science and several important pieces of philosophy and psychology.
The text also is already helping me refine and expand my thinking in other areas, such as in the course I’m teaching on TRIZ, a problem-solving methodology. For example, in formal logic, if A is a proposition, the consequences of the mutual exclusivity of A and not-A are the starting point for a vast exposition and development of powerful tools. In TRIZ by contrast, one of the methods for catalyzing problem solutions is to formulate a so-called “physical contradiction.” Here is an example of a physical contradiction: an object in a particular design situation must be heavy and it must not be heavy. Or a chemical in a particular context must be soluble and it must not be soluble. In other words, the categorical avoidance of contradiction is a starting point for formal logic, but the focusing of a conflict into a contradiction is a starting point for the problem solving heuristics of TRIZ. In Taoism, the idea of contradiction may also be seen to be generative, this time in still another way.
February 18th, 2007 at 9:54 am
Jayne’s book was a work in progress that was completed and published after his death. There’s lots of interesting material in it, but it certainly wouldn’t be appropriate for use as a textbook with undergraduate students. It’s at too high a level, the material is unpolished, and the focus on Jaynes’ particular approach to an “objective Bayesianism” is way too unbalanced.
There are lots of more appropriate introductory textbooks on Bayesian statistics and decision analysis. Some of these (like Jaynes) require a fair amount of mathematics background while others focus more on the philosophical issues. I happen to like David Williams’ book, “Weighing the Odds”.
February 18th, 2007 at 2:21 pm
Thanks for your suggestion. Eric did say that he wouldn’t recommend the Jaynes book as a textbook, more as a starting point for me in thinking about a course. The book is helping me so far - I will see what interesting bits I can get out of it while also looking for other sources. And I’ll certainly follow up on your recommendation of the Williams’ book.