December 28th, 2008

beartato phd

(no subject)

This is my favorite paragraph from Cosma Shalizi's review of Wolfram's "A New Kind of Science":
Wolfram refers incessantly to his "discovery" that simple rules can produce complex results. Now, the word "discovery" here is legitimate, but only in a special sense. When I took pre-calculus in high school, I came up with a method for solving systems of linear equations, independent of my textbook and my teacher: I discovered it. My teacher, more patient than I would be with adolescent arrogance, gently informed me that it was a standard technique, in any book on linear algebra, called "reduction to Jordan normal form", after the man who discovered it in the 1800s. Wolfram discovered simple rules producing complexity in just the same way that I discovered Jordan normal form.

This sort of "weak discovery" is utterly commonplace among serious researchers doing real research as well as high school students and cranks. It's just that they have more background knowledge than high school students, and at least better judgment than cranks, and have a decent shot at correctly guessing, based on the simplicity of the result or the history of the discipline(s) it could be relevant to, whether it is "weak" or something of some significance.

Or, the discoverer doesn't know the area well enough, and just doesn't know whether it's weak or not, but still has the humility to do some more due diligence before publishing a 1000-page ersatz cinderblock on the subject*. In this case, it seems necessary to fall back on asking experts if a putative new idea sounds familiar.

An open question: can we do any better than bugging experts who would probably prefer to be busy getting real work done? The mapping from "crazy new idea in a field that I'm not that familiar with that might not be new at all, but is in my own funny notation" to "canonical definition everyone's known about for 50 years" seems very tough and AI-complete. On the other hand, research professors are also often expected to teach in order to create the next generation of experts, so perhaps being "on call" for basic questions is rightly culturally part of that.

*hypothetically speaking, of course.