Thanks for pointing out the Gelman and Shalizi paper. Just skimmed it so far, but it looks like it really captures the zeitgeist of what reasonably thoughtful statisticians think of the framework they're in the business of developing and using.
Plus, their final footnote, describing their misgivings about elevating Bayesianism beyond a tool in the hypothetico-deductive toolbox, is great:
Ghosh and Ramamoorthi (2003, p. 112) see a similar attitude as discouraging inquiries into consistency: ‘the prior and the posterior given by Bayes theorem [sic] are imperatives arising out of axioms of rational behavior – and since we are already rational why worry about one more’ criterion, namely convergence to the truth?
I have started to put together a sort of curriculum for learning the subjects that lend themselves to rationality. It includes things like experimental methodology and cognitive psychology (obviously), along with "support disciplines" like computer science and economics. I think (though maybe I'm wrong) that mathematics is one of the most important things to understand.
Eliezer said in the simple math of everything:
I want to have access to outlook-changing insights. So, what math do I need to know? What are the generally applicable mathematical principles that are most worth learning? The above quote seems to indicate at least calculus, and everyone is a fan of Bayesian statistics (which I know little about).
Secondarily, what are some of the most important of that "drop-dead basic fundamental embarrassingly simple mathematics" from different fields? What fields are mathematically based, other than physics and evolutionary biology, and economics?
What is the most important math for an educated person to be familiar with?
As someone who took an honors calculus class in high school, liked it, and did alright in the class, but who has probably forgotten most of it by now and needs to relearn it, how should I go about learning that math?