Yes, concrete practice may be indispensable to the insight. But once you have the insight, do you ever need to calculate to help you with a practical problem? Almost never, I think.
Yes, concrete practice may be indispensable to the insight. But once you have the insight, do you ever need to calculate to help you with a practical problem? Almost never, I think.
When you know things, you discover uses for them. Knowing arithmetic, you can easily decide whether the supereconomy giant size really is a good deal. Knowing prob/stats/causality, you can dismiss a lot of reporting as junk, and be able to say exactly why. Quadratic equations are often used as an example of useless knowledge, and yet I find myself solving those from time to time, and not just at work (in the narrow sense of what people pay me to do).
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?