the supereconomy giant size really is a good deal
Yes, arithmetic does come in useful, for example in those cases.
It's not some minor trick, like how to fold a t-shirt, it's useful everywhere.
Can you give an example of when you have used actual arithmetical calculations to explain why some prob/stats/causality were junk, or where you solved a quadratic equation?
It's common enough that I don't even notice it as a thing. But for example, a political survey shows a 2% advantage for one party. The sample size is given and I know at once that the result is noise. (sigma = sqrt(pqN).) Knowing how correlation and causality relate to each other disposes of a lot of bad reporting, and some bad research. Or I want to generate random numbers with a certain distribution; that easily leads to pages of algebra and trigonomentry.
For a more extensive illustration of how knowing all this stuff enables you to see the world, see gwern's web site.
Certainly, it is useful everywhere to understand. But very few people actually run calculations (other than basic arithmetic). Gwern and you are very rare exceptions. I think the world could use more of that.
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?