I'd forgotten how spectacularly academic Wikipedia's math articles are. It actually seems a little better than it used to be, but for example good luck learning what the hell a quaternion is by reading the Wikipedia article, even if you have sufficient background to understand and use them in practice. The German article is much better.
Right. You don't want to try to learn something mathematical from the Wikipedia article on it - Quaternions are a great example. The trouble with most of the writing about monads is that it's all at the level of the opening paragraph of a Wikipedia math article.
We have to do better at finding a way to teach this stuff.
When I started using quaternions for rotations, which -- if we're honest -- is the #1 practical applications, I had much more success building my intuition around this Wikipedia section:
> The trouble with most of the writing about monads is that it's all at the level of the opening paragraph of a Wikipedia math article.
IME, that's not at all true; most of the theory-heavy sources I've seen are explicitly framed as alternatives to the large body of intuitionist tutorials that avoid theory almost entirely, focusing on a few popular applications (usually, collections and IO.)
Being able to use something and knowing the whys are two different things. Many people know Calculus(practice), but not many know Real Analysis(theory behind Calculus, the academical bit).
"In mathematics, the quaternions are a number system that extends the complex numbers."
Naturals are a subset of integers. Integers are a subset of rationals. Rational are a subset of reals. Reals are a subset of complex numbers. The latter are a subset of quaternions. It's not difficult to construct each number system. If you look inside any undergrad math textbook, you'll find exact same writing style showcased in the Wikipedia article on quaternions.
