I’ve recently found1 Better Explained, a website that tries to find explain math concepts in very non-traditional ways, but ways that help people truly grasp the underlying idea. Taken from the about page:
My mission is to help you truly understand new concepts. Let’s move past dry facts and share the Aha! moments that make learning fun and memorable.
The guiding philosophy is this Einstein quote: “If you can’t explain it simply, you don’t understand it well enough.”
If an intuition-first approach resonates with you, you’ll feel right at home. There’s no pretenses, no fuddy teacher, just an excited friend sharing what actually made an idea click.
I love the ethos of this philosophy — it’s the same mindset that I take towards my own explanations. When I teach math, everything from number theory to algebra, my goal is for my students to understand every concept from as intuitive of a level as possible. If formulas get memorized, or if a student uses the same technique repeatedly “just because it works”, then I haven’t done my job. One of my favorite moments from teaching math is when a student of mine figured out a clever combinatorics trick for counting the number of distinct rearrangements of “PAOLO”.2
It’s also a mindset that I like to take to my studies in economics. I think that this reason has been why I’ve particularly liked market design and behavioral economics and industrial organization (as opposed to macro-focused fields); these fields deal much more with the behavior of agents (particularly people), and I’m able to build up my intuition more organically than in fields where my background is much more limited.
When looking at resources for economics online, it makes me a bit sad that there aren’t well-developed resources for learning economics at anything beyond an introductory microeconomics and macroeconomics level (in particular, at the AP level). It means that most people’s understanding of economics will be reliant on the relatively simplified and coarse models introduced in high schools or an understanding reliant on politics and the media. Perhaps more importantly, it means that most people never have exposure to the many other interesting parts of economics, the parts that try to determine causality in the big, messy world, parts that focus on more than “how should a government run.”
Maybe one thing that I’ll try to do with this blog is to try and write intuitive explanations for some of my favorite concepts that I’ve seen in classes and new material that I find interesting as I learn it. In particular, I think that explanations of core econometrics concepts (particularly regressions and instrumental variables) would be incredibly interesting. Other concepts, like Arrow’s Impossibility Theorem, different macroeconomic models, and game theory concepts could also be interesting to try to explain from first principles as much as possible.
Refound? I feel like this kind of site is absolutely something I might have seen before. But I have no idea where, nor any memory of this site existing. ↩
The difficulty in this problem is that there are two Os – the easiest way around it is to pretend that they’re distinct, and then divide by 2. My student came up with this solution the same day I introduced the “combination” operation to them, and it made me very, very happy. ↩