11–20 of 68 posts
I'd read Yudkowsky's popular "An Intuitive Explanation of Bayes' Theorem" as well as a few others, but the article on this site made me feel like I actually understood it for the first time. The examples were clever, short, and simple, while still demonstrating how powerful Bayes' Theorem can be. The concise explanations here seem more helpful than semester-long university courses I've taken. I definitely look forwar…
I am often saddened by how much easier it has been for me to acquire computer science versus mathematical literacy. Embarrassingly, years after a poorly-timed calculus course left me thinking I had to be able to prove the central limit theorem in order to use calculus, the biggest barriers have turned out to be things programming as a discipline has learned to avoid; encouraging varied and/or terse notations, opaque…
But still, programming seems far more willing to fix mistakes than hard sciences/math. We've been clanking around with Pi instead of Tau for how many centuries?
I really like this cheatsheet, it is very inspiring actually. You should consider doing a version written for elementary school aged kids. You need to get buy in while they are still young!
My meta goal is to raise people's standards for what it means to understand something. ("If it didn't click, I should keep looking for a better explanation." vs. "It didn't click, I'm no good at this.")
I am often saddened by how much easier it has been for me to acquire computer science versus mathematical literacy. Embarrassingly, years after a poorly-timed calculus course left me thinking I had to be able to prove the central limit theorem in order to use calculus, the biggest barriers have turned out to be things programming as a discipline has learned to avoid; encouraging varied and/or terse notations, opaque…
To be fair, we drag around (and rigorously defend) many bad artifacts of past programming languages. Case sensitivity? Double-equals-sign for testing equality? But still, programming seems far more willing to fix mistakes than hard sciences/math. We've been clanking around with Pi instead of Tau for how many centuries?
Is case sensitivity a bad artifact? It doesn't seem like it is to me anymore, but my former self sure thought so.
I am often saddened by how much easier it has been for me to acquire computer science versus mathematical literacy. Embarrassingly, years after a poorly-timed calculus course left me thinking I had to be able to prove the central limit theorem in order to use calculus, the biggest barriers have turned out to be things programming as a discipline has learned to avoid; encouraging varied and/or terse notations, opaque…
(Kalid from BetterExplained here) Thanks for the comment. There's this weird notion in Calculus education that we need to start from first principles. Limits were invented a century after Newton died, yet they're taught first. "Oh, students won't understand calculus unless they can build it from first principles. I don't care if Newton worked out gravitation with his understanding, it's not good enough." My little ca…
Earlier quoted context omitted.
To be fair, we drag around (and rigorously defend) many bad artifacts of past programming languages. Case sensitivity? Double-equals-sign for testing equality? But still, programming seems far more willing to fix mistakes than hard sciences/math. We've been clanking around with Pi instead of Tau for how many centuries?
When I took my first programming course, one of things I was most surprised by was case sensitivity. It's kind of funny thinking about it now my perspective is entirely different -- "D" and "d" aren't the same value so why would they mean the same thing? Is case sensitivity a bad artifact? It doesn't seem like it is to me anymore, but my former self sure thought so.
Earlier quoted context omitted.
(Kalid from BetterExplained here) Thanks for the comment. There's this weird notion in Calculus education that we need to start from first principles. Limits were invented a century after Newton died, yet they're taught first. "Oh, students won't understand calculus unless they can build it from first principles. I don't care if Newton worked out gravitation with his understanding, it's not good enough." My little ca…
Kalid, I just read your article on Prime numbers (not-quite randomly selected from the homepage). I just wanted to say how well written I found it - even beyond the technical side of things, your writing style, tone, and humility ("if I didn't mess it up") are fabulous.
Earlier quoted context omitted.
(Kalid from BetterExplained here) Thanks for the comment. There's this weird notion in Calculus education that we need to start from first principles. Limits were invented a century after Newton died, yet they're taught first. "Oh, students won't understand calculus unless they can build it from first principles. I don't care if Newton worked out gravitation with his understanding, it's not good enough." My little ca…
Kalid, I just read your article on Prime numbers (not-quite randomly selected from the homepage). I just wanted to say how well written I found it - even beyond the technical side of things, your writing style, tone, and humility ("if I didn't mess it up") are fabulous.
This is terrific. I'm mathy enough to know e to several places, and use it in programs occasionally, but if you'd asked me how it might be intuitively derived I'd have been at a loss. And that's just for something inside my comfort zone - the article on linear algebra is just as illuminating. This looks like it will be my commute reading for the week. But more than that it just makes me happy that it exists.