Trying to actually understand what equations describe is something I'm always trying to do in school, but I find my teachers positively trained in the art of superficiality and dark-side teaching. Allow me to share two actual conversations with my Maths and Physics teachers from school.:
(Teacher derives an equation, then suddenly makes it into an iterative formula, with no explanation of why)
Me: Woah, why has it suddenly become an iterative formula? What's that got to do with anything?
Teacher: Well, do you agree with the equation when it's not an iterative formula?
Me: Yes.
Teacher: And how about if I make it an iterative formula?
Me: But why do you do that?
Friend: Oh, I see.
Me: Do you see why it works?
Friend: Yes. Well, no. But I see it gets the right answer.
Me: But sir, can you explain why it gets the right answer?
Teacher: Ooh Ben, you're asking one of your tough questions again.
(Physics class)
Me: Can you explain that sir?
Teacher: Look, Ben, sometimesnot understanding things is a good thing.
And yet to most people, I can't even vent the ridiculousness of a teacher actually saying this; they just think it's the norm!
I haven't seen them mentioned in this thread, so thought I'd add them, since they're probably valid and worth thinking about:
the utility of a math understanding, combined with the skills required for doing things such as mathematical proofs (or having a deep understanding of physics) is low for most humans. much lower than rote memorization of some simple mathematical and algebraic rules. consider, especially, the level of education that most will attain, and that the amount of abstract math and physics exposure in that time is very small. teaching such
Another month has passed and here is a new rationality quotes thread. The usual rules are:
And one new rule: