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I think these conversations of top down vs bottom up, are frequently a case where people are talking past each other due to using different definitions, and hav

I think these conversations of top down vs bottom up, are frequently a case where people are talking past each other due to using different definitions, and having different goals. And I think this is especially common when one of the people is a software engineer, and the other is not. For software, the tooling and the abstractions are so powerful that you can make incredible software without knowing what's really happening under the surface. Imagine an "abstraction ladder", with each level building on the previous level. Frequently in software development, you only need to understand a single level n, and maybe a little of n-1, to make great software. So the advice of "just jump in" is often great advice because you're jumping into a "shallow pool". (P.S, I love the work you're doing with MathAcademy, though I wish there was discounted price for "casual" learners that only have an hour or two a month)

JustinSkycak 2y ago
Agree, it depends highly on goals. Using off-the-shelf ML/AI models (to make great software) requires far less background knowledge than implementing new models being introduced in papers, which in turn requires far less background knowledge than producing new models that improve upon the state-of-the-art. Thanks for the kind words about Math Academy! It's true that we focus on students who are trying to acquire math skills to the highest degree possible -- we teach math as if we were training a professional athlete or musician. We maximize learning efficiency in the sense that we minimize the amount of work required to learn math to the fullest extent. I realize that there are many learners who only want to devote an hour or two per month, but, at least right now, such learners would be better served elsewhere. It's a totally different optimization problem -- maximize surface-level coverage subject to some fixed, miniscule amount of work -- and as a result it would require different different curriculum and possibly different training techniques (or at least, differently calibrated techniques). But it's definitely an idea to think about in the future. :)

JustinSkycak 2y ago

Agree, it depends highly on goals. Using off-the-shelf ML/AI models (to make great software) requires far less background knowledge than implementing new models being introduced in papers, which in turn requires far less background knowledge than producing new models that improve upon the state-of-the-art. Thanks for the kind words about Math Academy! It's true that we focus on students who are trying to acquire math skills to the highest degree possible -- we teach math as if we were training a professional athlete or musician. We maximize learning efficiency in the sense that we minimize the amount of work required to learn math to the fullest extent. I realize that there are many learners who only want to devote an hour or two per month, but, at least right now, such learners would be better served elsewhere. It's a totally different optimization problem -- maximize surface-level coverage subject to some fixed, miniscule amount of work -- and as a result it would require different different curriculum and possibly different training techniques (or at least, differently calibrated techniques). But it's definitely an idea to think about in the future. :)