I think we may be talking past each other. You say
What Feynman recommended was to learn a topic, then put the book aside and see if you can rederive what you have supposedly learned on your own.
That’s what I meant when I said “Feynman recommends that students always derive physics and math from scratch when learning.” You know the context. You know the evidence. You know, in the form of propositional statements, what the answer is. So make an attempt at deriving it yourself from the evidence, not the other way around.
In doing so, I often find that I didn’t really understand the original theory. What is built up in the from-scratch derivation is an intuitional understanding that is far more useful than the “book knowledge” you get from traditional learning. So, I would say, you never really learned it in the first place. But now we’re debating word definitions.
The other thing that you develop is experience deriving things “from scratch,” with just a couple of hints as necessary along the way, which sets you up for doing innovative research once you hit the frontier of knowledge. Otherwise you fall victim to hindsight bias in thinking that all those theorems you read in books seemed so obvious, but discovering something new seems so hard. In reality, there is a skill to research that you only pick up by doing, and not practicing that skill now when the answers could be looked up when you get stuck, is a lost opportunity.
I think we may be talking past each other. You say
That’s what I meant when I said “Feynman recommends that students always derive physics and math from scratch when learning.” You know the context. You know the evidence. You know, in the form of propositional statements, what the answer is. So make an attempt at deriving it yourself from the evidence, not the other way around.
In doing so, I often find that I didn’t really understand the original theory. What is built up in the from-scratch derivation is an intuitional understanding that is far more useful than the “book knowledge” you get from traditional learning. So, I would say, you never really learned it in the first place. But now we’re debating word definitions.
The other thing that you develop is experience deriving things “from scratch,” with just a couple of hints as necessary along the way, which sets you up for doing innovative research once you hit the frontier of knowledge. Otherwise you fall victim to hindsight bias in thinking that all those theorems you read in books seemed so obvious, but discovering something new seems so hard. In reality, there is a skill to research that you only pick up by doing, and not practicing that skill now when the answers could be looked up when you get stuck, is a lost opportunity.