This is awesome! That’s exactly the kind of post I wanted you to make!
About the lessons themselves:
I agree with the value of anki, but I have trouble finding things to ankify. My first impulse what to ankify everything under the sun, which lead to an anki burnout. Now I have the inverse problem of not finding much to put in Anki, mostly because I want to know/understand the concept before ankifying it. Or maybe I just don’t read enough maths these days.
I want to disagree with the “read several textbook at once”, but I think you’re right. It’s just that I’m trying so hard to focus on things and not jump from one to another all the time that reading multiple textbooks at once triggers all my internal alarms. I’ll try to find a safe way for me to do that.
About not reading the whole textbook, I think I agree with the gist but I disagree with what you actually write. I definitely think that you should read most of a textbook if what you’re doing is reading the textbook. On the other hand, you shouldn’t try to master every detail in it. If you want to apply the pareto principle, then go through papers and write everything that you don’t know. Then go search that in textbook. That’s the efficient way. But reading a textbook is for getting a general impression of the field and building a map. So the latter chapters are useful. Just don’t spend 20 hours on them.
The “read easier textbooks” advice looks like a rephrasing of “go just outside of your comfort zone”. It makes sense to me.
I generally don’t have the “approximate models” problem. But I also mostly read maths and computer science, which is additive instead of corrective.
And a problem this was. In early 2020, I had an interview where I was asked to compute ∫xlogxdx. I was stumped, even though this was simple high school calculus (just integrate by parts!). I failed the interview and then went back to learning algebraic topology and functional analysis and representation theory. You know, nothing difficult like high school calculus.
I think this is symptomatic of a problem I have myself, and which I only understood lately. I want to learn the cool shit, and I studied a lot of the fundamentals in my first two years after high-school (where we did 12 hours of maths a week). So I should remember how to do basic calculus! But somehow I forgot. And everytime I study a more advanced book, I feel like I should brush up my analysis and my linear algebra and all that if I want to really understand.
Yet that’s wrong, because I mostly read these advanced textbooks for one reason: getting a map of the territory. Then I will know where to look when I need something that looks like that. And for that purpose, getting all the details perfectly right is not important.
On the other hand, there are some parts of maths in which I want skills. There I should actually take the time to learn how to do it, instead of simply knowing that it exists and the big picture description.
About not reading the whole textbook, I think I agree with the gist but I disagree with what you actually write. I definitely think that you should read most of a textbook if what you’re doing is reading the textbook. On the other hand, you shouldn’t try to master every detail in it. If you want to apply the pareto principle, then go through papers and write everything that you don’t know. Then go search that in textbook. That’s the efficient way. But reading a textbook is for getting a general impression of the field and building a map. So the latter chapters are useful. Just don’t spend 20 hours on them.
I agree; I should have written “don’t complete textbooks”, and have edited that part accordingly. I’m thinking some combination of “don’t do all of the exercises” and “don’t spend time learning every single concept in the book.”
This is awesome! That’s exactly the kind of post I wanted you to make!
About the lessons themselves:
I agree with the value of anki, but I have trouble finding things to ankify. My first impulse what to ankify everything under the sun, which lead to an anki burnout. Now I have the inverse problem of not finding much to put in Anki, mostly because I want to know/understand the concept before ankifying it. Or maybe I just don’t read enough maths these days.
I want to disagree with the “read several textbook at once”, but I think you’re right. It’s just that I’m trying so hard to focus on things and not jump from one to another all the time that reading multiple textbooks at once triggers all my internal alarms.
I’ll try to find a safe way for me to do that.
About not reading the whole textbook, I think I agree with the gist but I disagree with what you actually write. I definitely think that you should read most of a textbook if what you’re doing is reading the textbook. On the other hand, you shouldn’t try to master every detail in it.
If you want to apply the pareto principle, then go through papers and write everything that you don’t know. Then go search that in textbook. That’s the efficient way. But reading a textbook is for getting a general impression of the field and building a map. So the latter chapters are useful. Just don’t spend 20 hours on them.
The “read easier textbooks” advice looks like a rephrasing of “go just outside of your comfort zone”. It makes sense to me.
I generally don’t have the “approximate models” problem. But I also mostly read maths and computer science, which is additive instead of corrective.
I think this is symptomatic of a problem I have myself, and which I only understood lately. I want to learn the cool shit, and I studied a lot of the fundamentals in my first two years after high-school (where we did 12 hours of maths a week). So I should remember how to do basic calculus! But somehow I forgot. And everytime I study a more advanced book, I feel like I should brush up my analysis and my linear algebra and all that if I want to really understand.
Yet that’s wrong, because I mostly read these advanced textbooks for one reason: getting a map of the territory. Then I will know where to look when I need something that looks like that. And for that purpose, getting all the details perfectly right is not important.
On the other hand, there are some parts of maths in which I want skills. There I should actually take the time to learn how to do it, instead of simply knowing that it exists and the big picture description.
I agree; I should have written “don’t complete textbooks”, and have edited that part accordingly. I’m thinking some combination of “don’t do all of the exercises” and “don’t spend time learning every single concept in the book.”