I'm similar. This from your top link stood out to me:

"It’s a little like building with lego bricks or something – spaced repetition helps ensure all the tiny pieces are in the right place, so that the big castle can happen without structural integrity issues."

The book Make it Stick (by Henry L. Roediger III) had a similar idea they called 'Structure Building'. Very similar to what you described, more experienced and effective learners were creating mental schemas of how the little, but crucial parts of a subject fit together, and successfully cut through the noise.

Structure Building was associated with interleaved practice (shuffling of problem types) and spaced retrieval practice.

I really enjoyed both blog posts, thank you for sharing! And I have to say, your explanation of the subexponential distribution property was remarkably clear for someone without a background in statistics :)

Would you mind sharing the flashcards you generated to build this intuition? I've been using Anki for a while and really trying to focus now on improving my prompt writing; would love to see how you managed it for this problem.

As much as I would like to, I think getting to that understanding required at least 500 flashcards on general statistical and probability concepts, ranging from fundamentals to extreme value theory. Most of those are only barely relevant at face value, but still contribute to understanding.

It's not that I set out to understand this specific thing but that I had studied statistics with flashcard support for a year and that happened to work after a few attempts.

Completely makes sense, appreciate the thoughtful reply. Any tips for writing flashcards when studying a textbook?

I've long wanted to write about this but never been able to think of anything original to say, but your question forced me to face this with effort. Thanks!

When making flashcards I draw a lot from the softer type of theory-building they do in social sciences. I ask questions like

- What are the properties of this?

- What variants of this exist? I.e. how would I recognise this in the wild, or in other shapes?

- What subcomponents can this be deconstructed into?

- Into which bigger picture does this fit?

- What are the consequences of this? What are its antecedents?

- What is this a special case of? What would a generalisation of this look like?

- Which are other related things? What are their similarities and differences?

- In what context might I need to know this?

Whenever I encounter what seems like a significant thing I loosely ask some of these questions, and try to construct atomic, focused flashcards from the answers.

I say loosely because it would take forever to to through all questions for all flashcards I make, so there's some bit of intuition that attracts me to which I think are the most significant questions for any given thing.

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One trick to make flashcards more specific that I use (maybe even abuse) is putting part of the answer into the prompt. Instead of prompting "What is the property of subexponential distributions I found meaningful in this book?" I might prompt "What behaviour do subexponential distributions have around high barriers that others don't?" -- I'm giving away part of the answer by including "high barrier" in the prompt, but I'm okay with that.

If I'm concerned about that, I might create a second flashcard prompting something like "What can a subexponential distribution do in one step that a more well-behaved distribution needs many steps to do?" with the answer "clear a high barrier". That captures both sides of the property without making too general a prompt.

I also do this a lot with "why" questions. Instead of prompting "what is the definition of y?" I might prompt "why is the definition of y=f(x)?" That gives away essentially the entire answer but focuses on the why instead.

You're always memorizing something at some level, even in math where you can derive so much after memorizing some core concepts and deductions.

This is similar to a loose life-thought i've had for a while, though i lack a catchy phrase for it lol.

My thought is: You're always practicing a behavior whether you like it or not.

Your mind is always setting you up to do more of whatever it is you're doing now. Both physical and mental. To do it more efficiently. With more ease. With more frequency. etc.

It's good motivation for me to mitigate a lot of negative behaviors. Angry in traffic, self anger, etc. If i can reason at least, of course. As i'm not interested in doing a lot of things more than i am, so i should avoid doing them now - if possible.

Math proof and derivations are a bit like remembering a walking route. You've seen the start and end, and the main turns taken, and there's also a general "walking" skill you need.

My argument is that it is worth memorising also the derivations, rather than re-deriving from scratch each time.

Meorising the derivation makes it easier to derive a second-order derivation, and so on. At some level of abstraction, going from first principles becomes prohibitively expensive and caching intermediary results, or so to speak, unlocks that again.

Sometimes yes, just like jargon is sometimes useful. Why use long-winded terms or descriptions when shorthand works between professionals.

Anki flash cards?

I use org-drill in Emacs but it's the same idea, yes.

The trick is not so much which software or settings one uses, but writing high-quality prompts.