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The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

justinmath.com

1–10 of 74 posts

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#3
That's the same principle which makes it wise to first do some copy pasting before you abstract stuff into a common library. Gathering some (more than two) concrete use cases before you factor out the common functionality makes much better library functions.

A common sign of prematurely deduplicated code is a common function with lots of boolean flags and other knobs to tweak its behaviour for every use case added after it was written.

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#5

Relatedly: struggling is learning [0]. [0] https://news.stanford.edu/stories/2019/09/embrace-struggle-e...

FYI that article is an interview with Jo Boaler, the main architect of removing middle school Algebra in SF and California (attempted). Her views are pretty controversial among those promoting math excellence.

That's not to say there isn't anything worthwhile in the article, but figured people would want that context.

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#6
Yes, exactly. See [0] for a concrete example of an abstraction that can't be grokked without grinding concrete examples, and how people who have already grokked it forget this fact.

[0]: https://byorgey.wordpress.com/2009/01/12/abstraction-intuiti...

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#7
Makes sense. I always intuitively understood that going from for example electronic engineering to computer science is probably easier than the other way around, but this article makes a great point. Without some low-level knowledge, you do not fully understand the higher level. Then you can only parrot the higher level (I’m also looking at you here LLM).

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#8
This is presumably about math problems, but I always approach programming problems this way.

One issue I have with math problems is that sometimes I wish I could immediately go down one level of abstraction and see something like a physics or programming problem that applies that specific or related problem I'm working on. I haven't found a resource like this yet.

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#9
Yes. I think I did well in math/physics classes in college and grad school just because I found the most effective way to study, for me, was to grind out as many problems as possible. Go through the old homework, old exams, books, anywhere you can find relevant problems with solutions to check against.

Re: The Need to Grind Concrete Examples Before Jumping Up a Level of Abstraction

#10
This was something that really lacked in my statistics degree. We were always learning different distributions, proofs and estimation methods but very rarely applied them to actual problems. I feel like you can kinda get away with this type of thing in math more, but in statistics, it makes things super hard to learn.
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