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"that is unlikely to change even today" - huh? Doesn't the internet make it much easier to discover and access resources?



While the internet does make it easier to access educational and useful materials, it also makes it easier to access X,000 hours of $videoGame or X0,000 dopamine hits from endless TikTok videos. Perhaps parent comment meant that there does not appear to be a significant trend towards more people reading or making use of these types of resources.


Yes and no. Yes there are more resources, and yes they're easier to discover, but you implied that was all that GP meant, but his point was they can be hard to find still. At least resources that try and give you intuition, so that's the "no" part. In terms of your question more availability of resources in general doesn't always mean you have better odds of finding good to great available resources for giving you these intuitions. The problem we have today, I believe, is the signal to noise ratio is low to build your intuition. It's a problem one of my professors explained once that so much of grade school and even required college math for most students is filled with the solve this equation mentality that you kind of miss the purpose of a lot of what higher level math is about. Sure part of it is still solving equations, but some other parts just as an example are about discovering truths (through for example a proof) that we didn't know before hand or hadn't built the intuition for before hand and that part of math is fun, but you do need a foundation for that too. It can be disheartening to learn that so much of math kind of kills that joy, and only focuses on the foundation of it the solving of the equations.

We often find ourselves sifting through materials that always assume you have (or can figure out) the intuition and make it hard to find something that digs a little deeper and allows something to stick. This happens in math, programming, and you name it. We kind of assume the intuition is already developed most the time. Writing depends on our audience. If you're a programmer like me imagine someone trying to explain a modern and complex algorithm to you while simultaneously explaining every small part of how a program executes all the way down to machine code. That would be a horrific way to try to learn just the algorithm itself and it would be drudgery to try and fight through finishing an article or book that contained that much information, and because of that it would be a waste of the author's time writing such a thing. The simple answer is usually is to either stick with simpler examples and try to build intuition like this book does (though that doesn't mean there is no complexity in the example still due to digging into the example from a fresh perspective), or to just write a book full of rules and examples through problem sets (think like a textbook on math).

I swear this is related, but my favorite course in college was Discrete Mathematics which is sometimes titled something like Mathematics of Computer Science. The interesting thing is it was the first time in Math and at school that someone has explained to me the meaning of things that build a foundation in Logic in mathematics like "for all", "there exists", logical operators, and the negation of any of those things and what they mean. It was enlightening to say the least. It gave me an intuition behind the language of proofs. It allowed me to write my own proofs and to be able to read other proofs. Which proofs are everywhere in mathematics and understanding a proof is exactly like building an intuition of the underlying math. I couldn't believe after taking that one course that I actually understand textbooks way more often, and could understand that most the learning didn't happen by going example to example and solution to solution, but by understanding the underlying rule. Math always seemed, so much more ambiguous to me before then like the rules didn't clearly define every edge case and outcome, but they almost always certainly do.




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