Comment by jgerrish | Hacker News Reader

Comment by jgerrish | Hacker News Reader

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> Nothing in your comment makes me want to go learn more theory, and I would argue that it's nonsense to anyone who is not a mathematician.

What a coincidence this came up today.

I'm not a mathematician. I minored in math, but even the undergrad work was honestly difficult for me.

For most people, this might be nonsense. But it doesnt have to be.

I'm trying to learn about Fast Fourier Transforms because they're relevant for an embedded device system I'm investigating. I'm also not an Electrical Engineer so it is mostly new to me.

To understand the language of FFTs, linear bases and the like, I've started working through Axler's Linear Algebra Done Right.

First, just learning more theory shows me we can learn and grow in our old age.

This week I worked through linear spaces. I'm actively asking myself questions and working with other fields besides the reals and complex numbers so I can understand coding theory in general more.

And the parent's comment about quotient rings is directly related to an active learning question I asked myself about whether the set with only the zero element is a linear space. I don't think it is a field if 0 is the multiplicative identity, 0 can't be 1, so it can't be a linear space, right?

But it works. I guess the set of the field for the scalar in a linear space is always assumed to contain more elements. It's a different set than the linear space. It seems like, duh, of course it is. But you don't see it until you work through it. And I'm guessing my experience can inform teaching others.

It's confusing to me, maybe because the notation is sparse in explicitly defining the set of the linear space and the set of the associated linear space.

But this helps me truly understand linear codes down the line, and Linear Feedback Shift Registers and FFTs. It's not just theory to me, I can now understand what my peers are saying and contribute my own thoughts.

OK now you're getting into some more useful topics. Linear algebra is a great one with tons of applications. But if you want my advice, prioritize useful stuff and spend less time on theoretical baubles or bedrock-level boilerplate. This is unless, of course, you enjoy puzzles and hard work with little application.

> This is unless, of course, you enjoy puzzles and hard work with little application.

Wouldn't that be great? If we could teach our kids that learning for the sake of learning is awesome? If only that was all this world was.

But you're right, you and the thousands of others posting, it's not. You have that voice, and the hundreds of online stories about college losing value have that political voice.

In the post-AI future I can imagine recreational mathematics being a socially approved past time. It helps with age-related cognitive decline, etc.

But I can also understand people in that post-AI future who had smart political ideas that were more important to them than smart math ideas.

Impactful ideas.

Just getting snapshots and puzzling out that post-AI future I don't know if we'll have the right space to encourage positive care for our mental and physical landscapes.

I'm not making any political statement here, or at least that was not my intention. Life is short and there are infinite things we could be learning about. The advanced math I'm talking about avoiding here is not recreational math, but you could potentially apply the same logic to recreational math. Personally I see a big difference between "routine" abstract/advanced math and recreational math, though there can be some overlap. People have written books about what makes a pleasant puzzle, for example. Some puzzles are deceptively simple to state and impossible to solve without elite level theories. I think one of the characteristics of a good puzzle is that it can be solved with reasonable effort and not consume your whole life. Another is that it not be so contrived and abstract, that you need to be heavily initiated to even understand it. The worst are the ones that require a ton of mechanical computations even after you figure out the key insight. I don't think those are very fun either. But then again, there are people who don't get tired of Sudoku lol...

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