4 ms·

Those "stupid computations" comprise the bulk of useful work in the world. If one learns enough to do that, there may be no reason to go further. You're proving

Those "stupid computations" comprise the bulk of useful work in the world. If one learns enough to do that, there may be no reason to go further. You're proving my point about the pretentiousness of insisting on the theory when one doesn't need it. 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. Imagine arguing that the only way to understand or appreciate basic set logic is to know all about infinite sets and ZF axioms... Most people, even mathematicians, will not understand all of that and have only heard about it in the most basics if at all. A similar phenomenon happens with philosophy. Imagine arguing that simple logic is "stupid" and that one can only reason well if they have a total understanding of epistemology. I happen to think epistemology matters, and that people can benefit from at least being aware of it, but it is really a separate topic from actual mechanical logic and argumentation.

aleph_minus_one 25d ago
> 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. You are free to ignore mathematics that is not completely trivial. I prefer (and would rather recommend) to understand it, and use this understanding to build a >1-billion-USD/EUR application out of it. :-)
- wakawaka28 24d ago
  I often ignore mathematics that is not completely useful to me these days lol. I get the appeal of learning neat theories and feeling like you got it all figured out, but I'd rather limit my studies to topics that are likely to bear fruit in my life. Complication and abstraction does not necessarily deter me, but it has been my observation that overly complicated or abstract ideas rarely pay off in my endeavors.
jgerrish 24d ago
> 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 fields and rings is directly related to a question I asked myself about the
jgerrish 24d ago
> 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.
- wakawaka28 24d ago
  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.
  - jgerrish 24d ago
    > 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.

aleph_minus_one 25d ago

> 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. You are free to ignore mathematics that is not completely trivial. I prefer (and would rather recommend) to understand it, and use this understanding to build a >1-billion-USD/EUR application out of it. :-)

wakawaka28 24d ago
I often ignore mathematics that is not completely useful to me these days lol. I get the appeal of learning neat theories and feeling like you got it all figured out, but I'd rather limit my studies to topics that are likely to bear fruit in my life. Complication and abstraction does not necessarily deter me, but it has been my observation that overly complicated or abstract ideas rarely pay off in my endeavors.

jgerrish 24d ago

> 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.

wakawaka28 24d ago
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.
- jgerrish 24d ago
  > 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.