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That's a really interesting case, and my gut feeling is that you are definitely very weird lol, not that that's a bad thing. How do you end up understanding lin

That's a really interesting case, and my gut feeling is that you are definitely very weird lol, not that that's a bad thing. How do you end up understanding linear algebra but turning to youtube videos to understand the fourier transform? My gut feeling is that 99% of people who understand linear algebra would learn fourier transforms through the same mechanism they used to learn advanced math (textbooks, university courses, etc) where the default way of introducing the subject would be something like 'just an orthogonal matrix you multiply onto a vector,' an otherwise unintuitive explanation that leaves a void that said youtube videos are trying to fill. For example the 3b1b video has to gently re-introduce why complex numbers are useful - different target audience you know?

Sharlin 2y ago
People who are good at algebra aren’t necessarily good at calculus/analysis and vice versa. It sounds perfectly reasonable that someone might struggle with the continuous FT (integrals, brrh!) but grok the discrete version perfectly well (just a sum of basis functions).
- code_biologist 2y ago
  Heh, my college signals courses first taught continuous time systems then focused on discrete time in a follow-up course. They assumed you knew enough calculus at the start that Laplace transforms wouldn't be a huge hurdle, even if you hadn't seen them before. Discrete time / Z-transform was treated as more "advanced". But I agree, I've done enough integrals for a lifetime!
  - Sharlin 2y ago
    Computer scientists and programmers live in an inherently discrete world where there’s algebra everywhere you look but very little calculus outside certain niches. I’m reminded of the Feynman and the Connection Machine story [1] where he ended up analyzing some complex binary circuits in terms of differential equations because as a physicist he lived and breathed the continuum – unlike his computer engineer coworkers! [1] https://longnow.org/essays/richard-feynman-connection-machine/ https://longnow.org/essays/richard-feynman-connection-machin...
thomasahle 2y ago
> How do you end up understanding linear algebra but turning to youtube videos to understand the fourier transform? As a computer scientist I never actually had a calculus class where we used fourier series. I just ran into them often enough, through stuff like the fast fourier transform for computing convolutions, that I thought I should understand it better. So I googled the topic, and stuff like 3b1b is what came up, and what everyone said were the most intuitive explanations. I eventually did a course on binary functional analysis, and it thought the discrete boolean fourier transform.

Sharlin 2y ago

People who are good at algebra aren’t necessarily good at calculus/analysis and vice versa. It sounds perfectly reasonable that someone might struggle with the continuous FT (integrals, brrh!) but grok the discrete version perfectly well (just a sum of basis functions).

code_biologist 2y ago
Heh, my college signals courses first taught continuous time systems then focused on discrete time in a follow-up course. They assumed you knew enough calculus at the start that Laplace transforms wouldn't be a huge hurdle, even if you hadn't seen them before. Discrete time / Z-transform was treated as more "advanced". But I agree, I've done enough integrals for a lifetime!
- Sharlin 2y ago
  Computer scientists and programmers live in an inherently discrete world where there’s algebra everywhere you look but very little calculus outside certain niches. I’m reminded of the Feynman and the Connection Machine story [1] where he ended up analyzing some complex binary circuits in terms of differential equations because as a physicist he lived and breathed the continuum – unlike his computer engineer coworkers! [1] https://longnow.org/essays/richard-feynman-connection-machine/ https://longnow.org/essays/richard-feynman-connection-machin...

thomasahle 2y ago

> How do you end up understanding linear algebra but turning to youtube videos to understand the fourier transform? As a computer scientist I never actually had a calculus class where we used fourier series. I just ran into them often enough, through stuff like the fast fourier transform for computing convolutions, that I thought I should understand it better. So I googled the topic, and stuff like 3b1b is what came up, and what everyone said were the most intuitive explanations. I eventually did a course on binary functional analysis, and it thought the discrete boolean fourier transform.