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I didn't mean to imply that there is anything wrong with visualization. I feel they're easier to understand than equations for the vast majority of people. But

by geokon 5y ago

I didn't mean to imply that there is anything wrong with visualization. I feel they're easier to understand than equations for the vast majority of people. But as a concrete example, to understand the Fourier transform it probably took me a couple of weeks of reading different textbooks in my spare time to really grok how the math works here.. it took some effort and I'm not some autistic savant that sees things in equations - so it has nothing to do with learning styles. Looking at some diagrams and videos for certain topics is a lazy and harmful approach to learning because some problems are just not conducive to visualization. Efforts to force a visualization ends up being actively bad and give viewers the wrong idea. My comment was a point by point explanation of how this ends up happening. At least in this particular case, with the Fourier Transform, the visualizations in effect made it harder for me personally to understand how the math works b/c they are so sloppy and emphasis all the wrong points. In the grand scheme of things, having a half-assed popsci understanding is generally worse than not know anything. You can get a sense of overconfidence and then go on to apply these techniques incorrectly and make broken/fragile systems that make no mathematical sense (or publish insane papers) If you really work with signal processing and don't understand the mathematics of the fourier transform then that's frankly a little scary. I'd really recommend taking the time to understand it b/c I think it really pays off - but yes, it takes a bit more effort than watching a youtube video..

anon_tor_12345 5y ago
>Looking at some diagrams and videos for certain topics is a lazy and harmful approach to learning god my eyes can't roll farther back in my head. your point would be less absurd if it weren't for the fact that algebraic geometry is an enormously powerful and productive area of math whose whole ass founding principle is that geometric interpretations of algebraic objects are extremely useful. AND spectral theory (what fourier analysis is called today) is an extremely geometric area owing to the dependence of convergence on the metric. >In the grand scheme of things, having a half-assed popsci understanding is generally worse than not know anything yes because this is a resource for rocket scientists and not interested people (probably high school and college students)? >If you really work with signal processing and don't understand the mathematics of the fourier transform then that's frankly a little scary. bro this isn't oppenheim. it's just a nice intro for people that might be curious or are learning for the first time.
stainforth 5y ago
>But as a concrete example, to understand the Fourier transform it probably took me a couple of weeks of reading different textbooks in my spare time to really grok how the math works here.. it took some effort and I'm not some autistic savant that sees things in equations - so it has nothing to do with learning styles. So you're still claiming your experience covers all.
kortex 5y ago
When did I say anything about not understanding the math of the FT? I took a whole semester of classes in signals, control theory, comms, etc. Derived FT, FFT, and friends, from scratch. I understand the math. But I have limited intuition about what I can do with the math. I can look it up in a book, or plug and chug, but it's not very fluid. The amount of times I've needed to manipulate equations since that class is zero. Yikes.

by geokon 5y ago

anon_tor_12345 5y ago

>Looking at some diagrams and videos for certain topics is a lazy and harmful approach to learning god my eyes can't roll farther back in my head. your point would be less absurd if it weren't for the fact that algebraic geometry is an enormously powerful and productive area of math whose whole ass founding principle is that geometric interpretations of algebraic objects are extremely useful. AND spectral theory (what fourier analysis is called today) is an extremely geometric area owing to the dependence of convergence on the metric. >In the grand scheme of things, having a half-assed popsci understanding is generally worse than not know anything yes because this is a resource for rocket scientists and not interested people (probably high school and college students)? >If you really work with signal processing and don't understand the mathematics of the fourier transform then that's frankly a little scary. bro this isn't oppenheim. it's just a nice intro for people that might be curious or are learning for the first time.

stainforth 5y ago

>But as a concrete example, to understand the Fourier transform it probably took me a couple of weeks of reading different textbooks in my spare time to really grok how the math works here.. it took some effort and I'm not some autistic savant that sees things in equations - so it has nothing to do with learning styles. So you're still claiming your experience covers all.

kortex 5y ago

When did I say anything about not understanding the math of the FT? I took a whole semester of classes in signals, control theory, comms, etc. Derived FT, FFT, and friends, from scratch. I understand the math. But I have limited intuition about what I can do with the math. I can look it up in a book, or plug and chug, but it's not very fluid. The amount of times I've needed to manipulate equations since that class is zero. Yikes.