7 ms·

I'm not sure how you would define the Fourier Transform geometrically without needing 4 spatial dimensions, at which point intuitive geometric reasoning is impo

by anon4 11y ago

I'm not sure how you would define the Fourier Transform geometrically without needing 4 spatial dimensions, at which point intuitive geometric reasoning is impossible.

lordCarbonFiber 11y ago
Far from impossible, it's even reasonably intutitive. Wikipedia has an excellent graphic https://en.wikipedia.org/wiki/File:Fourier_transform_time_and_frequency_domains_%28small%29.gif https://en.wikipedia.org/wiki/File:Fourier_transform_time_an.... Then for people for which that's too abstract, I find this graphic helps a lot in explaining. http://static.nautil.us/1635_42a3964579017f3cb42b26605b9ae8ef.png http://static.nautil.us/1635_42a3964579017f3cb42b26605b9ae8e... You picked a really bad example for the unintutiveness of mathematics.
- occamrazor 11y ago
  I'd suggest most of homological algebra as an example. It's called "abstract nonsense" for a reason. Personally, my intuition gives up at spectral sequences.
- BurritoAlPastor 11y ago
  Speaking in my capacity as a person who doesn't understand Fourier transforms, I'm afraid I have to say that your "intuitive" graphics are anything but. I can't even make sense of your second graphic. Just a data point for you.
  - lordCarbonFiber 11y ago
    Fair enough, it works a lot better as a gif. Out of curiosity, does this clear things up, or just as confusing? https://upload.wikimedia.org/wikipedia/commons/1/1a/Fourier_series_square_wave_circles_animation.gif https://upload.wikimedia.org/wikipedia/commons/1/1a/Fourier_...
    - BurritoAlPastor 11y ago
      Oooh. Yes, actually; I think I have an idea about what's going on (and why they're so damn useful) now. Thank you!
echo_oddly 11y ago
Doing a Fourier transform is simply applying a set of inner products from the function, f, onto a set of orthonormal basis functions. Put a post in the ground, measure the length of the shadow cast by the sun. That's how to do an inner product. So you can at least describe the process using few dimensions. Then you can scale it up to higher dimensions from there.

by anon4 11y ago

I'm not sure how you would define the Fourier Transform geometrically without needing 4 spatial dimensions, at which point intuitive geometric reasoning is impossible.

lordCarbonFiber 11y ago

Far from impossible, it's even reasonably intutitive. Wikipedia has an excellent graphic https://en.wikipedia.org/wiki/File:Fourier_transform_time_and_frequency_domains_%28small%29.gif https://en.wikipedia.org/wiki/File:Fourier_transform_time_an.... Then for people for which that's too abstract, I find this graphic helps a lot in explaining. http://static.nautil.us/1635_42a3964579017f3cb42b26605b9ae8ef.png http://static.nautil.us/1635_42a3964579017f3cb42b26605b9ae8e... You picked a really bad example for the unintutiveness of mathematics.

occamrazor 11y ago
I'd suggest most of homological algebra as an example. It's called "abstract nonsense" for a reason. Personally, my intuition gives up at spectral sequences.
BurritoAlPastor 11y ago
Speaking in my capacity as a person who doesn't understand Fourier transforms, I'm afraid I have to say that your "intuitive" graphics are anything but. I can't even make sense of your second graphic. Just a data point for you.
- lordCarbonFiber 11y ago
  Fair enough, it works a lot better as a gif. Out of curiosity, does this clear things up, or just as confusing? https://upload.wikimedia.org/wikipedia/commons/1/1a/Fourier_series_square_wave_circles_animation.gif https://upload.wikimedia.org/wikipedia/commons/1/1a/Fourier_...
  - BurritoAlPastor 11y ago
    Oooh. Yes, actually; I think I have an idea about what's going on (and why they're so damn useful) now. Thank you!

echo_oddly 11y ago

Doing a Fourier transform is simply applying a set of inner products from the function, f, onto a set of orthonormal basis functions. Put a post in the ground, measure the length of the shadow cast by the sun. That's how to do an inner product. So you can at least describe the process using few dimensions. Then you can scale it up to higher dimensions from there.