I would heartily recommend Sebastian Lague's latest video, which covers this in a very approachable way: https://www.youtube.com/watch?v=08mmKNLQVHU
The unreasonable effectiveness of the Fourier transform
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Re: The unreasonable effectiveness of the Fourier transform
#22Re: The unreasonable effectiveness of the Fourier transform
#23My favorite story about the Fourier Transform is that Carl Friedrich Gauss stumbled upon the algorithm for the Fast Fourier Algorthim over a century before Cooley and Tukey’s publication in 1965 (which itself revolutionized digital signal processing).[1] He was apparently studying the motion of the asteroids Pallas and Juno and wrote the algorithm down in his notes but it never made it into public knowledge.
[1] https://www.cis.rit.edu/class/simg716/Gauss_History_FFT.pdf
Re: The unreasonable effectiveness of the Fourier transform
#24Re: The unreasonable effectiveness of the Fourier transform
#25Okay, who's gonna write the story > The unreasonable effectiveness of The Unreasonable Effectiveness title?
Agreed, these kind of titles are very silly. FTs are actually very reasonable, in the sense that they are a easy to reason about conceptually and in practice. There's another title referenced in that link which is equally asinine: "Eugene Wigner's original discussion, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". " Like, wtf? Mathematics is the language of science, science would not compoun…
> Mathematics is the language of science
So, biology and medicine are not sciences? Or are only sciences to the extent they can be mathematically described?
The scientific method and models are much more than math. Equating the reality with the math has let to myriad misconceptions, like vanishing cats.
And silly is good for a title -- descriptive and enticing -- to serve the purpose of eliciting the attention without which the content would be pointless.
Re: The unreasonable effectiveness of the Fourier transform
#26My favorite story about the Fourier Transform is that Carl Friedrich Gauss stumbled upon the algorithm for the Fast Fourier Algorthim over a century before Cooley and Tukey’s publication in 1965 (which itself revolutionized digital signal processing).[1] He was apparently studying the motion of the asteroids Pallas and Juno and wrote the algorithm down in his notes but it never made it into public knowledge. [1] http…
Gauss's notes and margins is riddled with proofs he didn't bother to publish - he was wild.
Not sure if true, but allegedy he insisted his son not go into maths, as he would simply end up in his father's shadow as he deemed it utterly Impossible to surpass his brilliance in maths :'D
Re: The unreasonable effectiveness of the Fourier transform
#27My favorite story about the Fourier Transform is that Carl Friedrich Gauss stumbled upon the algorithm for the Fast Fourier Algorthim over a century before Cooley and Tukey’s publication in 1965 (which itself revolutionized digital signal processing).[1] He was apparently studying the motion of the asteroids Pallas and Juno and wrote the algorithm down in his notes but it never made it into public knowledge. [1] http…
There is a saying about Gauss: when another mathematician came to show him a new result, Gauss would remark that he had already worked on it, open a drawer in his desk, and pull out a pile of papers on the same topic.
Re: The unreasonable effectiveness of the Fourier transform
#28I dont like the Fourier Transform. It is infinite which makes it coarse and rough and it it gets everywhere.