21–30 of 214 posts
Earlier quoted context omitted.
Only if it is band-limited.
And of infinite duration, if you want to split hairs.
The real world is somewhere in between. It must involve quantum mechanics (in a way I don't really understand), as maximum bandwidth/minimum wavelength bump up against limits such as the Planck length and virtual particles in a vacuum.
Always blew my mind that every signal can be recreated simply by adding different sine waves together.
Back in my uni days I did not get why that works. Why are sine waves special? Turns out... they are not! You can do the same thing using a different set of functions, like Legendre polynomials, or wavelets.
Yup, any set of orthogonal functions! The special thing about sines is that they form an exceptionally easy-to-understand orthogonal basis, with a bunch of other nice properties to boot.
Always blew my mind that every signal can be recreated simply by adding different sine waves together.
Like you can make any vector in R^3 `` by adding together a linear combination of ` `, ` `, ` `, turns out you can also do it using `0/30), exp(j2pi0/31), exp(j2pi0/32)>`, `1/30), exp(j2pi1/31), exp(j2pi1/32)>`, and `2/30), exp(j2pi2/31), exp(j2pi2/32)>`.
You can actually do it with a lot of different bases. You just need them to be linearly independent.
For the continuous case, it isn't all that different from how you can use a linear combination of polynomials 1,x,x^2,x^3,... to approximate functions (like Taylor series).
Always blew my mind that every signal can be recreated simply by adding different sine waves together.
Back in my uni days I did not get why that works. Why are sine waves special? Turns out... they are not! You can do the same thing using a different set of functions, like Legendre polynomials, or wavelets.
Which to your point: You're absolutely correct that you can use a bunch of different sets of functions for your decomposition. Linear algebra just says that you might as well use the most convenient one!
(Fractional fourier transform on the top face of the cube)
And for short time fourier transform showing how a filter kernel is shiftes across the signal. [2]
Always blew my mind that every signal can be recreated simply by adding different sine waves together.
Only if it is band-limited.
Essentially it's just projection in infinite-dimensional vector spaces.
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Extraordinary claims require extraordinary evidence. Especially considering that a decent fraction of the CS/ML researchers that I know have solid physics and math backgrounds. Just of the top of my head, Marcus Hutter, David MacKay, Bernhard Scholkopf, Alex Smola, Max Welling, Christopher Bishop, etc. are/were prominent researchers with strong math and physics backgrounds. More recently Jared Kaplan and Dario Amodei at Anthropic also have physics backgrounds, as well as plenty of people at DeepMind.
To claim that you have noticed something in "100 years of physics and math research" that all of those people (and more) have missed and you didn't is pure hubris.
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On your site you make the claim that: "Our thesis is that there is 100 years of physics and math research that has gone unnoticed by the CS/ML communities and we intend to rectify that." Extraordinary claims require extraordinary evidence. Especially considering that a decent fraction of the CS/ML researchers that I know have solid physics and math backgrounds. Just of the top of my head, Marcus Hutter, David MacKay,…
Cliche phrase is cliche. And yeah, no shit, we are working on it.
Re: your other points: cool, yeah there are people in ML that studied physics. Do you feel like much of physics has made it to ML? Do we have scalable energy-based models? If not, why not?