What Is the Fourier Transform?

This kind of statement is too vague to be useful. I even know all the words in there and I still don't know what you mean.

Ask away.

Hmm I always viewed it as sum over orthogonal bases. Sine/Cosine is choice, while there can be many other bases, like Legendre polynomials. Can you explain more how FT is linked to 'a sum over equivalence classes'?

Your earlier post comes off as link-spam, as it uses general language to connect something tangentially related to what you're interested in to drive traffic to your website. This is not conducive to questions.

You can still ask.

A high level explanation is that a trace counts how many times each equivalence classes appears. In sense, it is similar to a multiset, it associates a count with some input.

In the case of the Fourier transform, it maps from time domain to frequency domain. In the frequency domain, we can see the amplitude (count) of the signal at each frequency.

I know and use wavelet, Fourier, and other transforms on a daily basis, but your post did not stimulate any interest in me. Also, your reply on the other thread does not strike me as particularly insightful (I'd argue that your 'frequency decomposition' interpretation is flat-out wrong).

Are you familiar with the partition function?

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, 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.

> Extraordinary claims require extraordinary evidence.

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?

Nah it's on you to be coherent, there's nothing interesting to ask about

You got confused before we even started so maybe you are not the target audience.

If you can't communicate clearly there's no reason to try to take you seriously.

Is there a reason to take you seriously?