Accept it in the spirit it was meant: if you have mental illnesses like this, you need treatment.

I'd wager there's 95% of the benefit for 0.1% of the CPU cycles just by having a "search transcript for term" feature, since in most of those cases I've already got a clear agenda for what kind of information I'm seeking.

Many years ago I make a little proof-of-concept for displaying the transcript (closed captions) of a YouTube video as text, and highlighting a word would navigate to that timestamp and vice-versa. Such a thing might be valuable as a browser extension, now that I think of it.

Those people are intelligent, they’re just selfish and have no qualms over making money off the repugnant crap they’re doing.

people are getting in very real world trouble for saying negative things about certain people or their friends.

i’m not sure if you’ve seen how many people have lost their jobs for saying truths about kurk or how many people are losing jobs, scholarships, visas, education etc for saying things about a certain regime, but it’s happening, for real. they’re actively pushing to force people to turn over their social media accounts for review.

we can’t blame this poster for vagueposting here. i often pushback against vagueposting but in today’s climate we cant blame people for taking their personal safety seriously when it comes to vocalizing their criticisms.

No, that was the purpose of high school. As not practiced in public schools, as not practiced in the US

That this needs to exist is deeply disturbing.

If you restrict yourself to Lebesque-integrable functions, can’t you take the complex Fourier transform of the function and call the terms of the Fourier series a basis, with the coefficients being the components of the vector of the function? This is a bit above my current mathematical paygrade, so forgive me if I’m not expressing the idea accurately but I’m learning a lot both from the article and the ensuing discussion - hopefully you understand what I’m getting at.

I think what I may be asking is “Does the complex Fourier transform make a Hilbert space?” but I might be wrong both about that and about that being the right question.

    f(x) = sum_(k = 0 to infinity) (a_k sin(kx) + b_k cos(kx))

I agree but we're using functions for different things here. Yes some specific families of functions can be treated as vector spaces. In this article it seems like the author is pretending to take all real->real functions and treating them as if they are a vector space, whatever the content of the functions, quote :

  we’ve built a vector space of functions

and later he admits it is impossible

  Ideally, we could express an arbitrary function f as a linear combination of these basis functions. However, there are uncountably many of them—and we can’t simply write down a sum over the reals. Still, considering their linear combination is illustrative:

They are uncountable because they are aleph1

Eligible voters that did not vote due to apathy/laziness/politics are complicit.

>Pigs aren't special.

Apparently pigs can be possessed with sprints. I always assumed that was why they were considered unclean.

From Mark 5: So the demons begged him, "Send us among the pigs, so that we can go into them!" So he let them do this. The unclean spirits came out of the man and went into the pigs

https://biblehub.com/isv/mark/5.htm