LolWolf

It's so wild to have a whole paper about this... that's also LLM written.

What are we even doing here?

what were your favorite projects?

The whole thing is unbelievable slop ! I think the whole article is llm-generated unfortunately (just reading the first paragraph I got an immediate smell).

ha, thank you! it's very fun to write these

hopefully you also enjoy the next one which imo makes a fun connection between the linear algebraic CRT and the fourier transform :)

yes, definitely some of it is (purposefully) fast and loose, though (ideally!) mostly unambiguous with reasonable assumptions

I think that part should've been "vector subspaces" rather than vector spaces since that is how U and W are defined in the paragraph prior.

I'll add this as a note, thanks!

Fair on all accounts! Surely, this could be made way more lively if I were in front of a blackboard waving my hands and drawing images, but alas, the medium is what it is :)

Thanks for reading though!

well, the statement is: is there a single operation, built from elementary operations, such that all _other_ elementary operations have finite representations.

this preprint answers that in the affirmative

otoh, (x, y) -> 1/(x-y) does not answer this question at all. you can argue that the preprint does so "via the infinite series in an operation" (which I have no idea what that means; surely if exp(x) qualifies then so must 1/(x-y) if we pick a monomial basis?) but ¯\_(ツ)_/¯

now, do I think that this is groundbreaking magical research (as I'm currently seeing on twitter) no... But it's neat!

I think the point is that it is _finite_. if you allow infinite expressions then the basic monomial basis or quotients thereof are “even simpler”