ikrima

From my experience of working in this problem domain for the last year, I'd say it is pretty powerful but the "too good to be true part" comes from that EML buys elegance through exponential expression blow-up. Multiplication alone requires depth-8 trees with 41+ leaves i.e. minimal operator vocabulary trades off against expression length. There's likely an information-theoretic sweet spot between these extremes.

It's interesting to see his EML approach whereas mine was more on generating a context sensitive homoiconic grammar.

I've had lots of success combining spectral neural nets (GNNs, FNOs, Neural Tangent Kernels) with symbolic regression and using Operad Theory and Category Theory as my guiding mathematical machinery

Yeah, sorry! You're 100% right. I really wish I could have this conversation in person! I can barely have it normally as it stretches at the edge of my math abilities and didn't think it through before I autistically responded :P

thank you!

:P I had a stroke; typing is literally difficult. I'm trying to say don't read too much into it, i can't really have a conversation on a comment thread b/c of brain injury. I think the emoji's get stripped out so maybe my tone seems more abrasive than whimsical

but also, i mean you are just flat out wrong on some very big parts. E.g.: i think in 2024 or 2023, there was a big breakthrough in geometrization of Langlands. IIRC, there was a second big break through on the discrete-continuum connection relating to primes in some manner but can't remember specifics off top of my head.

i think you're confusing maybe what Beth numbers are used for vs. what i'm proposing that they be repurposed for. You're right, no one is using them the way i referenced but that's kind of what math research is...?

"no, it wasn't clear. I wouldn't generally take "I nerd-sniped myself. Here's a more fleshed-out sketch of ..." to mean "Here's something written for me by an LLM". I'd take it to imply that the person had done the fleshing-out themself."

aaaaaaaah, I think you finally helped me notice something subtle in the way I use LLMs than other people. It sounds obvious now that I think about it but I never considered people use LLMs like google whereas I use it more like a real time thought transcriber (e.g. Dragon Naturally Speaking but not shite :P) Since it's trained on a RAG based off of my own polished thoughts, I've set it up as a meta-circular evaluator to do linguistic filtration (basically Fourier kernels on clip embedding space that map to various measures of "conceptual clarity").

So the LLM-ness of it to me is a clear-flag that this is hastily dictated.

also you're onto the actual quantum mechanics paper I'm working on. QM/QFT is modern day epicycles: arbitrarily complex because it was the aliasing the natural deeper representation which was Fourier/Spectral analysis.

Reformulating our entire ontology around relational mechanics is the answer imho. So Carlo Ravoli's RQM is right but I think it doesn't go far enough. Construct a grothendeik topos with a spacetime cohomology around different scales of both space and time with some sort of indefinite conservation and you get collision less Planck hyper volumes that map naturally to particle-wave duality interpretations of QM.

Yup, it's 100% generated by an LLM. I thought that was intentionally clear? (I'm recovering from a TBI so I'm still adjusting to figuring out how to relearn typing; I use the LLMs as my voice mediated interface to typing out thoughts).

I'm not sure there's an argument I'm hearing here other than you seem to have triggered some internal heuristic of "this was written by an LLM" x "It contains math words I don't understand" => "this is bullshit"

which you wouldn't be wrong but I am making a specific constructionist modal logic here using infinity-groupoids from category theory. infinite dimensional categories are a thing and that's what these transfinite numbers represent

you have hyperreal constructionists of the reals as well which follows nonstandard analysis. you can also use the Weil cohomology which IIRC gets us most of calculus without the axiom of choice but someone check me on that.

so....again, not sure what your specific critique is?

I mean you wouldn't be wrong to assume so but how can you expect anyone to saliently condense the entirety of a 10 year long proof of Grothendieck topos to 3 or 4 sentences my guy!