Maybe we should define and spec what is an Open Platform, say RSS, Mastodon, grandma cookies recipe in a txt in an Apache, etc. Then paint a beautiful "open platform" logo and start making some collective noises, some pinky flower good-guy psiops. If reply is it alrady exists, it ain't rather working. Currently civil life is being shaped for the algos and the money, that is ok in business terms, we civilians are not coaxed to post or follow Twitter or Facebook as in an Orwellian bad dream. We rather opt-in, yet the politic process is not more illustrated despite all factual discussions at a chat distance of resolution, rational debate is penalized for being boring and much we are offered is as gamified as the Aliexpress user experience. Let's convince ourselves first that the parallel non-profit internet is a grand place to find the full spectrum of human rant in all its glory and gore. Hail the guy in his basement that made and documented a COTS parts scanning tunnel microscope. That is open platform content. Heck, remember webrings? Megacorps are not the problem, it is us being lazy even as spectators.
People don't gravitate to open or closed platforms, or platforms at all. They gravitate to something else. I think it's the ability to reply to a global conversation and feel like you're doing something, like I am right now.
The Epoch Capabilities Index uses an Elo-based aggregation method that dynamically adjusts for benchmark difficulty and they put error bars on their scores, both of which put them miles ahead of Artificial Analysis: https://epoch.ai/eci?view=graph&tab=leaderboard
That is a very valid question. I happen to want to get Claude Code muscle memory under my belt for professional reasons in addition to get side projects advanced, could have settled for Codex else. Also OpenCode with eastern models gets part of the job done. In CC beyond using Luna for the cheap, I am using DeepSeek flash v4 for subagents, that is a further cost shaver. Not sure if in Codex I could do that.
The multiplication they call an "alternating [skew-symmetric?] invariant form": Q0 in symbols I think?
Basically a polynomial function in the components of the "superoctonions" that go into the product.that how I'd vibesplain to a fellow non-pro, anyways
P10, sec 2.4 Lemma 2.8
The complex structure itself is much more complicated.. or else alpoge would have posted a one line verification of the result? But a summary that excites everybody can only be done by a pro...
The next relevant thing in the paper though, that I might be able to attempt to vibesplain using my uh consumer knowhow, is "integrability" (starting in the section labelled "Context")
yep I have feet wet with complex geometry/analysis but not to decipher lemma 2.8. But instead of asking ELI10 I asked about S^6 complex structure helping to cure O non-associativity and got open research directions for sibling goals more than clear cut "yes, if the paper pass validation we've got some new associative octonions". That may need some healthy challenging.
Apropos, Wikipedia says at a picture: "(Left) The von Mangoldt function, approximated by zeta zero waves.(Right) The Fourier transform of the von Mangoldt function gives a spectrum with imaginary parts of Riemann zeta zeros as spikes." [1]. [2] explains the details very gently, one can skip parts. So this is a machine with input a function very close to prime counts, and outputs info about zeta zeros. And the machine is Fourier transform.
That is a sensible way of turning chaos into order, but let a contrarian voice tell an alternative story. I think filesystem pdf organizing is underrated. I have been curating a tree along years and now I know where to park new pdfs by heart in there. Wrote an arxiv button adder with grease-monkey to save pdfs with title, year and authors as file-name. Windows have a nice abstract property system that can use pdf (bib) metadata by installing a shell extension, that you can use in Explorer, where you can customize displayed fields. Classic Windows search offers a good background indexed database of content and metadata for local files. You just need an "IFilter" component to let it see inside the pdf text layer (suamtraPDF cames with one). It is the kind of functionality one would expect of a commercial product, just for the windows license. Beyond File Explorer, You can query the index from scripting or dot-net. I wrote a flow-launcher plugin to making searching faster than from Explorer search text input. Search supports "saved searches", saving queries in xml. I use a lot two, listing the saved pdfs of the last week and the last month. Windows is weird in having that cute infra built-in, but just having left unfinished the last glue code needed to give some good user experiences managing docs.
I think Gödel undecidable sentence is always relative to a formal system (the title of the paper spoke about systems in the expressive power rank of Russell's Principia, of which he gives one particular example assuming it shows how his methods apply to the whole family of systems), but now Hilbert problem #6 still stands for the lack of a comprehensive axiomatization of Physics, as its modern heir the mass-gap millennium problem, that still also lingers, so we don't have a controllable notion of naked/absolute undecidability for physical phenomena or for arbitrary assertions unbound by explicit logic rules in general.
mmh I'd don't say that much, I think the logic and math foundations is common in both classic and quantum theories, only content changing, so you would say "import mathlib" from both classic-phys.lean and quant-phys.lean if writing Lean proof assistant code (I am guessing the "import" command). Concepts from linear algebra as eigendecomposition, to say something, will be used in both applications.
I participated there and couldn't guess for the life of me how does Baez gathers the amount of energy needed to put together all the materials, setup all the exercises and review and comment all the participation in a tuition free everybody-welcomed online experience such as that, beyond his normal academic duties. In the link there are the e-lectures but all the online forum give-and-take is sadly lost.
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