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this feels like excellent foundations for a board game. fascinating!


It's not necessary, but is significantly more radio-quiet than a lunar orbit. And secondly, though unfortunately not something we could really exploit this time, the stable temperatures of the lunar night greatly help with calibration for sensitive measurements like the 21cm Dark Ages signal


on the other hand and orbiter could have a much larger effective telescope diameter by SAR.


This is quite seriously missing the point: computational theorem-provers and contributions to mathlib (for Lean, anyway) allow for checking "correctness". The LLM is one of the many ways to search for tactics that help complete a proof for a theorem not yet in mathlib.

The LLM is not done until the theorem-prover says it is done - at which point we can be sure of the correctness of the assertion in the context. AFAIK there is no debate about inaccuracy with theorem-provers. Their real limitation continues to be converging in realistic timescales and efficient search over all combinations of proof tactics.


> The LLM is not done until the theorem-prover says it is done - at which point we can be sure of the correctness of the assertion in the context. AFAIK there is no debate about inaccuracy with theorem-provers.

Your "in the context" is doing a lot of heavy lifting here, see:

- The Math Is Haunted : https://news.ycombinator.com/item?id=44739315 : https://overreacted.io/the-math-is-haunted/

- Three ways formally verified code can go wrong in practice : https://news.ycombinator.com/item?id=45555727 : https://buttondown.com/hillelwayne/archive/three-ways-formal...

- Breaking “provably correct” Leftpad : https://news.ycombinator.com/item?id=45492274 : https://lukeplant.me.uk/blog/posts/breaking-provably-correct...

- what does a lean proof prove? : https://news.ycombinator.com/item?id=46286605 : https://supaiku.com/what-does-a-lean-proof-prove

> Their real limitation continues to be converging in realistic timescales and efficient search over all combinations of proof tactics.

I agree "efficient search over all combination of proof tactics" will be a defining moment in the field. I disagree these LLMs are it.


makes me wonder if a sufficiently large number of connected nodes can represent bits via their online/offline status, and their network graph representing "memory"


How was the interactivity achieved? Could you maybe link to the source so I can learn? I have been trying to get something like this working with quarto, but it is getting way too complicated.


I wrote everything from scratch in javascript and webgl. You can check the entire source code of the article here: https://imadr.me/pbr/main.js

Beaware though, it's a 8000+ lines of code js file that is very badly organized, it's by no mean a reference for good quality code. However I find writing everything by hand easier in the long term than using already existing libraries for example.

The code includes all the math functions, mesh primitive generation, shaders and even a sketchy text renderer using sdf fonts.

If I had to make it again I would use typescript, type errors were the biggest source of bugs.


How long did it take you to write that code / this article?

I'm a big fan of zero-dependency code (or at the very least with any dependency vendored/hosted locally), it means this page will still work and look as it does today in 25 years time.

I don't know if TS runs natively in browsers yet, but v8 / NodeJS does support it (just strips off Typescript specific tokens).


I took me about 3 months working on it on and off, it amounts to about 3 weeks of full time work. For my other projects I'm just writing everything to a single typescript file and compiling it with tsc, works like a charm and zero dependencies!


Love it! For typescript, esbuild has been my favorite tool for turning typescript into browser-readable js, and then I check type errors separately using the ide plugin.


and also how to lie with visual proofs: https://www.youtube.com/watch?v=VYQVlVoWoPY


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