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Comment by amelius | Hacker News Reader

But what if the critic is just hard reality? If you ask an LLM to write a computer program, instead of criticizing it, you can run it and test it. If you ask an LLM to prove a theorem, let it write the proof in a formal logic language so it can be verified. Etcetera.

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Generated code only works because "test" part (compile/validate/analyze etc.) is completely external and written before any mass-market LLMs. There is no such external validator for new theorems, books, pictures, text guides etc. You can't just run hard_reality.exe on a generated poem or a scientific paper to deem it "correct". It is only possible with programming languages, and even then not always.

Science is falsifiable by definition, and writing poems/books is not the kind of problem of interest here.

> There is no such external validator for new theorems

There are formal logic languages that will allow you to do this.

Your proposed approach to science would result in the extremely tiny subset of math, probably theorems being proven by automation. And it is questionable if those theorems would be even useful. A good mathematician with CS experience can probably write a generator of new useless theorems, something along "are every sequential cube plus square of a number divisible by a root of seventh smallest prime multiplied by logn of than number plus blabla...". One can generate such theorrems and formally prove or disprove them, yes.

On the other hand any novel science usually requires deep and wide exploratory research, often involving hard or flawed experimentation or observation. One can train LLM on a PhD curriculum in astrophysics, then provide that LLM with API to some new observatory and instruct it to "go prove cosmological constant". And it will do so, but the result will be generated garbage because there is no formal way to prove such results. There is no formal way to prove why pharaohs decided to stop building pyramids, despite there being some decent theories. This is science too, you know. You can't formally prove that some gene sequence is responsible for trait X etc.

I would say a majority of science is not formally provable.

And lastly, you dismiss books/texts, but that is a huge chunk of intellectual and creative work of humans. Say you are an engineer and you have a CAD model with a list of parts and parameters for rocket for example. Now you need to write a guide for it. LLM can do that, it can generate guide-looking output. The issue is that there is no way to automatically proof it or find issues in it. And there are lots of items like that.

I think the problem here is that you assume the LLM has to operate isolated from the world, i.e. without interaction. If you put a human scientist in isolation, then you cannot have high expectations either.

I assume not that LLM would be isolated, I assume that LLM would be incapable of interacting in any meaningful way on its own (i.e. not triggered by direct input from a programmer).

> You can't formally prove that some gene sequence is responsible for trait X etc.

Maybe not formally in some kind of mathematical sense. But you certainly could have simulation models of protein synthesis, and maybe even higher order simulation of tissues and organs. You could also let the ai scientist verify the experimental hypothesis by giving access to robotic lab processes. In fact it seems we are going down both fronts right now.

Nobody argues that LLMs aren't useful for some bulk processing of billion datapoints or looking for obscure correlations in the unedited data. But the premise of the Gwern's article is that to be considered thinking, LLM must initiate such search on it's own and arrive to a novel conclusion on it's own.

Basically if:

A) Scientist has an idea > triggers LLM program to sift through a ton of data > LLM print out correlation results > scientist read them and proves/disproves an idea. In this case, while LLM did a bulk of work here, it did not arrive at a breakthrough on its own.

B) LLM is idling > then LLM triggers some API to get some specific set of data > LLM correlates results > LLM prints out a complete hypothesis with proof (or disproves it). In this case we can say that LLM did a breakthrough.

IME, on a daily basis, Claude Code (supposed SoTA agent) constantly disables and bypasses tests and checks on my codebase - despite following clear prompting guidelines and all the /woo/ like ultrathink etc.

I think if we can have a good enough simulation of reality, and a fast one. Something like an accelerable minecraft with real world physics. Then this idea might actually work. But the hard reality we currenly could generate efficiently and feed into LLMs usually has a narrow scope. It feels liking teaching only textbook math to a kid for several years but nothing else. The LLM mostly overoptimize in these very specific fields, but the overall performance might even be worse.

Its gotta be G-Mod

There will never be a computer powerful enough to simulate that many paperclips and explosive barrels.

Those things are being done. Program testing is now off-the-shelf tech, and as for math proofs, see: https://www.geeky-gadgets.com/google-deepmind-alphaproof/

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