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by anvuong 5 days ago
Well, how many humans do you think are able to prompt this to the LLM?

"The homogeneity in x is an intertwining between a dilation (x,r,u) to (lambda x, r,u) and a dilation (P,Q,R) to (lambda^-2 P, lambda^-1 Q, lambda R) which seems to collapse the 3d jacobian to a sort of twisted 2d jacobian. Is there a general theory of such twisted jacobians and do you have any sense why those particular dilation weights were used?"

"I can see why the five-dimensional Jacobian has a nice monomial form in rho. Why does this make the three-dimensional Jacobian after restricting to c_2 = rho = 1 and eliminating the delta, eps variables also a monomial (now in x)? Is there some block-diagonal structure or something in the 5D Hessian that allows for a nice reduction? I would have expected some sort of Schur's complement type operation to appear."

I, and probably most people on here, won't be able to get the LLM to write such a detailed conversation, because we are not experts in this field. They are tools.
3 comments
bananaflag 5 days ago
Read these 4 prompts and tell me again how in the future we shall still need human expertise:

https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0...

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butlike 4 days ago
Because the 4 prompts were actually still prompting for the original prompt (ugh.) in that the computer did not come up with a "complete unconditional counterexample" and the human expertise is required to discern that.
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ivell 5 days ago
There was an article on Rudi Mandl who pestered Einstein into working on gravitational lensing.

This happened because Rudi was persistent and Einstein was kind enough.

In future, citizen scientists have a chance to work on their ideas using AI, eventhough they don't have the deep domain skills. Of course, an expert would still need to review it as usual. But it is a useful tool to democratize science further.

https://www.sciencenews.org/blog/context/amateur-who-helped-...

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falcor84 5 days ago
I don't get the argument. It sounds to me like you're saying that because my own chess skills are insufficient to allow me to have a proper game with a grandmaster and I end up losing on move 10 because after a stupid blunder, then I should conclude that this grandmaster is just a tool?
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