I may be misremembering Godel's proof or misunderstanding your last paragraph, but I thought Godel's proof actually presented a specific undecidable statement. The hope then was that somehow undecidable statements could be cordoned off from decidable statements, and Turing's result showed that that wasn't possible. Perhaps that's what you mean by "the nonexistence of a single algorithm that correctly answers every instance in that family"?
replyI may have been making this claim, I need to think about this for a while and re read what you have written.
replyThis is very helpful though, thank you.
If I am wrong, please pardon. I suspect I am. But was this comment edited by Claude? I ask specifically because it is well written, substantive, all which is expected here, but the "push back" part, to me, must be a) an artifact of Claude, either by osmotic assimilation (Which is happening to many innocent users) or b) Claude itself.
replyFeel free to flag this comment if I get an answer. I do want to know.
No Claude was not involved in any way in me writing it, and honestly it's kind of getting depressing how many comments are constantly questioning peoples use of LLMs.
replyJust a heads up, "I want to push back on" is an idiom Claude frequently uses.
replyIt is depressing though, writing feels like it's in part becoming a game of outpacing the latest LLM's idiosyncrasies so we can signal authenticity, which perversely, is achieved through using an LLM enough so that you can become familiar with its flavor of communication.
This is what makes me sad about the AI age; many articles now have the same phrasing, the same analogies, the same quips, structure, the same wording; once you start to see it there's no going back.
replyI actually laughed quite a lot to begin with, GPT models saying things like "...might look like P, but is NP wearing a hat and a lab coat..." and "...is a haunted house disguised as a git repository..."; but alas when you've heard them a million times everywhere it really starts to bite.
Yeah, that's why I invited the flag. But do not overlook how fucking depressing the endless LLM generated comments actually are too.
replyMy apologies, and I do appreciate your reply.