> The whole situation seems completely grounded in that mathematicians are greedy for status and clout trying to write their name on new discoveries in blood and publish as many papers as possible
You're gonna get downvoted but this is absolutely true. People who've never been in real professional academia don't understand but this is exactly what most very successful academics are like.
> When you remove this greed and status seeking you might actually end up with a healthy environment.
Nah I think you're just gonna have collapse because you've removed all incentive.
I don't disagree but I don't think that matters here where we're debating whether there's a skill to be learned and you compared to something else which is not deterministic.
> Friendly reminder that if you look at population numbers
i think it's funny that you tried to cast doubt but couldn't even do that because you lead with the glaring flaw in your reasoning instead of your rhetorical point. congrats.
i think what they are saying is that if you really so certain that the proof is incorrect, you would put on that claim and rest assured that you would win. Especially since the position you are claiming is currently at less than 10%, you stand to win a large amount of money.
The person you are arguing with made no such claim of certainty either one way or the other, so they have no reason to bet anything.
I understood what they were saying but if they're not willing to bet any money then they should refrain from commenting entirely since that seems to be the bar they are setting for others.
I think you misunderstood. His mouth was not at "the proof is correct". His mouth was at "you are not really certain that the proof is incorrect". Those two are not the same thing, so flipping the accusation back at him and saying "you should've bet on the proof being correct then" does not actually make any sense.
edit: in other words, if there is anything that he should bet on, it's "the other guy wasn't really certain that the proof is wrong, he is just bloviating". That's a different bet than "the proof is correct".
Sorry I need you to state your axioms here because as I stated above, "standard" semantical interpretation of the word "certain" implies you should be betting lots of money. Since you're not, I have to conclude you have some goofy unorthodox semantical interpretation.
By standard semantics, if you state that believing with certainty that the proof is incorrect is stupid, then you surely believe with certainty that it's correct.
Unless you want the negate the certainty part, but then the nudge to gambling is less coherent.
> By standard semantics, if you state that believing with certainty that the proof is incorrect is stupid, then you surely believe with certainty that it's correct.
you might want to think a little bit harder on this
> It was completely wrong but the outputs were surprisingly close to reality.
that's not how physics works. epicycles weren't wrong. there is no wrong/right - modern scientists don't believe in platonism. physics is a collection of models which are empirically tested. if epicycles makes predictions to more decimal places than relativity then epicycles are "right" and relativity is "wrong".
> physics is a collection of models which are empirically tested. if epicycles makes predictions to more decimal places than relativity then epicycles are "right" and relativity is "wrong".
Most models have relation to each other so it does not suffice to take one in isolation. It's one continuous world (in our knowledge) so almost everything relates to one other. The truthiness of something is not whether it fits some particular phenomena, but how does it generalize.
After an ansatz, which constitutes nothing more than an assumption, has been established, the equations are solved more precisely for the general function of interest, which then constitutes a confirmation of the assumption. In essence, an ansatz makes assumptions about the form of the solution to a problem so as to make the solution easier to find
I don't see where this contradict my statement. A good answer does not means the formula used is correct.
Is it useful to invoke it though? Once two people claim to know the actual truth, yet they disagree, you're at an impasse. There's no method for resolving which allegedly obvious claim is in fact the truth.
Predictive power on the other hand, gives you a framework to decide which story is more useful.
Brother you're wrong and there's ample scholarship you can consult to correct your misunderstanding. The Wikipedia with sufficient citations is right there. Feel free to educate yourself.
Not defending GP, but your claim that actual truth "obviously exists" is equally condescending and empty of backing evidence.
Would you say the continuum hypothesis (or its negation) is "actual truth"? Or does the "actual truth" become something closer to "actually, there are models of ZFC where CH holds as well as models where it doesn't hold, or maybe ZFC is already inconsistent; we don't really know, nor can we."?
Similarly, on the subject of astronomical reference frames, I'd argue the "actual truth" is closer to this:
> Any reference frame that locally obeys Newton's law of inertia is equally valid. Some are more useful than others depending on the problem you are studying. The notion of an "absolute center" is purely semantic, and a meaningless human construct, until one places bounds on the system under study, wherein the center of mass becomes the most reasonable choice at sub-cosmological scales.
Saying "there are models of ZFC where CH holds as well as models where it doesn't hold" sounds to me like talking about truth.
If I say "there are countries with an access to a sea, and there are also countries without an access to a sea" does it mean that there is no truth about whether seas exist or not?
> "actual truth" obviously exists regardless of your ability to measure or perceive it.
a reasonable person would at least peruse the literature before making such strong claims as
> Either state your argument coherently so as to address my completely valid objection, or move on if you're not interested in having a discussion.
i'm not interested in educating you on thousands (literally dating back to plato) of years of scholarship/philosophical discourse on the topic of epistemology. that's not my responsibility because you are not paying me for this - typically people charge large amounts of money for this kind of work (uni professors are well compensated).
lucky for you others have done lots of work making this information available to you for the low low price of "reading". that's why i provided the link.
Sorry, you're the one making ridiculously strong claims like "actual truth doesn't exist". The onus is on you to prove them.
Like I said in a different thread: thousands of years from now, it might literally not be possible to prove that you ever existed, but that wouldn't change the "actual truth" - the fact that you did exist, and do things. Stuff happens outside of your person, in the real world, without regard for our ability to perceive/articulate/"know" it. It's only possible to say things like "actual truth doesn't exist" if you think your mind is the only thing that really exists.
> i'm not interested in educating you on thousands (literally dating back to plato) of years of scholarship/philosophical discourse on the topic of epistemology.
> thousands of years from now, it might literally not be possible to prove that you ever existed, but that wouldn't change the "actual truth" - the fact that you did exist, and do things.
My man forget thousands of years in the future you don't know whether I exist today lololol
> Cool. Then don't start a discussion with m
I didn't? I told you were wrong and that's it (and then you got pissy). I know that's what happened because each of ours responses are recorded on this indelible/irrefutable medium lololol
> One is that AI will continue hallucinating in a manner that is not easy to verify, second is that AI will not be enhanced to produced more simplified amd robust outputs, and third that a human will be required to do that.
There is literally not a single shred of evidence to indicate either of your supposed eventualities. The core technology of an LLM is sampling from a distribution so there is literally no way to make it deterministically robust (only probabilistically).
The direction and pace of capability improvement has already been demonstrated by all models. The latest breakthroughs make that pretty evident, but there have been production systems that are based on probability since the beginning of computing.
What has been demonstrated is a process that outputs lean proofs based on those probabilities. This happened after decades markov chain producing garbled texts and very shortly after gpt2 producing stories about unicorns.
> The core technology of an LLM is sampling from a distribution so there is literally no way to make it deterministically robust (only probabilistically).
An LLM mostly deterministically (except parallel processing nondeterminism that can be mitigated) produces a probability distribution that can be sampled deterministically: just take the highest probability token or use beam search.
I think people on here tend to somewhat fixate on the determinism issue. Even with a deterministic LLM - stabilising the floating point arithmetic, and choosing from the distribution by a fixed method, or just save the random seeds - there is still a kind of a chaotic unpredictability that can exist between its inputs and outputs. However maybe that is a price that needs to be paid to get creativity.
Deterministic yes, robust deterministic no. The most likely conjunction is not always the best nor representative of what the model is considering unless its certainty is high.
No evidence other than the fact that this has been happening steadily in all areas for many years?
You might have a point if the goal was to have LLMs that spit out a correct proof without chain of thought or tool use. LLMs + agent harnesses are more than capable of self verification and course correction.
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