This weekly roundup thread is intended for all culture war posts. 'Culture war' is vaguely defined, but it basically means controversial issues that fall along set tribal lines. Arguments over culture war issues generate a lot of heat and little light, and few deeply entrenched people ever change their minds. This thread is for voicing opinions and analyzing the state of the discussion while trying to optimize for light over heat.
Optimistically, we think that engaging with people you disagree with is worth your time, and so is being nice! Pessimistically, there are many dynamics that can lead discussions on Culture War topics to become unproductive. There's a human tendency to divide along tribal lines, praising your ingroup and vilifying your outgroup - and if you think you find it easy to criticize your ingroup, then it may be that your outgroup is not who you think it is. Extremists with opposing positions can feed off each other, highlighting each other's worst points to justify their own angry rhetoric, which becomes in turn a new example of bad behavior for the other side to highlight.
We would like to avoid these negative dynamics. Accordingly, we ask that you do not use this thread for waging the Culture War. Examples of waging the Culture War:
-
Shaming.
-
Attempting to 'build consensus' or enforce ideological conformity.
-
Making sweeping generalizations to vilify a group you dislike.
-
Recruiting for a cause.
-
Posting links that could be summarized as 'Boo outgroup!' Basically, if your content is 'Can you believe what Those People did this week?' then you should either refrain from posting, or do some very patient work to contextualize and/or steel-man the relevant viewpoint.
In general, you should argue to understand, not to win. This thread is not territory to be claimed by one group or another; indeed, the aim is to have many different viewpoints represented here. Thus, we also ask that you follow some guidelines:
-
Speak plainly. Avoid sarcasm and mockery. When disagreeing with someone, state your objections explicitly.
-
Be as precise and charitable as you can. Don't paraphrase unflatteringly.
-
Don't imply that someone said something they did not say, even if you think it follows from what they said.
-
Write like everyone is reading and you want them to be included in the discussion.
On an ad hoc basis, the mods will try to compile a list of the best posts/comments from the previous week, posted in Quality Contribution threads and archived at /r/TheThread. You may nominate a comment for this list by clicking on 'report' at the bottom of the post and typing 'Actually a quality contribution' as the report reason.
Jump in the discussion.
No email address required.
Notes -
I think the development of formal proof verifiers like Lean mostly quelled the practical concerns about computer-assisted proofs. Nobody's going to trust some two hundred page "proof" just because an LLM spat it out, but formalize it and properly verify the proof steps via a smaller verifier that's been itself closely manually examined, and then the remaining parts of it you have to check manually are more like definitions (when Lean verifies that "All Foos are Bars", does its definition of "Foo" and "Bar" match ours?) and much easier to understand and review. There's a real synergy here in iterating between proof verifiers (which will reliably state whether a proof is correct, but weren't very popular by themselves because they require the proof to be spelled out in tedious precise detail) and large language models (which will translate a colloquial proof into tedious precise detail, but aren't very useful by themselves because they aren't reliable enough to trust without rigorous checking).
The aesthetic concerns are still there, though. There are proofs that you can read through (the highlights of, not the every-trivial-step that you have in something formalized) and they enhance your understanding of the subject, and then there are proofs that just make it from point A to point B via some kind of hideous brute force, and there's a reasonable fear that computer-generated proofs or even just computer-assisted proofs are going to have a lot more of the latter instead of the former. There was quite a lot of excitement recently about a couple newly-AI-proven conjectures (IIRC one on primitive sets, another on Ramsey numbers, both on asymptotic behavior?) because, not only were these about questions that human mathematicians had taken more than a passing interest in, but the proofs were short and insightful. Candidates for proofs "from The Book", to use Erdös' old phrase.
Well, everybody agrees that if you accept it then you get certain nice things and certain nasty ones, and that you can have consistent models that accept it and consistent models that don't. There's still a disagreement here, but it's again a disagreement over aesthetics more than over fact.
It's a big disagreement over aesthetics, admittedly. The joke goes: "The Axiom of Choice is obviously true, the Well-ordering principle obviously false, and who knows about Zorn's lemma", and the humor is that emotionally that all feels true even though logically those three things are provably equivalent.
There might even be increasing common ground in the aesthetic question. The Axiom of Dependent Choice is sufficient to prove a ton (I hesitate to say "all", since in my own field we typically just throw up our hands and assume full AC, and I'd love to learn of any results that really do make full AC necessary) of the classic real-analysis and functional-analysis theorems that Zermelo-Fraenkel alone doesn't give you, but it isn't sufficient to force the existence of ugly-seeming things like non-measurable subsets of ℝ, or of insane-seeming things like Banach-Tarski.
Okay, there's "every vector space has a Hamel basis", which may have important implications I don't realize since I just use Schauder bases in spaces where the distinction matters.
More options
Context Copy link
More options
Context Copy link