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PaperclipPerfector  1d ago (text post)   4685 thread views

Culture War Roundup for the week of August 31, 2026

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Together with the Arday scandal, social science is really having a bad time right now. The killer is that these are not just random researchers, but professors, and not just professors, but celebrated stars with multiple books, regular media appearances and political contacts. They are likely to impact actual policy and general large-scale decision-making. And to add insult to injury, it's getting increasingly obvious that a) competent fabrication would be undetectable in practice, especially this much later and b) nobody actually cares enough to check in general. They were just both incompetent enough and people pretty much stumbled over it.

I'm unsure whether social science in its current form is salvageable. It comes down to feedback loops: Math has a direct feedback loop with reality through the structure of proofs. You can set up implausible assumptions, yes, but since you have to state them clearly you can always be called out on it. And it's still relevant information that, if the assumptions are true, it follows whatever you have shown in the proof. In physics, you usually can turn a model into predictions which will eventually be measurable, even if through rather elaborate channels such as measuring red shifts of far-way celestial bodies or by ramming very small particles into each other.

And so on further down the line; My own field, medical genetics, is a lot worse than those as well but we also have at least some points of connection with reality; IF I find a variant that is plausibly connected to a serious disability, and IF there is a medication that can effectively bypass that variant (for example, producing the protein that became malformed), we will usually see a noticeable positive impact on patients, even if it does not fully cure them.

But social science? Almost any result can be interpreted in almost any way one may choose; Surveys and closed, short-term experiments are possibly more connected to social desirability bias than to anything else, real-life cohorts are probably mostly selection effects, and controlling for them is usually somewhere between illegal and impossible. There is not zero good research, but it's completely drowned out by the bad, and even where people attempt to do it well, it's hard to say; For example, I like discontinuity design, and it imo works well for entry tests (barely made it into an university vs barely didn't make it), but exactly the same design for school area impact is probably nonsense bc people can deliberately move into those neighbourhoods so barely inside vs barely outside of the area is again mostly selection effects.

In such an environment, and given considerable pressure on them to deliver convenient results (again, unlike math and most of physics) which also results in substantial rewards outside academia, social science predictably devolves into near-pure high-school style popularity contests.

In physics, you usually can turn a model into predictions which will eventually be measurable,

For a while, the String Theory folks got a lot of funding, but never seemed to deliver practically testable predictions. I'm not sure this is as true in physics as you'd like it to be, but it is certainly moreso than the humanities.

In fairness, doesn’t theoretical physics deliver lots of results that require either exotic technology or bajillions of dollars to actually test?

The complaints I recall hearing from the less-theoretical physicists is that the string theorists were taking up a large share of the available funding effectively navel-gazing daydreaming about the pretty symmetries of strings without actually producing testable hypotheses even at "LHC" scales of "testable". Those folks are used to expensive tests, but the string theory results needed like 3-4 or more orders of magnitude in scale.

I actually had the string theory folks on my mind while writing this, whether I should put a caveat there. There's always a "but". The key to me is that with almost everyone I've talked with who is sufficiently familiar with physics, they mention string theory, and they always clearly acknowledge their lack of predictions is bad. At least some number of those theorists tried to find something testable. And as you imply, it seems to be on the downturn in funding (unsurprising, the EU tries to pick up the slack somewhat, they certainly have impeccable timing). Altogether, that's good enough for me.

Math has a direct feedback loop with reality through the structure of proofs.

This is unfortunately a merely aspirational statement. The practice of mathematics involves writing proofs in a heavily intuitive manner, and their verification in turn involves people who have been socialised to share the same intuitions, which is a process that rarely involves proper reduction to the axiomatic basics but more often looks like "your elders and betters assert that it is trivial and look at you with mild disappointment, and all your peers seem to already have gotten it, so get on with it and flog your brain into producing the 'this is obviously true' qualium already". There were a handful of examples where local cultures/status hierarchies perpetuated a body of wrong mathematics this way, such as the "Italian school of algebraic geometry" and more recently (most likely) the Mochizuki abc conjecture incident.

We can be quite glad that it has not yet happened that the lines of a wrong intuition-subculture have aligned with general tribalism yet. If Interuniversal Teichmüller Theory were an invention of the likes of Arday, we would be seeing its detractors decried as racist and proper mathematicians performatively weaving it into the body of accepted and otherwise sound mathematics. Even if this did in fact cause further downstream inconsistencies to open a path to excision and repair, discovering those is (disproving abc)-complete, and that's something we have tried and failed for a long time.

The practice of mathematics involves writing proofs in a heavily intuitive manner, and their verification in turn involves people who have been socialised to share the same intuitions

I'm struggling to understand what you mean. At this point we have systems for automatic verification of formal proofs. In what sense are those systems socialized to share the same intuitions?

Those systems are not, but automatically verifiable proofs are still only a tiny sliver of frontier mathematics. Maybe AI can fix that, but AI can fix social science too. Just require that credit for AI research always has to go to some human, allocate token budgets by protected class, and you can ensure the Ardays stay ahead without requiring them to lie.

The intuitions required for formal proof verification are "it's worth rewriting this proof in another language that's an order of magnitude more verbose just so you can get a computer to tell you what you're sure you already know" and "the verifier doesn't have any soundness bugs that will invalidate any of its verifications" Historically the latter has sometimes been untrue and the former has usually been untrue. LLMs are fixing the first problem, which is exposing and leading to fixes for the second problem, but that's all a relatively new development. It's going to take a while to go back through all the mathematical literature and see how much of it might have problems due to predating the coming era of formal verification.

Consider the recent construction of a complex structure on the six-sphere. The simplest English explanation I've seen is under a thousand lines of (admittedly difficult!) writing and mathematical notation. The Lean formalization is a quarter-million lines of code. It's ... probably correct, people seem to think? But if it is correct, the construction would (reportedly; this is outside my field and way beyond me) contradict a 2020 paper (which itself was a correction to a 1998 paper), so we're almost certainly either producing new broken proofs or revealing old invalid proofs here.

Sure, you can fuck up everything. As noted in the wiki entry (presuming it's correct), there was no problem with formal proofs; The problem was first going for informal arguments (the start of the slippery slope, though as so often it worked fine-ish for awhile) and then lowering the standards until anything goes. I also think it's notable that the majority of mathematicians has so far refused to accept the Mochizuki proof until it's understood more widely. Both were also mostly localised incidents.

Admittedly I've always been on the more informal end of math myself as well (back when I did research in a field that could be described as mostly-theoretical math), but even there I could simply double-check my conjectures with simulations, which is just yet another way of a feedback with reality.

I think you underestimate the power of proofs. If you make a conjecture, try to write a proof, and not just fail, but you find obvious counterexamples, there just isn't much left to salvage. Or the other way around, if you find multiple different proofs to arrive at the same conclusion and nobody you meet can generate any counterexample or find a clear hole in the proofs. It's true that there is some social element, it would be silly to claim otherwise, but proofs aren't just arbitrary arguments at triviality, either.

I'm familiar enough with the practice of maths (being an actual researcher in adjacent-enough TCS, and having had one foot in extremal combinatorics through a big part of my toil towards the degree), and I think you really overestimate the rigour of proofs as usually written up. The incidents I mentioned are for sure geographically localised, but in the case of the Italians it's not like the situation was that they believed it, and everyone else disagreed; for the longest time it was instead that they believed it, and nobody elsewhere cared but probably would have assumed that their fellow mathematicians knew what they were doing if they had to build upon one of their results.

There are other examples where, due to insufficient rigour of proofs as allowed and encouraged in the field, wrong proofs stood for quite a while. This was the case for like 10 years for some of the earliest claimed proofs of the 4-color theorem (an undergrad assignment actually had us find the counterexample to the core lemma there), more recently for some pretty celebrated random matrices "result" by Avi Wigderson et al. (hardly nobodies!) which stood for several months, and when writing a summarising essay on some cluster of Erdös papers I learned about a key lemma that was straight up wrong as stated, but people in the community thought essentially "something like it is clearly true, the core ideas of the proof are fine, and it's okay for the situation where we use it" (no proof of any of those things committed to paper). Correction eventually happened in the cases we know about, but can we really rely on the mechanism? Mochizuki has intimidated a big part of his department to ignore the refutations, and Japan is hardly a backwater, and there are political forces out there that are stronger than "this guy is one of our country's best, we should stand by him".

Man, I remember struggling with mathematical proofs in University. I kept just not getting it; it was never explained what made a valid proof. I eventually just learned to intuit what my professors expected, barely well enough to make it through, but I never truly got it.

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