다섯 분야가 같은 수학을 독립적으로 발견했습니다 – 아무도 몰랐습니다

Five disciplines discovered the same math independently – none of them knew

62 pointsby energyscholar2026. 2. 8.47 comments

요약

물리학, 생물학, 금융, 기계 학습, 전력망, 교통 흐름 등 여러 분야의 연구자들이 복잡한 시스템의 티핑 포인트를 예측하기 위한 동일한 수학적 도구를 독립적으로 개발했습니다. 1935년부터 2004년 사이에 다른 이름으로 다른 학술지에 발표된 이러한 발견은 상당한 노력의 중복과 응용 지연을 강조하며, 시간, 자원 낭비를 초래하고 잠재적으로 인프라 취약성으로 이어졌습니다. arXiv의 논문은 이러한 수렴적 발견을 분석하고 학제 간 전문화 또는 구조적 인센티브가 이러한 파편화를 유지했는지 의문을 제기합니다.

energyscholar•4시간 전

Author here. We found the same mathematical structure appearing independently in physics (phase transitions), finance (market crashes), ecology (extinction cascades), neuroscience(neural criticality), and network science (cascade failures).

Each field derived it from first principles. Each named it differently. Minimal cross-citation. The affiliated scientific paper traces this convergent discovery and asks: if the same structure keeps emerging, what does that tell us about how we organize knowledge?

intrasight•3시간 전

It tells me that knowledge takes time to propagate.

Good math is universal, which means it's probably been discovered millions of times across the universe.

HPsquared•3시간 전

Phase transitions are a really nice way to explain to someone how a complex system can appear to flip from one state to another. Especially the importance of looking at the right variable. If you look at water at 99°C or 101°C (at standard pressure) it appears like a sudden change. But if you consider energy balance, it's not like it just flips: it takes substantial energy input to boil water. If you measure energy input, you see a gradual change of phase (mass fraction slowly turning from liquid to vapour) as more energy is supplied. But then you can also have superheated water in the microwave and it's just waiting to (partially) boil... So many analogies.

vscode-rest•3시간 전

I’m no mathematician (studied up to diff eq, linear algebra, discrete), but from glancing through the paper I do not really have an ability to apply this concept to a problem of my own, though it does seem useful.

Do you think this is something that should be taught generally? In which class would it fit? It feels generally diffeq-ish.

stared•3시간 전

I have serious doubts that these discoveries were truly independent.

Phase transitions and statistical mechanics have a long history in physics. Over time, physicists and applied mathematicians began applying these techniques to other domains under the banner of "complex systems" (see, for example, https://complexsystemstheory.net/murray-gell-mann/).

Rather than independent reinvention, it seems much more likely that these fields adopted existing physics machinery. It wouldn't be the first time authors claimed novelty for applied concepts; if they tried this within physics, they’d be eaten alive. However, in other fields, reviewers might accept these techniques as novel simply because they lack the background in statistical mechanics.

abracos•3시간 전

Is the main goal to see if LLM can do this sort of research and cross-pollination?

PlatoIsADisease•2시간 전

Everything you mentioned is a simplified system that applies in specific defined cases.

Its almost like the math came first, then the problem later.

You might want to read about induction vs deduction, this is deduction. I don't totally agree with Karl Popper, but at least he can explain why we see this math in multiple places.

bonsai_spool•3시간 전

I wish authors would use their own voice instead of an LLM, especially in a rhetorical piece. I like the history of science, and might have otherwise read the authors' paper, but the use of LLM-isms throughout this page makes me worry that the arxiv submission will show the same lack of care/effort.

Here's the manuscript at any rate, somewhat hard to find on the webpage:

Convergent Discovery of Critical Phenomena Mathematics Across Disciplines: A Cross-Domain Analysis https://arxiv.org/abs/2601.22389

energyscholar•3시간 전

Fair call on the website — we built it fast and it shows. The paper itself is a traditional literature review and citation analysis. I am one of two human authors. We use standard methodology. Didier Sornette endorsed it for arXiv.

Thanks for pulling out the direct link. I'll change the site to make it more prominent. This is my first serious attempt at social media engagement. Thanks for pointing out flaws and where there's room for improvment.

zozbot234•3시간 전

OP's comments in this thread are also pure clanker speak, which is disappointing and shows a lack of awareness of what HN is for.[0] It would be nice if an established scholar in this area of mathematics (complex systems) could comment re: this proposed correspondence and whether it has been noticed before. To be sure, similarly duplicative developments, gratuitous differences in terminology, etc. are discovered all the time, this isn't huge news. Statistics and ML is a well-known example.

[0] I haven't actually tried this, but I'm pretty sure that even just telling the robot "please write tersely, follow the typical style for HN comments" would make the output less annoying.

jmcgough•2시간 전

I felt the same way reading the linked webpage. Reads like minimally edited LLM output, which makes me question how much effort was put into the research itself. Was the research all LLM too? How much of the paper was LLM?

arjie•3시간 전

It reminds me of “Tai’s method” of integration - an approximation discovered in 1994.

https://academia.stackexchange.com/questions/9602/rediscover...

I think I found it in that other world that is the past on Slashdot - which was a Hacker News from another era https://m.slashdot.org/story/144664

energyscholar•2시간 전

I agree that's a good parallel. I had not seen it before. Thanks for the link.

[삭제된 댓글]

mastermedo•3시간 전

https://arxiv.org/pdf/2601.22389

jlund-molfese•3시간 전

It’s kind of lame to post the same clickbait three times in under 24 hours. I guess it’s nothing new, but feels inorganic.

energyscholar•3시간 전

Dude, I'm sorry to offend you. And sharp of you to notice. I failed to get substantive engagement the first two times (1 point and 4 points) so I tried again. This time I got some engagement.

Re. the title, I started with a boring conservative title and got precisely zero engagement, so I changed the title to be a bit more clickbaitish. Just like most of the other titles in New. Did I do wrong?

As I said, this is my first serious attempt at social media engagement and I'm just learning how it works.

ajkjk•2시간 전

and every comment here is also AI.

bob1029•3시간 전

https://en.wikipedia.org/wiki/Giant_component#Giant_componen...

clarity_hacker•3시간 전

The convergence isn't surprising once you notice that these domains all study systems near criticality — the point where small changes cascade into large effects. Phase transitions, market crashes, and extinction events are all hitting the same mathematical boundary condition: nonlinearity plus feedback. The structure is universal because the constraint is. Similar to how Zipf's law appears everywhere that optimization under resource scarcity matters.

PlatoIsADisease•2시간 전

I'm usually pretty pro-blog. I like when people have an interest in things. No ads, just someone wanting to prove their intelligence and popularity. But... OP... You didn't even explain the math.

Anyway, none of this is that surprising since deduction takes higher level ideas and tests them on lower level to prove the hypothesis.

If anyone wants to read Karl Popper, this will seem significantly less noteworthy.

profsummergig•2시간 전

There's a Taleb vs. Sornette debate (argument) on YouTube.

I thought Taleb won (complex system outcomes, in the sociopolitical realm, cannot be predicted). But then I'm a Taleb fanboy.

Sornette (my first and last exposure to him) came across as a relic from a different age. Pitifully out of touch.

MarkusQ•2시간 전

And they don't even seem to have noticed Catastrophe Theory, which was based on the study of exactly this.

https://en.wikipedia.org/wiki/Catastrophe_theory

sxzygz•2시간 전

You and your coauthor need to write up a detailed account of your “Metatron model”. This paper, if it were to count as research, should be how other phenomena can be simulated by choices of parameters for your model.

Otherwise, you’ve just described yet another synthetic model that exhibits criticality (without proof no less). Which is not particularly interesting, unless your model subsumes other phenomena.

다섯 분야가 같은 수학을 독립적으로 발견했습니다 – 아무도 몰랐습니다

요약

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