Five disciplines discovered the same math independently

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

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.

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?

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.

I know for a fact [1] that the neuroscientific discoveries were not independent of physics: the people doing the developing were largely former physicists. They likely didn't cite anything because why would you cite phase transitions or criticality? You learn about them in class as a physicist. I strongly suspect the ecology results weren't independent either, but all the theoretical ecologists I know are relatively young (if mostly former physicists) so no first person accounts.

The part of this that could totally be true is that a clinical application somewhere along the way "independently" "reinvented" it. There's a hilarious collection of peer-reviewed journal articles out there inventing a "new" method of calculating the sizes of shapes and areas under the curve. The method involves adding up really small rectangles. (I think a top comment already mentioned the Tai article [2])

[1] source: my doctoral advisor was a really really old theoretical neuroscientist who trained as an electrical engineer and mathematician. If you want a more concrete example, the work of Bard Ermentrout on neural criticality starting in the 70's or 80's. He read a lot of physics textbooks.

[2] https://science.slashdot.org/story/10/12/06/0416250/medical-...

You're raising the right question, and the paper addresses it directly. The transfer wasn't as clean as "physicists applied their tools to other fields."

Some specific cases: Wissel (1984) derived critical slowing down for ecology independently and was ignored for 20 years. The actual import to ecology came via economist Buz Brock, not a physicist. Nolasco & Dahlen (1968) derived period-doubling for cardiac tissue before Feigenbaum's universality result. Jaeger (2001) derived the edge-of-chaos condition for recurrent neural networks without citing Bak, Kauffman, or Langton.

The complex systems movement you reference existed. The paper documents that it didn't actually solve the transfer problem. The cross-citation analysis shows the gaps persisted through the 2000s and 2010s.

You're right that some domains imported rather than reinvented. The paper maps where each transfer was independent, where it was imported, and where it was partial. That's the point — the pattern is messier and more interesting than either "all independent" or "all imported."

I mean, introducing a technique from one field in another is innovative.

You don't get to claim you invented it, but a lot of progress happens by finding connections between things that are individually well known.

Exactly right. The phase transition analogy is powerful precisely because it's not just analogy — the same mathematical operators that describe water at criticality also describe markets approaching crashes, ecosystems approaching collapse, and cardiac rhythms approaching fibrillation.

What surprised us was how many fields derived this independently. The superheated water intuition you describe maps directly to what ecologists call "critical slowing down" and what financial engineers call "increased autocorrelation near instability." Same math, three different names, minimal cross-citation.

> it's not like it just flips.

Does this apply to that cool chem trick where a solution goes from black to transparent and back again a few times? I don't know enough to know if that's relevant or not, but I remember seeing that and be puzzled about how "sudden" the reaction appears.

The propagation time is the interesting part. Critical slowing down was in physics textbooks by the 1970s. Ecology didn't import it until 2003 — via a chance conversation at a conference bar. Cardiology took until the 1990s. The FDA approved the resulting cardiac test in 2001.

That's not normal diffusion. Those are 30-year gaps for math with direct life-safety applications. The paper asks why, and finds structural explanations in how we organize knowledge.

and every comment here is also AI.

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.

Good question. It's closest to dynamical systems, which usually lives in applied math or physics departments. But that's kind of the problem — it gets taught as theory in one department and never reaches the engineers and clinicians who'd actually use it.

If you've done diffeq and linear algebra you have the prerequisites. Appendix B (page 17 of the paper) is our attempt at making it practical — worked examples rather than proofs. Would be curious if it lands for someone with your background.

We plan to do a follow-up paper that provides a standard format for this math that could be taught across domains. That doesn't belong in this first paper. First priority was to show the pattern and get people thinking about it.

No, the goal is documenting the convergence pattern itself. We did use LLMs as research tools — acknowledged in the paper — but the cross-domain analysis and citation mapping are human work.

I'll explain how we got to this point. I had previously mentored my friend, Robin Macomber, in math & physics for several years. Robin Macomber independently discovered a variation of criticality math and asked me to evaluate. After due consideration I recognized a pattern: his work echoed that of Kenneth Wilson's renormalization group theory, which I'd previously studied. I then conducted a detailed survey of all academic fields that touched on criticality (using an LLM!) and found, to my great surprise, that this same math had been independently discovered many times in many domains. So I wrote a paper about it.