Five disciplines discovered the same math independently • Hacker News Board

Re: Five disciplines discovered the same math independently

#31

Post by energyscholar » Sun, Feb 08, 2026, 5:30 PM UTC

asgraham wrote: post #21

stared wrote: post #11

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 tha…

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…

Good correction! Ermentrout is a fair example. You're right that a lot of neuroscience criticality work came from retrained physicists. The paper distinguishes between independent derivation and cross-trained import. The title for this post over-simplifies this. I made this change to try to increase engagement, since the full detailed title got zero engagement.

Where I'd push back: even after physicists brought the tools into neuroscience, the receiving field didn't connect it back to the parallel work in ecology or cardiology. Ermentrout's neural work and Goldberger's cardiac work used the same underlying math but didn't cross-cite. The silos reformed around the imported tools.

You're correct that "none of them knew" is too strong. Fair point. "Most of them didn't talk to each other even after import" is closer to what the citation data actually shows.

Re: Five disciplines discovered the same math independently

#32

Post by HPsquared » Sun, Feb 08, 2026, 5:31 PM UTC

NitpickLawyer wrote: post #13

HPsquared wrote: post #5

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 i…

> 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.

That sounds like something sufficiently strong at absorbing light where it appears to be black at a fairly low concentration, so even if the concentration changes smoothly (maybe a sine wave) but to our eyes it looks more like a step change near the bottom.

Re: Five disciplines discovered the same math independently

#33

Post by ajkjk » Sun, Feb 08, 2026, 5:31 PM UTC

energyscholar wrote: post #14

stared wrote: post #11

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 tha…

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 be…

AI comment?

Re: Five disciplines discovered the same math independently

#34

Post by shermantanktop » Sun, Feb 08, 2026, 5:31 PM UTC

energyscholar wrote: post #14

stared wrote: post #11

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 tha…

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 be…

> You're raising the right question

> You're right that…

> That's the point —

Re: Five disciplines discovered the same math independently

#35

Post by ajkjk » Sun, Feb 08, 2026, 5:33 PM UTC

jlund-molfese wrote: post #19

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.

and every comment here is also AI.

Re: Five disciplines discovered the same math independently

#36

Post by energyscholar » Sun, Feb 08, 2026, 5:33 PM UTC

vscode-rest wrote: post #9

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.

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.

Re: Five disciplines discovered the same math independently

#37

Post by energyscholar » Sun, Feb 08, 2026, 5:35 PM UTC

arjie wrote: post #8

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

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

Re: Five disciplines discovered the same math independently

#38

Post by energyscholar » Sun, Feb 08, 2026, 5:37 PM UTC

webdoodle wrote: post #22

energyscholar wrote: post #6

Earlier quoted context omitted.

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 ex…

Do you consider the possibility that the knowledge was intentionally suppressed, the seed poisoned, or Ego driven suppression? Simply looking at things clinically can obscure intentional deception, to slow progress. The concept is called an information hazard. Consider during the cold war, that the U.S. created fake nuclear designs, then allowed them to fall into the hands of the KGB. The KGB and Russian nuclear engi…

[flagged]

Re: Five disciplines discovered the same math independently

#39

Post by PlatoIsADisease » Sun, Feb 08, 2026, 5:37 PM UTC

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.

Re: Five disciplines discovered the same math independently

#40

Post by jmcgough » Sun, Feb 08, 2026, 5:42 PM UTC

bonsai_spool wrote: post #4

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 Mat…

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?