Five disciplines discovered the same math independently (freethemath.org)

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.

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

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.

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’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.

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.

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

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.

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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.

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.

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.

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

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.

Can you in plain English explain exactly what unifies these discoveries? I have a hard time seeing what unifies traffic congestion with eigenvalue analysis of ESNs. While many systems contain thresholds, a traffic jam is not chaotic in the same way that an epileptic seizure is.

Contrarian view with a dusting of generative AI spiciness:

Generative AI may be just the type of thing to connect these types of previously solved problems across disciplines.

This phenomena was also described/characterized in prior Hegelian literature as part of the law of quantitative into qualitative change, though, not formulated mathematically at the time. Interestingly enough, and In the context of how cross discipline this discovery has historically been, iirc, Lenin played around with mathematically characterizing the phenomenon, though, I am not aware of the extent to which he did. Very universal phenomenon for sure.