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Five disciplines discovered the same math independently

freethemath.org

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Re: Five disciplines discovered the same math independently

#11

Post by stared »

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.

Re: Five disciplines discovered the same math independently

#13

Post by NitpickLawyer »

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.

Re: Five disciplines discovered the same math independently

#14

Post by energyscholar »

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 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."

Re: Five disciplines discovered the same math independently

#15

Post by svara »

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 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.

Re: Five disciplines discovered the same math independently

#17

Post by smitty1e »

svara wrote: post #15
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 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.

> You don't get to claim you invented it

Re-inventing the wheel is completely in order, so long as one makes the wheel more round.

Re: Five disciplines discovered the same math independently

#18

Post by energyscholar »

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…

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.

Re: Five disciplines discovered the same math independently

#20

Post by zozbot234 »

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…

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.

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