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Five disciplines discovered the same math independently

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Re: Five disciplines discovered the same math independently

#21

Post by asgraham »

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 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-...

Re: Five disciplines discovered the same math independently

#22

Post by webdoodle »

energyscholar wrote: post #6
intrasight wrote: post #3

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.

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 engineers then wasted significant time trying to build nuclear devices that failed to work, and could have been dangerous.

Re: Five disciplines discovered the same math independently

#23

Post by stared »

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…

Well, just because someone published does not mean that it was not (even implicitly) based. For example, there was a paper rediscovering trapezoid method of integration https://academia.stackexchange.com/questions/9602/rediscover... A scientist may had been not aware of the method - yet, mathematics used for that is thought in high school.

Note that phase transitions are 100 years old or so. If someone genuinely does not know statistical mechanics, they still may know a lot of tools derived from it (a famous one - Shannon entropy).

I am not saying it is impossible to independently discover something (it happens all the time), but if discoveries are not (more or less) as the same time, likely there was some knowledge diffusion before.

Re: Five disciplines discovered the same math independently

#25

Post by energyscholar »

abracos wrote: post #12

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

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.

Re: Five disciplines discovered the same math independently

#26

Post by speedgoose »

energyscholar wrote: post #18
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…

That’s a bold use of an em dash.

Re: Five disciplines discovered the same math independently

#28

Post by energyscholar »

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.

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.

Re: Five disciplines discovered the same math independently

#29

Post by zozbot234 »

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…

> because why would you cite phase transitions or criticality? You learn about them in class as a physicist

I'm not sure if you're being entirely serious with that remark, but clearly citing the earlier work would have bolstered their credibility: interdisciplinary research is a plus and hardly something to hide. If it's something that's taught in physics class, you can cite a common textbook.

Re: Five disciplines discovered the same math independently

#30

Post by [deleted] »

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…

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