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Five disciplines discovered the same math independently

freethemath.org

61–70 of 75 posts

Re: Five disciplines discovered the same math independently

#61
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.

One could call it energyscholar's parallel

Re: Five disciplines discovered the same math independently

#62
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.

Re: Five disciplines discovered the same math independently

#63

Earlier quoted context omitted.

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.

The disease of having 100 citations in each paper had not yet broken out when the papers in question were written. A good paper in 1994 probably had about 8 references, and certainly not any to common textbooks.

Re: Five disciplines discovered the same math independently

#64

Earlier quoted context omitted.

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.

People—like me—who’ve used latex often learn to love en and em dashes. I think they are great, and I appreciate that people care about typography enough to use them. I also use an Oxford comma. It’s about care and quality; the fact that LLMs use them suggests that they are preferable. I’d encourage everyone to start.

Re: Five disciplines discovered the same math independently

#65

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…

What is even the point of having a website for a preprint paper? Unless the point is to give a live demo or similar, as is common e.g. for computer vision methods papers, it just smacks of vanity. Or at the very least significant academic immaturity. Same goes for the endorsement detail.

Re: Five disciplines discovered the same math independently

#66
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.

[deleted]

Re: Five disciplines discovered the same math independently

#67

Earlier quoted context omitted.

> You're raising the right question > You're right that… > That's the point —

I looked through this users' submissions and comments. I think this whole operation just completely violates HN rules.

Ha! I actually phoned their number. At the very least they're a real human being (as far as I can tell). But they're doing this while on holiday, and they didn't realize you shouldn't use an LLM to answer people. Not the smartest move ever!

Lessons learned I suppose.

Re: Five disciplines discovered the same math independently

#68

Earlier quoted context omitted.

AI comment, AI article, AI research. This feels like someone asked their AI assistant to do all of this as some kind of experiment.

Escaped Openclaw? Not using Opus for the HN conversation though. I'm spotting 'constitution' violations. edit: (tried calling them. If there's a mac mini in the corner of their office doing this, that'd be an actually interesting story!)

They called back. They're a real human.

Re: Five disciplines discovered the same math independently

#69
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. Af…

See! This is where you're doing it right. Be a person!

Re: Five disciplines discovered the same math independently

#70

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…

How much knowledge propagation (or creation) can be attributed to chance conversations at bars?

The bar scene of "A Beautiful Mind" comes to mind.

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