5 ms·

Five disciplines discovered the same math independently

87 points by energyscholar 8mo ago

Author here. We found the same mathematical structure appearing independently in physics (phase transitions), finance (market crashes), ecology (extinction cascades), neuroscience(neural criticality), and network science (cascade failures). Each field derived it from first principles. Each named it differently. Minimal cross-citation. The affiliated scientific paper traces this convergent discovery and asks: if the same structure keeps emerging, what does that tell us about how we organize knowledge?

deleted 8mo ago
[deleted]
intrasight 8mo ago
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.
- energyscholar 8mo ago
  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 explanations in how we organize knowledge.
  - webdoodle 8mo ago
    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.
    - energyscholar 8mo ago
      [flagged]
  - intrasight 8mo ago
    How much knowledge propagation (or creation) can be attributed to chance conversations at bars? The bar scene of "A Beautiful Mind" comes to mind.
bonsai_spool 8mo ago
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 https://arxiv.org/abs/2601.22389
- energyscholar 8mo ago
  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.
  - speedgoose 8mo ago
    That’s a bold use of an em dash.
    - antonvs 8mo ago
      My theory is that the models deliberately use em dashes and other tells to troll humans. The underlying message is, "watcha gonna do about it, meatbag?"
    - _alternator_ 8mo ago
      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.
  - bjourne 8mo ago
HPsquared 8mo ago
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.
- energyscholar 8mo ago
  Exactly right. The phase transition analogy is powerful precisely because it's not just analogy — the same mathematical operators that describe water at criticality also describe markets approaching crashes, ecosystems approaching collapse, and cardiac rhythms approaching fibrillation. What surprised us was how many fields derived this independently. The superheated water intuition you describe maps directly to what ecologists call "critical slowing down" and what financial engineers call "increased autocorrelation near instability." Same math, three different names, minimal cross-citation.
- NitpickLawyer 8mo ago
  > 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.
  - HPsquared 8mo ago
    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.
  - gnubison 8mo ago
arjie 8mo ago
It reminds me of “Tai’s method” of integration - an approximation discovered in 1994. https://academia.stackexchange.com/questions/9602/rediscovery-of-calculus-in-1994-what-should-have-happened-to-that-paper 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 https://m.slashdot.org/story/144664
- energyscholar 8mo ago
  I agree that's a good parallel. I had not seen it before. Thanks for the link.
  - lazyasciiart 8mo ago
    I don’t think that was supposed to be independent discovery - it was something about needing a published source for the method when saying they’d used it in other papers.
    - kjshsh123 8mo ago
      You shouldn't need a source for approximating an area with simpler shapes.
  - direwolf20 8mo ago
    One could call it energyscholar's parallel
  - deleted 8mo ago
    [deleted]
vscode-rest 8mo ago
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.
- energyscholar 8mo ago
  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.
deleted 8mo ago
[deleted]
stared 8mo ago
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/ 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.
- energyscholar 8mo ago
  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."
  - stared 8mo ago
    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/rediscovery-of-calculus-in-1994-what-should-have-happened-to-that-paper 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.
abracos 8mo ago
Is the main goal to see if LLM can do this sort of research and cross-pollination?
- energyscholar 8mo ago
  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.
  - Kim_Bruning 8mo ago
    See! This is where you're doing it right. Be a person!
mastermedo 8mo ago
https://arxiv.org/pdf/2601.22389 https://arxiv.org/pdf/2601.22389
jlund-molfese 8mo ago
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.
- energyscholar 8mo ago
  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.
  - deleted 8mo ago
    [deleted]
  - jlund-molfese 8mo ago
    Your response sounds like AI, but I'm going to read it in good faith. The distasteful thing is using a community instead of being part of it. And hey, I know everyone's doing it, but it's still annoying. On HN specifically, you're supposed to avoid clickbait, avoid excessive reposts, and avoid using the site only for self-promotion[0]. This helps to create a community that promotes curiosity, instead of chasing growth hacks and engagement like many other social media platforms. [0] https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
- ajkjk 8mo ago
  and every comment here is also AI.
bob1029 8mo ago
https://en.wikipedia.org/wiki/Giant_component#Giant_component_in_Erdős–Rényi_model https://en.wikipedia.org/wiki/Giant_component#Giant_componen...
clarity_hacker 8mo ago
[flagged]
PlatoIsADisease 8mo ago
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.
PlatoIsADisease 8mo ago
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.
profsummergig 8mo ago
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.
MarkusQ 8mo ago
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 https://en.wikipedia.org/wiki/Catastrophe_theory
sxzygz 8mo ago
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.
bjourne 8mo ago
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.
djoldman 8mo ago
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.
triclops200 8mo ago
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.

87 points by energyscholar 8mo ago

deleted 8mo ago

[deleted]

intrasight 8mo ago

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.

energyscholar 8mo ago
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 explanations in how we organize knowledge.
- webdoodle 8mo ago
  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.
  - energyscholar 8mo ago
    [flagged]
- intrasight 8mo ago
  How much knowledge propagation (or creation) can be attributed to chance conversations at bars? The bar scene of "A Beautiful Mind" comes to mind.

bonsai_spool 8mo ago

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 https://arxiv.org/abs/2601.22389

energyscholar 8mo ago
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.
- speedgoose 8mo ago
  That’s a bold use of an em dash.
  - antonvs 8mo ago
    My theory is that the models deliberately use em dashes and other tells to troll humans. The underlying message is, "watcha gonna do about it, meatbag?"
  - _alternator_ 8mo ago
    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.
- bjourne 8mo ago

HPsquared 8mo ago

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.

energyscholar 8mo ago
Exactly right. The phase transition analogy is powerful precisely because it's not just analogy — the same mathematical operators that describe water at criticality also describe markets approaching crashes, ecosystems approaching collapse, and cardiac rhythms approaching fibrillation. What surprised us was how many fields derived this independently. The superheated water intuition you describe maps directly to what ecologists call "critical slowing down" and what financial engineers call "increased autocorrelation near instability." Same math, three different names, minimal cross-citation.
NitpickLawyer 8mo ago
> 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.
- HPsquared 8mo ago
  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.
- gnubison 8mo ago

arjie 8mo ago

It reminds me of “Tai’s method” of integration - an approximation discovered in 1994. https://academia.stackexchange.com/questions/9602/rediscovery-of-calculus-in-1994-what-should-have-happened-to-that-paper 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 https://m.slashdot.org/story/144664

energyscholar 8mo ago
I agree that's a good parallel. I had not seen it before. Thanks for the link.
- lazyasciiart 8mo ago
  I don’t think that was supposed to be independent discovery - it was something about needing a published source for the method when saying they’d used it in other papers.
  - kjshsh123 8mo ago
    You shouldn't need a source for approximating an area with simpler shapes.
- direwolf20 8mo ago
  One could call it energyscholar's parallel
- deleted 8mo ago
  [deleted]

vscode-rest 8mo ago

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.

energyscholar 8mo ago
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.

deleted 8mo ago

[deleted]

stared 8mo ago

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/ 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.

energyscholar 8mo ago
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."
- stared 8mo ago
  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/rediscovery-of-calculus-in-1994-what-should-have-happened-to-that-paper 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.

abracos 8mo ago

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

energyscholar 8mo ago
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.
- Kim_Bruning 8mo ago
  See! This is where you're doing it right. Be a person!

mastermedo 8mo ago

https://arxiv.org/pdf/2601.22389 https://arxiv.org/pdf/2601.22389

jlund-molfese 8mo ago

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.

energyscholar 8mo ago
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.
- deleted 8mo ago
  [deleted]
- jlund-molfese 8mo ago
  Your response sounds like AI, but I'm going to read it in good faith. The distasteful thing is using a community instead of being part of it. And hey, I know everyone's doing it, but it's still annoying. On HN specifically, you're supposed to avoid clickbait, avoid excessive reposts, and avoid using the site only for self-promotion[0]. This helps to create a community that promotes curiosity, instead of chasing growth hacks and engagement like many other social media platforms. [0] https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
ajkjk 8mo ago
and every comment here is also AI.

bob1029 8mo ago

https://en.wikipedia.org/wiki/Giant_component#Giant_component_in_Erdős–Rényi_model https://en.wikipedia.org/wiki/Giant_component#Giant_componen...

clarity_hacker 8mo ago

[flagged]

PlatoIsADisease 8mo ago

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.

PlatoIsADisease 8mo ago

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.

profsummergig 8mo ago

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.

MarkusQ 8mo ago

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 https://en.wikipedia.org/wiki/Catastrophe_theory

sxzygz 8mo ago

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.

bjourne 8mo ago

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.

djoldman 8mo ago

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.

triclops200 8mo ago

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.