5 ms·
'Entropy bagels' and other complex structures emerge from simple rules
- optimalsolver 3y agoNot a single mention of Stephen Wolfram?
- rdtsc 3y agoI thought of that too. I think at this point most researches don't have much respect for him. If you listen to him or read his book, he sure likes to take credit for a lot stuff and make large claims about revolutionizing science and such. "I discovered this, I did that, etc...". So I can't blame others for avoiding mentioning him and just pretending he doesn't exist. At the same time this comes from a math background while Wolfram sort of bases his theory on cellular automata with rules, cells, Turing Machines etc.
- passion__desire 3y ago[flagged]
- deleted 3y ago[deleted]
- paulpauper 3y agoHis ideas are not mathematically rigorous and would not pass peer review. his ideas are too hand-wavy. I don't think he has ever published anything in peer review or even in a journal format. A doorstop-sized book does not count. No one wants to read all that.
- jjtheblunt 3y agoHe has a PhD from CalTech at age 20, under Richard Feynman. Those are published.
- senderista 3y agoHe was a theoretical physics wunderkind before he created Mathematica and became a crank. There are other great physicists like 't Hooft who became cranks in their later years (arguably including Einstein).
- bubblyworld 3y agoI think Wolfram's work is quite different in flavour - he focuses on discrete dynamical systems (graphs/cellular automata, stuff like that) whereas OP is about continuous iterated systems like the Mandelbrot set (which afaik have a much older history in mathematics).
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- colpabar 3y agoIs there a reason why the bagel/donut shape seems to appear so much in math/physics? Just yesterday I was watching a kurzgesagt video that explored the idea of the universe being a "hyperdonut", or something. There probably isn't a simple answer but I'd appreciate any attempt to explain it in laymen's terms.
- thegabez 3y agoThe bagel looks like a black hole
- hnhg 3y agoI think it’s because they can be modelled “easily” as a 2D plane with no edge in any direction but i am not an expert
- groby_b 3y agoIt's the simplest two-dimensional surface[1] with at least one hole in it. In topology - the math branch that deals with properties of geometric objects and how they can be deformed - it's one of the two simplest objects, the other being a sphere. (There's a lot of those, too). Donuts ("tori") have the advantage that they're a bit more complex, so they're more interesting, and have interesting properties. Nobody gets much excited by spheres anymore ;) That also means they get a bit more attention. That means you'd expect it to be very common. Not having a lot of donuts would be weird. (Now there's a maxim to live by!) Yes, it's extremely handwavy, and there are probably explanations that are much better and more detailed. Sorry. Best I have. [1] I lie. It's a compact orientable 2-manifold, not a 2D surface. For laymen's terms, I hope the math folks will let me get away with "surface" though.
- davkan 3y agoVsauce has an interesting video regarding topology[0]. Probably a bit rudimentary for anyone already familiar with the math, but still entertaining in the typical vsauce way. [0] https://youtu.be/egEraZP9yXQ?si=P1BzLzBVW4q1aZ3D https://youtu.be/egEraZP9yXQ?si=P1BzLzBVW4q1aZ3D
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- snitzr 3y agoI recommend James Gleick's Chaos book. It will change your perspective on the world.
- passion__desire 3y agoc = -3/2 produces nice "hyperbolic" behavior has been discussed in this video https://www.youtube.com/watch?v=eC9-1wY7FvU https://www.youtube.com/watch?v=eC9-1wY7FvU
- backitup 3y agoAnother good one is "Complexity" by Melanie Mitchell. She was a grad student of Douglas Hofstadter's and is with the Sante Fe Institute right now if memory serves.
- klysm 3y agoI read this as a kid and was totally enamored by cellular automata
- renewiltord 3y agoSelf-iteration seems to produce so much complexity from so few rules. The root of so many chaotic things, the collatz conjecture, fractals. And the chemical root of complex life. Funny.
- theGnuMe 3y agoIf feel like there is a connection to differential equations here. In those there is quite a lot known about chaos etc... anyone have any insights on that connection? I feel like the mathematicians would have probably covered this.
- rocqua 3y agoChaos theory knows two branches. discrete time and continuous time. They are surprisingly different branches. differential equations are clearly in the continuous camp, and the basis of most if not all continuous chaos theory.
- bubblyworld 3y agoAwesome! You can get another beautiful bagel by plotting the roots of polynomials with integer coefficients: https://math.ucr.edu/home/baez/roots/ https://math.ucr.edu/home/baez/roots/ (edit: hang on, am I crazy or do these bagels look remarkably similar? despite very different definitions)
- jerf 3y agoIt might be worth emailing the two groups of people and putting them in contact with each other. Nobody can know everything and be everywhere at once.
- Jarmsy 3y agoThe author of the article linked in the comment above yours has been discussing this here: https://mathstodon.xyz/@gregeganSF/112007010957379619 https://mathstodon.xyz/@gregeganSF/112007010957379619
- 3abiton 3y agoThis finding is so funny, it's like despite the interconnectedness in the 21st century things like this still happen.
- koliber 3y agoAbsolutely! The bagel 3D-like image and the 3rd image in your link are showing the same thing. Look at the inside of the ring and compare the images side by side. The features align in both images.
- madcaptenor 3y agoNot just you. I knew I'd seen these somewhere before.
- vinnyvichy 3y agoThe qm article says "A number is totally real if it satisfies a polynomial equation with integer coefficients" etc but I love your spirit and it's totally on quantamags for not stating their inputs up front
- freeqaz 3y agoIs there any value in these types of systems in a cryptography context? I was just thinking about that after reading the article.
- rocqua 3y agoThere is quadratic circuits used in Zero Knowledge Proofs, and there is shamir secret sharing, which uses arbitrary degree polynomials. In general though, cryptography will use polynomials over finite fields. That is very different from these fractals which work on infinite sets that require infinite precision.
- ash-ishh 3y agoReminded me of this recent observation of fractals in nn training https://sohl-dickstein.github.io/2024/02/12/fractal.html https://sohl-dickstein.github.io/2024/02/12/fractal.html
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- quickthrower2 3y agoA bit like Collatz conjecture
- foobarbecue 3y agohttps://getyarn.io/yarn-clip/ad99367f-7c77-4566-b160-50efca7517bd https://getyarn.io/yarn-clip/ad99367f-7c77-4566-b160-50efca7...