Forwarded from архив темных двадцатых (danya)
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Стрелец в ахуе слушает разгоны дочери Виктории Бони про 4Д реальность
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Вы когда-нибудь думали о плазмасфере земли? А о её приливных эффектах? Вот я тоже
https://x.com/explorecosmos_/status/1623430834954059776?s=46
https://www.nature.com/articles/s41567-022-01882-8
https://x.com/explorecosmos_/status/1623430834954059776?s=46
https://www.nature.com/articles/s41567-022-01882-8
Basically a knot is a 1-dimensional object (the rope) embedded in 3-dimensional space. If you generalize knot theory into higher dimensions by taking a 1-dimensional object embedded in 4-dimensional space, then you get an essentially uninteresting theory because all knots can be untied.
https://www.reddit.com/r/askscience/comments/17fk8e/ive_been_told_that_knots_only_work_in_three/
Forwarded from Transcendent App
Alexander
https://openai.com/index/navier-stokes-solution/
- The Navier–Stokes Millennium Prize Problem is a web page documenting OpenAI's resolution of one of the seven Millennium Prize Problems regarding the existence and smoothness of three-dimensional fluid motion.
- OpenAI's internal AI system proved that the Navier-Stokes equations for fluid motion can develop a singularity, meaning fluid speed can grow without bound in finite time.
- The proof is supported by both an analytical writeup and a formal verification conducted using the Lean programming language.
- The solution centers on a vortex that spirals inward and elongates, where the dynamics allow for a singularity while maintaining finite energy.
- The research effort utilized approximately 10,000 concurrent AI agents organized into coordinating groups to analyze different variants of the problem.
- The multi-agent system reached its resolution in approximately 88 hours, with an additional 17 hours required for Lean formalization.
- Agents successfully resolved the related Euler regularity problem for unforced flows, which served as a precursor and inspiration for the Navier-Stokes effort.
- OpenAI clarified that it does not intend to claim the Millennium Prize for this achievement, emphasizing that the work serves as a demonstration of AI's accelerated research capabilities.
- The company acknowledged the concurrent work of mathematicians Levent Alpöge and Tristan Buckmaster, noting that their respective proofs differ in approach and focus.
- This achievement is presented as a snapshot of rapid progress in AI development, highlighting the necessity for responsible pacing and steerability in future model advancement.
- OpenAI's internal AI system proved that the Navier-Stokes equations for fluid motion can develop a singularity, meaning fluid speed can grow without bound in finite time.
- The proof is supported by both an analytical writeup and a formal verification conducted using the Lean programming language.
- The solution centers on a vortex that spirals inward and elongates, where the dynamics allow for a singularity while maintaining finite energy.
- The research effort utilized approximately 10,000 concurrent AI agents organized into coordinating groups to analyze different variants of the problem.
- The multi-agent system reached its resolution in approximately 88 hours, with an additional 17 hours required for Lean formalization.
- Agents successfully resolved the related Euler regularity problem for unforced flows, which served as a precursor and inspiration for the Navier-Stokes effort.
- OpenAI clarified that it does not intend to claim the Millennium Prize for this achievement, emphasizing that the work serves as a demonstration of AI's accelerated research capabilities.
- The company acknowledged the concurrent work of mathematicians Levent Alpöge and Tristan Buckmaster, noting that their respective proofs differ in approach and focus.
- This achievement is presented as a snapshot of rapid progress in AI development, highlighting the necessity for responsible pacing and steerability in future model advancement.
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