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Mathematician Eva Miranda returns with a groundbreaking new result: a real physical system (fluid motion) has been proven to be Turing-complete. This means some fluid paths are logically undecidable. In this mind-bending episode, she walks us through the implications for chaos theory, the Navier-Stokes equations, and uncomputability in nature, confirming long-held suspicions of thinkers like Roger Penrose and Terence Tao. Featuring rubber ducks, Alan Turing, and the limits of knowledge itself.
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Listen on Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e
Timestamps:
00:00 Introduction
01:10 Expect the Unexpected
02:52 Stories of Uncertainty
04:45 The Impact of Alan Turing
06:35 The Halting Problem Explained
09:29 Limits of Mathematical Knowledge
12:40 From Certainty to Uncertainty
16:19 The Rubber Duck Phenomenon
19:29 Unpredictability vs. Undecidability
20:18 Classical Chaos and the Butterfly Effect
27:12 Asteroids and Chaos Theory
34:32 The Navier-Stokes Riddle
41:18 The Cantor Set and Computation
46:18 Bridging Discrete and Continuous
49:21 Turing Completeness in Fluid Dynamics
1:02:39 The Quest for Navier-Stokes Solutions
1:06:53 The Role of Viscosity
1:12:09 Hybrid Computers and Fluid Dynamics
1:26:57 Unpredictability in Deterministic Systems
1:31:44 The Future of Computational Models
Links Mentioned:
• Eva’s First Appearance [TOE]: https://youtu.be/6XyMepn-AZo
• Moby Duck [Book]: https://amzn.to/4ldoYsZ
• Roger Penrose [TOE]: https://youtu.be/sGm505TFMbU
• The Emperor’s New Mind [Book]: https://amzn.to/44jHpGK
• Edward Frenkel [TOE]: https://youtu.be/RX1tZv_Nv4Y
• Richard Borcherds [TOE]: https://youtu.be/U3pQWkE2KqM
• Clay Mathematics Institute: https://www.claymath.org/
• Eva’s Papers: https://scholar.google.com/citations?user=werIoRQAAAAJ&hl=en
• Topological Kleene Field Theories [Paper]: https://arxiv.org/pdf/2503.16100
• Ted Jacobson [TOE]: https://youtu.be/3mhctWlXyV8
• Stephen Wolfram [TOE]: https://youtu.be/0YRlQQw0d-4
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