Eva Miranda: Fluid Motion Is Turing-Complete (Proving Penrose Right)

Mathematician Eva Miranda reveals a new proof that fluid motion can be Turing‑complete, making certain fluid paths undecidable. The episode explores the consequences for chaos theory, the Navier‑Stokes equations and the long‑standing ideas of Penrose and Tao.- 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 ModelsSPONSORS:- I personally subscribe to The Economist. TOE listeners get 35% off the annual subscription. No other podcast has this! https://economist.com/TOE- YouTube Member (Early Access Videos): https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join- Patreon: https://patreon.com/curtjaimungal- Coinbase (Crypto): Crypto: https://nowpayments.io/donation/TOE- PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4Every episode days early, ad-free, plus my essays: https://curtjaimungal.substack.com/subscribeRESOURCES:- 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- My Substack (Personal Writings): https://curtjaimungal.substack.com- Listen on Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e- Twitter: https://twitter.com/TOEwithCurt- Discord Invite: https://discord.com/invite/kBcnfNVwqs Theories of Everything with Curt Jaimungal features long-form, technically detailed interviews with leading researchers in physics, mathematics, consciousness, and philosophy, exploring topics at the level of active research. For academics, graduate students, and anyone seeking depth beyond popular science. Learn more about your ad choices. Visit megaphone.fm/adchoices