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

Theories of Everything with Curt Jaimungal

Curt Jaimungal

Physics, Philosophy, Society & Culture, Science

4.6 • 606 Ratings

🗓️ 7 July 2025

⏱️ 109 minutes

🔗️ Recording | iTunes | RSS

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Summary

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): https://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9- PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4RESOURCES:- 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 Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices Learn more about your ad choices. Visit megaphone.fm/adchoices

Transcript

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0:00.0	Professor Eva Miranda, I'm extremely excited to be here and be speaking with you again.
0:05.6	The last time we spoke, it went viral, so I'm super excited to have you on again because the audience
0:11.0	just loves you. We're going to talk about hot topics, what you're presenting here, you're
0:15.3	presenting for the first time in a manner that's introductory, so requires no background.
0:22.8	The topics will include complexity,
0:28.5	chaos theory, especially as contrasted with the standard chaos theory that the audience may already be acquainted with. Navier Stokes, of course, what it means to go beyond what's
0:33.3	computational, and how all of this is connected to geometry, to physics, to the ideas of Penrose and
0:40.4	Terry Tao. Welcome. Yes. Thank you very much. I'm excited to be here again. I'm so, so happy to be here
0:49.4	and looking forward to this new adventure, and ready to disclose something new.
0:55.1	Let's see if people like it.
0:56.5	I'm very happy about all the followers, all the questions.
1:00.6	I'm sorry I couldn't answer all the questions.
1:02.9	I'll go and answer them little by little as I can.
1:06.8	Great.
1:07.1	And it's a great pleasure to be here with all of you now.
1:11.0	Okay. I call this of you now. Okay.
1:11.8	I call this expect the unexpected.
1:15.1	And what does it mean?
1:17.7	Well, you know, we all know David Hilbert, the famous mathematician, right?
1:23.1	Who said, we must know, we will know.
1:27.7	This was, let's say, his most famous sentence.
1:33.2	And indeed, this was a little bit the idea of his idea that everything could be formalized mathematically
	...

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