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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