As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit 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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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]:
• Moby Duck [Book]:
• Roger Penrose [TOE]:
• The Emperor’s New Mind [Book]:
• Edward Frenkel [TOE]:
• Richard Borcherds [TOE]:
• Clay Mathematics Institute:
• Eva’s Papers:
• Topological Kleene Field Theories [Paper]:
• Ted Jacobson [TOE]:
• Stephen Wolfram [TOE]:
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