Theories of Everything with Curt Jaimungal Eva Miranda: Fluid Motion Is Turing-Complete (Proving Penrose Right)
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Jul 7, 2025 
Mathematician Eva Miranda shares her groundbreaking work proving that fluid motion can be Turing-complete, echoing the theories of legends like Roger Penrose and Terence Tao. She dives into the implications of chaos theory and the Navier-Stokes equations, revealing that certain fluid paths are logically undecidable. The discussion takes whimsical turns, featuring rubber ducks to illustrate complex concepts, and poses big questions about the limits of knowledge and predictability in nature.
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Rubber Ducks as Chaos Metaphor
- A 1992 ship lost 29,000 rubber ducks, which later appeared unpredictably across the world, defying simulations.
- This real story illustrates undecidability and complexity in nature, used as a metaphor for undecidable fluid paths.
Unpredictability vs Undecidability
- Unpredictability in physics can stem from insufficient information or from logical undecidability.
- Classical chaos is about sensitivity to initial conditions; undecidability is a deeper barrier where no prediction algorithm exists.
Classical Chaos and Sensitivity
- Classical chaos theory shows tiny changes in initial conditions cause large differences in outcomes, such as weather unpredictability.
- This sensitivity limits long-term predictions, illustrated by asteroid path uncertainty and the butterfly effect.
