Department Christmas Colloquium - Eva Miranda

Title: Can water compute?

Speaker: Eva Miranda (Professor at Universitat Politecnica Catalunya and CRM, Barcelona, and Humboldt Professor at Universität zu Köln).

Abstract:  We explore whether physical systems - specifically fluids - can perform computations, building on foundational insights from Alan Turing and Roger Penrose, as well as recent advances in fluid dynamics and geometry.

We begin by discussing Cris Moore's connection between universal Turing machines and transformations of the square Cantor set. By extending this to three dimensions, we uncover Turing-complete Reeb vector fields. These fields yield stationary solutions of the Euler equations, effectively creating a universal Turing machine capable of simulating fluid motions. The undecidability of the halting problem - proved by Turing - reveals the existence of undecidable fluid paths, introducing a new form of "chaos" in the logical sense.

This theoretical framework gives rise to the concept of a fluid computer, with its fundamental computational unit called the "flubit." Inspired by Richard Feynman’s vision, we can formalize the process of "assembling flubits" into what we term TKFT (Topological Kleene Field Theory), named after the logician Stephen Kleene.