MathematischeGesellschaft Certainty in uncertain times |  |
Speaker:Prof. Eva Miranda, Universitat Politècnica de Catalunya in Barcelona
Organizer:Mathematisches Institut
Details:
"Wir müssen wissen. Wir werden wissen."
—David Hilbert, 1930
"To know, or not to know — that is the question."
—William Shakespeare (sort of)
Will the 2024 YR4 asteroid strike Earth?
Science’s answer: maybe. With shifting probabilities, it could make a dramatic arrival—on Christmas Eve of 2032, no less. Despite our reliance on mathematics and physics for precise predictions, history reminds us that certainty is often elusive.
Hilbert believed that all mathematical truths could, in time, be unveiled by logic. Turing—and the 20th century—had other plans.
In 1936, Turing proved the undecidability of the Halting Problem: there exists no general algorithm that can determine whether an arbitrary program will eventually halt or run forever. That same year, Kleene gave us the formal language to define what can—and crucially, cannot—be computed. Hilbert’s dream—ambitious, luminous—had met its first true limits.
Chaos theory later challenged predictability on another front: even simple deterministic systems can exhibit wildly unpredictable behaviour due to extreme sensitivity to initial conditions. Yet beyond classical chaos lies something deeper—logical chaos.
In recent work with Cardona, Peralta-Salas, and Presas, we proved that fluid flows can simulate the computations of a Turing machine. We constructed trajectories governed by the Euler equations whose fate cannot be predicted—not from lack of precision, but because prediction itself breaks down.
This talk traces a path from contact geometry to the frontiers of Topological Kleene Field Theory: a nascent framework where topology, geometry, and logic converge. These tools expose hidden barriers to prediction—not only in fluid dynamics, but perhaps also in celestial mechanics.
Faced with such limits, we are led to a provocative question:
Is the universe not merely unpredictable—but, at its core, incomputable?
—David Hilbert, 1930
"To know, or not to know — that is the question."
—William Shakespeare (sort of)
Will the 2024 YR4 asteroid strike Earth?
Science’s answer: maybe. With shifting probabilities, it could make a dramatic arrival—on Christmas Eve of 2032, no less. Despite our reliance on mathematics and physics for precise predictions, history reminds us that certainty is often elusive.
Hilbert believed that all mathematical truths could, in time, be unveiled by logic. Turing—and the 20th century—had other plans.
In 1936, Turing proved the undecidability of the Halting Problem: there exists no general algorithm that can determine whether an arbitrary program will eventually halt or run forever. That same year, Kleene gave us the formal language to define what can—and crucially, cannot—be computed. Hilbert’s dream—ambitious, luminous—had met its first true limits.
Chaos theory later challenged predictability on another front: even simple deterministic systems can exhibit wildly unpredictable behaviour due to extreme sensitivity to initial conditions. Yet beyond classical chaos lies something deeper—logical chaos.
In recent work with Cardona, Peralta-Salas, and Presas, we proved that fluid flows can simulate the computations of a Turing machine. We constructed trajectories governed by the Euler equations whose fate cannot be predicted—not from lack of precision, but because prediction itself breaks down.
This talk traces a path from contact geometry to the frontiers of Topological Kleene Field Theory: a nascent framework where topology, geometry, and logic converge. These tools expose hidden barriers to prediction—not only in fluid dynamics, but perhaps also in celestial mechanics.
Faced with such limits, we are led to a provocative question:
Is the universe not merely unpredictable—but, at its core, incomputable?
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Type:Colloquium
Language:English
Category:Research
Host:Prof. Dr. Thomas Schick
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Direct link to event:https://events.goettingen-campus.de/event?eventId=12484366
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