
Eva Miranda, professor of mathematics at the Universitat Politècnica de Catalunya (UPC) and affiliated researcher at the Centre de Recerca Matemàtica (CRM), is one of the featured experts in an article by the international publication Quanta Magazine that explores one of the most profound questions in modern science: are there limits to what we can ever know about the physical world?
The article, titled Next-Level Chaos Traces the True Limit of Predictability and published on March 7th, examines how chaos theory, originally concerned with systems sensitive to initial conditions, is evolving into a more radical conceptual landscape: undecidability. If classical chaos already shattered our hopes of perfect prediction by showing that small differences in starting conditions can lead to wildly different outcomes, undecidability goes a step further. It does not stem from imprecision, but from the intrinsic structure of certain systems that defy computation entirely.
As Miranda explains, classical chaos is the realm of the butterfly and the hurricane, a world where evolution is deterministic but practically unpredictable. “It’s the dance of shadows,” she says, “a choreography of dynamical systems that elude our grasp not because they lack order, but because that order escapes us.” Undecidability, by contrast, emerges when a physical system (a fluid, a planetary orbit, a mechanical structure) is so rich that it can encode any computation, like a Turing machine. And when that happens, the halting problem enters the picture: no algorithm can determine whether the system will evolve in one way or another.
“Undecidability is something else entirely; colder, more philosophical, and perhaps more disquieting,” she adds. “It’s a closed door we may knock on forever without knowing if it will ever open.”
Within this context, Miranda and her collaborators, Robert Cardona, Daniel Peralta-Salas, and Francisco Presas, designed a theoretical fluid system that encodes the operations of a Turing machine. In this setup, a particle (symbolically represented by a rubber duck) follows a trajectory that simulates a computation. Predicting whether the duck reaches a certain area is equivalent to solving the halting problem, a provably unresolvable problem. This means that, in principle, even with perfect knowledge of the system’s initial state, no definitive prediction can be made.
“Some systems are so complex, so capable of encoding processes, that they simulate any computation,” Miranda explains. “And when that happens, we enter the realm of problems that are not difficult, but impossible.”
Beyond the sensitivity to initial conditions lies a deeper void. “Some systems contain, at their core, regions of mathematical silence,” she says. “It is precisely this silence, this space where even logic cannot advance, that fascinates us. As Emily Dickinson wrote: ‘The brain is wider than the sky.’ But even that brain, reaching out through conjectures, proofs, and intuitions, sometimes meets skies that will never be crossed. And perhaps it is in those limits that we truly begin to understand.”
This contribution is part of a broader intellectual shift, one that Quanta Magazine has chronicled in its Quanta Fundamentals series. In a related piece, How Chaos Theory Makes the Future Unpredictable (March 31, 2025), the magazine revisits the origins of chaos theory, from Edward Lorenz’s butterfly effect to more recent understandings of nonlinear dynamics in fields ranging from meteorology to orbital mechanics.
Miranda sees the growing presence of undecidability in physics not as a limitation, but as a transformation. “The 20th century already cracked some certainties with relativity and quantum mechanics,” she says. “But now the shift is subtler, more internal. It doesn’t come from the lab or the telescope, but from a change in perspective: we’re beginning to suspect that some questions don’t just lack answers, they lack meaning within our systems.”
She highlights that these logical boundaries, long familiar to mathematicians, are now surfacing in concrete physical contexts: “In celestial mechanics, fluid evolution, and Hamiltonian systems with symmetries, we are beginning to encounter questions that may be undecidable, not because we lack data, but because of the system’s internal structure.”
In this changing landscape, Miranda also underscores the importance of high-level science communication. “Magazines like Quanta are a necessary exception in the midst of all the noise,” she says. She believes such platforms bridge the artificial divide between science and culture: “They remind us that doing mathematics or physics is also a way of seeing the world, of listening to it, of translating it. Communicating it well doesn’t mean watering it down, it means sharing its essence.”
|
CRM CommPau Varela
|
Guillem Blanco rep el Premi José Luis Rubio de Francia 2024
Guillem Blanco, professor de la UPC i investigador adscrit al CRM, ha estat guardonat amb el Premi José Luis Rubio de Francia 2024 per les seves contribucions a la teoria de les singularitats i els D-mòduls. El jurat ha destacat, entre altres...
Hypatia 2025 Brings Together Young Researchers in Mathematics
The fourth edition of the Hypatia Graduate Summer School took place from 16 to 19 June 2025 in Barcelona. Addressed to PhD students, the school combined two advanced courses in number theory with a public colloquium, a film screening, and...
Javier Gómez Serrano collaborates with Terence Tao and DeepMind on an AI project to solve open mathematical problems
Javier Gómez Serrano, former CRM member and professor at Brown University, is working with Terence Tao and DeepMind on AlphaEvolve, an AI tool that uses code evolution to solve complex math problems. For him, it signals a shift in how research is...
Closing Session of the SIJIMat Seminar: A Celebration of Young Mathematical Talent
Four young researchers (S. Dhyr, A. Garcia, L. Unamuno and R.Homs) at CRM present their work in geometry, neuroscience, environmental statistics, and algebraic methods in the final SIJIMat session of the academic year.On June 12, the Centre de Recerca Matemàtica (CRM)...
What is Open Science? From Data to Impact: Insights from the CRM
On June 11, the Centre de Recerca Matemàtica (CRM) hosted the Open Science Day, bringing together researchers to explore the principles, challenges, and transformative potential of open science. With a central talk by Ignasi Labastida and a roundtable featuring...
The IRP on Modern Fourier Analysis moves forward with its main conference at CRM
For one intense week, the CRM auditorium became a meeting point for some of the most active researchers in modern Fourier analysis. From June 2 to June 6, 2025, the Conference on Modern Trends in Fourier Analysis brought together senior experts,...
Welcoming Eleven New Affiliated Researchers to the Centre de Recerca Matemàtica
From left to right, top to bottom: Carles Broto (UAB-CRM), Álvaro Corral (UAB-CRM), Wolfgang Pitsch (UAB-CRM), Richard Lang (UPC - CRM), Simeon Ball (UPC - CRM), Lluís Vena (UPC - CRM), Jorge Antezana (UB-CRM), Leticia Pardo (UB-CRM), Guillem Blanco (UPC - CRM),...
El CRM acull una nova sessió del programa Bojos per les Matemàtiques
Dissabte passat, el Centre de Recerca Matemàtica va acollir una sessió del programa Bojos per les Matemàtiques, adreçat a estudiants de batxillerat amb interès i talent per aquesta disciplina. Una vintena de participants van assistir a dues...
Núria Fagella, nova degana de la Facultat de Matemàtiques i Informàtica de la UB
La professora i investigadora Núria Fagella ha estat escollida nova degana electa de la Facultat de Matemàtiques i Informàtica de la Universitat de Barcelona. Especialista en dinàmica complexa i adscrita al Centre de Recerca Matemàtica, el seu...
El CRM apropa el cervell al públic a la Festa de la Ciència amb l’activitat “Neural Code”
Aquest cap de setmana, el Centre de Recerca Matemàtica ha participat a la 18a Festa de la Ciència de Barcelona amb l’activitat Neural Code, un taller interactiu per explorar com el cervell transforma els senyals neuronals en moviment. L’activitat, organitzada en...
The CRM hosts the Advanced Course on Modern Aspects of Fourier Analysis
From May 26 to May 30, 2025, the Centre de Recerca Matemàtica (CRM) in Bellaterra welcomed more than 80 participants from institutions around the world for the Advanced Course on Modern Aspects of Fourier Analysis. The activity, held at the CRM Auditorium, was one of...
Could the Sun–Jupiter–Saturn System Truly Exist? A Computer-Assisted Approach Sheds New Light on Celestial Stability
Mathematicians Jordi-Lluís Figueras and Alex Haro have taken a step toward validating a long-standing astronomical hypothesis: that the Sun–Jupiter–Saturn system could sustain stable, quasiperiodic motion indefinitely, even in the face of chaotic...