
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
|
ESGI 2025: Mathematics Meets Industry at the CRM
Over the course of five days, ESGI 2025 turned the CRM into a collaborative lab where mathematics tackled questions raised by industry. From safer autonomous driving systems to smart water resource allocation and the financial uncertainties of wind...
Quatre noves figures s’incorporen a l’exposició del CRM sobre dones matemàtiques
Aquest estiu, el CRM ha ampliat fins a tretze els roll ups de la seva exposició sobre dones matemàtiques, incorporant quatre noves figures del context espanyol i català. La mostra aprofita l’afluència de visitants al centre per visibilitzar...
From Real Problems to Mathematical Applications: A Chronicle of the XI Iberian Modeling Week
From July 7 to 11, the CRM became a hub for collaborative problem-solving during the XI Iberian Modeling Week, an international training initiative that brought together nearly 30 students from diverse academic backgrounds to tackle real-world...
The Way DNA Folds Might Help Explain How Cells Decide What to Become
A new study by researchers from the University of Edinburgh, Oxford, and CRM reveals how the 3D structure of DNA and a microscopic molecular tug-of-war shape the identity of every cell in our...
The CRM hosts a new edition of the Barcelona Introduction to Mathematical Research summer school
From June 30 to July 25, 2025, the CRM is organising a new edition of the Barcelona Introduction to Mathematical Research (BIMR), a summer school hosted at the Universitat Autònoma de Barcelona. The programme brings together 30 undergraduate...
Niclas Rieger defends his PhD thesis on data-driven climate analysis and marine pollution
Niclas Rieger defended his PhD thesis at the Institut de Ciències del Mar, culminating a research journey focused on extracting insights from both massive climate datasets and scarce environmental observations. Developed within the European CAFE...
A Day of Higher Structures in Symplectic and Poisson Geometry, with Summer Tapas at UPC Barcelona
The event "A Summer Tapas Invitation to Higher Structures in Symplectic and Poisson Geometry I", held on July 7, 2025, at EPSEB–UPC, featured talks by Alejandro Cabrera, Chenchang Zhu, Miquel Cueca, and Mario Garcia-Fernandez, offering a rich and informal exploration...
Luís Álamo, premi al millor pòster a la SFMC 2025 per un treball dirigit per Jezabel Curbelo
Luís Álamo, estudiant del màster FISYMAT de la Universitat de Granada, ha guanyat el premi al millor pòster a la conferència 3rd Spanish Fluid Mechanics Conference (SFMC25) amb un treball sobre estructures coherents Lagrangianes, basat en el seu...
Three CRM Researchers Invited to Speak at the 2026 International Congress of Mathematicians
From left to right: Xavier Cabré, Joaquim Ortega (photo by Xènia Fuentes, UB), and Xavier Tolsa. Three researchers affiliated with the Centre de Recerca Matemàtica (CRM), Xavier Cabré, Joaquim Ortega-Cerdà and Xavier Tolsa, have been invited to...
Gissell Estrada, beca Leonardo 2025 per explorar la migració col·lectiva amb matemàtiques i robots
L’investigadora Gissell Estrada Rodríguez, professora a la UPC i adscrita al CRM, ha rebut una Beca Leonardo 2025 per desenvolupar un projecte que combina matemàtiques i robòtica per estudiar la migració col·lectiva en sistemes vius i artificials....
JISD 2025 – Where Dynamical Systems Meet PDEs
JISD 2025, held at the Centre de Recerca Matemàtica (CRM) from June 30 to July 4, 2025, featured four advanced minicourses delivered by Dmitry Dolgopyat (on averaging and Fermi acceleration in dynamical systems), Serena Dipierro (on the theory of nonlocal minimal...
CERCA llança la campanya “Recerca amb orgull” per promoure la diversitat LGBTI+ en la ciència
La institució CERCA ha llançat la campanya “Recerca amb orgull” per promoure la visibilitat i la inclusió de les persones LGBTI+ en l’àmbit científic. Amb el lema “Als centres CERCA, fem ciència amb diversitat”, la iniciativa denuncia les...