iiinova — where your digital self keeps evolving

Reposted by Eva Miranda

Science X / Phys.org @sciencex.bsky.social · 22/09/2026

A two-dimensional billiard table can simulate a universal Turing machine with one ball and fixed walls. Some long-term trajectory questions therefore cannot always be predicted by an algorithm. doi.org/hckdp6

phys.org

What billiard balls reveal about computers and the limits of prediction

When is a billiard ball not a billiard ball? When mathematicians get involved and view a popular game as a model computer.

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Reposted by Eva Miranda

Proceedings of the National Academy of Sciences @pnas.org · 22/09/2026

One of the most-viewed PNAS articles in the last week is “Two-dimensional billiards are Turing complete.” Explore the article here: ow.ly/zs8G50ZPTvY For more trending articles, visit ow.ly/YEYv50ZPTvZ.

Billiard dynamics implementing the read–write operation. The blue and red rays correspond to reading a 0 or a 1, respectively.

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Reposted by Eva Miranda

Terence Tao @teorth.bsky.social · 11/09/2026

A group of 25 Fields Medalists, including myself, have made a joint declaration on Math and AI: mathandai.org . We welcome additional signatories. See also this article in the Economist announcing the declaration: www.economist.com/science-and-...

mathandai.org

Declaration — Math and AI

Read the declaration and add your name.

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Eva Miranda @evamirandag.bsky.social · 11/09/2026

thanks for reposting Zamin 😊

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Reposted by Eva Miranda

Zamin Iqbal @zaminiqbal.bsky.social · 11/09/2026

2D billiards are Turing complete! "We show that, even in 2D, billiard trajectories can simulate arbitrary Turing machines...Our results place undecidability, alongside chaos, as a fundamental obstruction to long-term prediction even in low-dimensional classical dynamics" www.pnas.org/doi/abs/10.1...

pnas.org

Two-dimensional billiards are Turing complete | PNAS

We show that two-dimensional billiard systems can simulate universal Turing machines. Billiards serve as idealized models of particle motion with e...

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Eva Miranda @evamirandag.bsky.social · 11/09/2026

Before OpenAI announces the resolution of the next Millennium Prize Problem, allow me a little mathematical flex 😎. We proved that a single ball in a 2D billiard can simulate a universal Turing machine, solving a problem posed by Cris Moore.🎱🤖 Read it here @pnas.org: www.pnas.org/doi/10.1073/...

pnas.org

Two-dimensional billiards are Turing complete | PNAS

We show that two-dimensional billiard systems can simulate universal Turing machines. Billiards serve as idealized models of particle motion with e...

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Eva Miranda @evamirandag.bsky.social · 08/09/2026

The day is not over yet...here it comes an announcement of OpenAI for Navier-Stokes... cdn.openai.com/pdf/32d9f210... It's been a long day...

cdn.openai.com

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Eva Miranda @evamirandag.bsky.social · 08/09/2026

Before this becomes a story about which lab won: the ideas are Diego Córdoba's and Luis Martínez-Zoroa's. Buckmaster says so himself, and adds that he thinks Martínez-Zoroa deserves a Fields Medal. In the age of LLMs, who gets the credit, and who decides? cims.nyu.edu/~tristanb/st...

cims.nyu.edu

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Reposted by Eva Miranda

Barbara Fantechi @barbarafantechi.bsky.social · 23/06/2026

I wansn't paying attention and forgot to congratulate @evamirandag.bsky.social for this well deserved recognition!

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Eva Miranda @evamirandag.bsky.social · 23/06/2026

Los fluidos como el agua, el aire o la lava de un volcán esconden trayectorias imprevisibles, según un estudio de la UPC www.upc.edu/es/sala-de-p...

upc.edu

Los fluidos como el agua, el aire o la lava de un volcán esconden trayectorias imprevisibles, según un estudio de la UPC - UPC Universitat Politècnica de Catalunya

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Reposted by Eva Miranda

RACiencias @raciencias.bsky.social · 04/06/2026

Damos la bienvenida a dos nuevos miembros ⚡️Eva Miranda, matemática de @la_UPC y experta en geometría y topología @evamirandag.bsky.social 🧬 Federico Morán, catedrático de Biología Molecular de la @ucm.es, dirige desde 2019 la Fundación para el Conocimiento Madri+d

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Reposted by Eva Miranda

Gemma De les Coves @gemmadlc.bsky.social · 24/02/2026

Tomorrow I'll give a colloquium for Prof. @evamirandag.bsky.social 's group at the Maths Dept at UPC, Barcelona I'll talk about the scope of forms of universality and unreachability in logic, spin models, Boltzmann machines, and philosophy. Everybody is welcome! imtech.upc.edu/2026/01/26/g...

imtech.upc.edu

Gemma de les Coves – IMTech

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Reposted by Eva Miranda

J. Doyne Farmer @doynefarmer.bsky.social · 24/02/2026

This Thursday I'll be at @museuciencies.cat discussing chaos theory, time and its implications with @evamirandag.bsky.social and @ricardsole.bsky.social. Looking forward to it! museuciencies.cat/activitats/2...

museuciencies.cat

Teoria del caos: el món és predictible? | Museu de Ciències Naturals de Barcelona

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Reposted by Eva Miranda

Ricard Solé @ricardsole.bsky.social · 14/02/2026

Podem predir el futur mitjançant les matemàtiques? Què ens diu la teoria del caos? Quins són els límits de la nostra capacitat de predir la complexitat? Parlarem amb Doyne Farmer, un dels pares de la teoria, i amb la matemàtica Eva Miranda @evamirandag.bsky.social museuciencies.cat/activitats/2...

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Reposted by Eva Miranda

Elise Cutts @elisecutts.bsky.social · 22/01/2026

My 25th (!) newsletter post shares my main takeaway from the #RockyWorlds4 conference: Hot rocks are what's cool in rocky exoplanet research right now. Lava planets, especially look like they're about to teach us a *ton* about how rocky planets work. So come on in, the lava's fine! 🧪🔭

reviewertoo.com

Hot rocks are what's cool in rocky exoplanet research

Habitable zone? Pfft. For exciting planetary science discoveries, keep your eye on lava worlds and hot rocks.

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Eva Miranda @evamirandag.bsky.social · 09/01/2026

🎱 A ball. 🎱 A table. 🎱 A computation. With Isaac Ramos, we show that a sufficiently weird billiard table is Turing complete. 🕳️ The 8-ball hits the halting wall. Game over. Selected as one of the Papers of the Month by @elisecutts.bsky.social in Reviewer Too www.reviewertoo.com/paper-roundu...

reviewertoo.com

Paper Roundup December 2025: computing billiards, an impossible atmosphere, and Roman constructions

Papers on big questions at the frontiers of science, curated by hand each month

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Reposted by Eva Miranda

Elise Cutts @elisecutts.bsky.social · 08/01/2026

This month's paper roundup is live! This time around we've got 2D billiards that can compute, an atmosphere that shouldn't exist, a Roman construction site, and more. Check it out here: www.reviewertoo.com/paper-roundu... 🧪

reviewertoo.com

Paper Roundup December 2025: computing billiards, an impossible atmosphere, and Roman constructions

Papers on big questions at the frontiers of science, curated by hand each month

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Eva Miranda @evamirandag.bsky.social · 09/01/2026

Fascinated once again to see @walkingthedot.bsky.social work his magic, explaining this story with the perfect touch. Happy to have contributed a small grain to it. Congratulations on this piece! It beautifully captures the emotion of the moment and the roller-coaster nature of research 🎢

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Eva Miranda @evamirandag.bsky.social · 05/01/2026

What’s next? Billiards are toy models for near-collision dynamics in the 3-body problem. If billiards can compute, undecidability should be hiding in celestial mechanics. In 2026 we plan to address this for the 3-body problem with A. Gonzalez, D. Peralta #wisemen @crmatematica.bsky.social @upc.edu

wise-men bringing presents to Eva (this time undecidability of trajectories in the 3-body problem)

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Eva Miranda @evamirandag.bsky.social · 01/01/2026

2025, you were: The Sant Cugat Prize, a feeling of recognition and belonging Gauss in May A Chinese Dragon in July re-energising, unstoppable. Zurich in winter A private concert at the Petite Malmaison Bach Oratorium at the Fraumünster and vermicelli closing the circle Thank you!

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Reposted by Eva Miranda

Elixir of Progress @elucidating.extradimensional.space · 27/12/2025

This is exciting for a lot of reasons. But I am smug every time I see this stuff because it further reinforces my theory that computation or something directly related to it is in some sense universal, and perhaps even fundamental, to our universe.

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Reposted by Eva Miranda

Marcelo Rinesi @marcelorinesi.bsky.social · 27/12/2025

If there's an aesthetics of the intersection of CS and physics --and I think field-specific aesthetics is an insufficiently explored area in mathematics, programming, and data modeling-- this paper is surely in the purest Classical tradition.

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Reposted by Eva Miranda

John C. Baez @johncarlosbaez.bsky.social · 23/12/2025

It reaffirms my belief that anything sufficiently complex can serve as a universal computer and thus obeys the theorems regarding those. All is well.

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Reposted by Eva Miranda

dervishe the grey @dervishe.eurosky.social · 23/12/2025

After the Magic game, classical billiards as a Universal Turing Machine :)

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Reposted by Eva Miranda

John C. Baez @johncarlosbaez.bsky.social · 23/12/2025

Since the halting problem is undecidable, this means there are some yes-or-no questions about the eventual future behavior of a point bouncing around in this region of the plane that cannot be settled in a finite time by any computer program. (2/n) arxiv.org/abs/2512.19156

arxiv.org

Classical billiards can compute

We show that two-dimensional billiard systems are Turing complete by encoding their dynamics within the framework of Topological Kleene Field Theory. Billiards serve as idealized models of particle mo...

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Reposted by Eva Miranda

John C. Baez @johncarlosbaez.bsky.social · 23/12/2025

New result: you can build a universal computer using a single billiard ball on a carefully crafted table! More precisely: you can create a computer that can run any program, using just a single point moving frictionlessly in a region of the plane and bouncing off the walls elastically. (1/n)

Classical billiards can compute
Eva Miranda, Isaac Ramos

We show that two-dimensional billiard systems are Turing complete by encoding their dynamics within the framework of Topological Kleene Field Theory. Billiards serve as idealized models of particle motion with elastic reflections and arise naturally as limits of smooth Hamiltonian systems under steep confining potentials. Our results establish the existence of undecidable trajectories in physically natural billiard-type models, including billiard-type models arising in hard-sphere gases and in collision-chain limits of celestial mechanics.

Significance statement. Billiards are a textbook model of deterministic motion: a particle moves freely and reflects specularly from rigid walls. We show that, even in two dimensions, billiard trajectories can simulate arbitrary Turing machines. This universality implies a sharp limit on prediction: there is no general algorithm that can decide basic questions such as whether a trajectory is periodic. Because billiards also arise as limits of smooth Hamiltonian systems with increasingly steep confining potentials, these algorithmic barriers are not confined to idealized hard-wall models. Our results place undecidability, alongside chaos, as a fundamental obstruction to long-term prediction even in low-dimensional classical dynamics.

From here: https://arxiv.org/abs/2512.19156

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Eva Miranda @evamirandag.bsky.social · 23/12/2025

Happy Holidays! arxiv.org/abs/2512.19156

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Eva Miranda @evamirandag.bsky.social · 23/12/2025

This Christmas 🎄 the balls left the tree, bounced across a billiard table 🎱, and—inevitably—started computing. With Isaac Ramos, we show that billiard dynamics is undecidable: arxiv.org/abs/2512.19156 In the computational universe of Cris Moore and @stephenwolfram.bsky.social

arxiv.org

Classical billiards can compute

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Eva Miranda @evamirandag.bsky.social · 22/12/2025

Thanks. It is submitted to arxiv. I hope it appears tonight. I will send you the link when I have it.

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Eva Miranda @evamirandag.bsky.social · 21/12/2025

exactly! We have been working on this notion of Turing complete systems in the last years. We associate a Turing machine to a dynamical system in such a way that entering an open set (computable) corresponds to the halting state in the Turing machine.

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Eva Miranda @evamirandag.bsky.social · 21/12/2025

Indeed, it is a very interesting question. As our billiard systems uses our former TKFT it is robust from the computational perspective

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