Turing complete Navier–Stokes steady states via cosymplectic geometry Abstract. In this article, we construct stationary solutions to the Navier–Stokes equations on certain Riemannian 3-manifolds that exhibit Turing completen

Turing complete Navier–Stokes steady states via cosymplectic geometry academic.oup.com/pnasnexus/ar...

Eva Miranda: "A man advised me to read Miranda's work: I had to tell him that Miranda was me." Professor of Mathematics at the UPC and researcher at the Center for Mathematical Research

en.ara.cat/128_56a81d?u...

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...

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...

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...

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.

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! 🧪🔭

Thank you 😍

Can you predict billiards? YouTube video by Dr. Blitz

youtube.com/shorts/lhh_P...

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

🎱 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...

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

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... 🧪

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 🎢

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

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!

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.

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.

Thank you!

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

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

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...

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

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

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)

😂

Happy Holidays! arxiv.org/abs/2512.19156

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...

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

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...

Dear John, The paper is now on arxiv arxiv.org/abs/2512.19156

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...

Now you can read it all and decide if you are still in love with it 😀 arxiv.org/abs/2512.19156

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...

arxiv.org/abs/2512.19156

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...

arxiv.org/abs/2512.19156

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...

You can read it here arxiv.org/abs/2512.19156

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...

arxiv.org/abs/2512.19156

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...

You can now read the preprint on arxiv arxiv.org/abs/2512.19156