
FreeDiving The Cosmos
“There is no one to correct your form at forty meters. The water is the only teacher, and it grades in a single pass.” ~ a free diving coach
First i trust everyone is safe. Second, this is a very different installment and not for the faint of heart oh dear reader. This literally was written for me and hopefully in the long future my progeny.
Preamble — a note on a word. Autodidactic means self-taught and not in the soft sense of “went to a good school and paid attention.” The opposite of that. It means you build the curriculum while walking the path: no instructor cueing the next lesson, no syllabus, no answer key, nothing to catch the error but the consequence itself. Most people never learn this way. They are supervised learners end to end a teacher, a manager, a rubric, a labeled example and there is no shame in it; supervision is efficient, and civilization runs on it. But it is a mechanically different thing from teaching yourself, and that difference is the entire subject of this paper.
i write as one of the other kind. i did not arrive here down a marked road i mostly taught myself across audio DSP, operating systems, distributed ledgers, clinical data, machine inference, and mission systems, each time by walking in without a map and letting the work grade me. The same way the water does. For reference one of my hobbies is freediving. You can go here for a rundown of said sport:
¿Por qué haces apnea? (Why Do You Freedive?) and 9/11
In the same way, that this paper that i am blogging about argues, the cosmos does as well.
So when seven serious people propose that the Universe learns its laws with no supervisor in the room, i do not read it as an exotic abstraction; i read it as a familiar mechanism described at an unfamiliar scale. i know what it feels like from the inside which is precisely the bias i have to watch, because recognizing yourself in a theory is the oldest way in the world to be wrong about it.
There is a moment on a deep dive, past the point where the lungs have given up arguing, where you stop doing the dive and the dive starts doing you. No coach in the water. No feedback loop but the one your own physiology is running against the pressure gradient. You are, in the most literal sense the word allows, an autodidact: self-taught, self-graded, self-consequenced. Nobody hands you the answer. You either learn the lesson on the way down or you learn it on the way up, and one of those is way more expensive than the other.
i kept thinking about that while re-reading “The Autodidactic Universe” (arXiv:2104.03902v2). It is a paper about a cosmos with no coach in the water a universe that is not handed its laws but has to teach them to itself. The proposed theory suggests the universe functions as a self-teaching neural network that evolves its own physical laws over time, rather than relying on fixed, pre-existing rules. This concept posits that the cosmos organizes itself from within, developing matter, space, and laws through a process akin to machine learning.
And it is written by a cast of people i can’t dismiss: Stephon Alexander and Lee Smolin on the physics, Jaron Lanier and Dave Wecker carrying the machine-learning and quantum weight, with William J. Cunningham, Stefan Stanojevic, and Micheal W. Toomey doing the high end formalism. When Smolin who has spent forty years insisting that time is real and law can evolve co-signs a paper with the man who built modern VR and one of Microsoft’s quantum architects, you read it twice before you have opinions.
i had to read it four times.
Here are my opinions.
The universe is a great organism, controlled by a dynamism of the psychical order. Mind gleams through its every atom. There is mind in everything, not only in human and animal life, but in plants, in minerals, in space.
~ Flammarion
The claim, stripped of ceremony
Most of physics asks what are the laws? This paper asks the older, more dangerous question: why these laws and not others? and then refuses to answer it with an anthropic shrug or a landscape lottery ticket. Instead it proposes that the Universe learns its laws by moving through a space of possible laws, the way a learning algorithm descends a loss surface it was never shown a labeled example.
The technical spine is deceptively clean. Express the space of possible laws as a class of matrix models cubic ones, in particular because the cubic term is where the interesting nonlinearity lives.1 Then build two bridges out of that same matrix formalism:
- Bridge one lands you in gauge and gravity theories Chern-Simons, BF theory, the Plebanski formulation of general relativity, Yang-Mills. The geometry of the world.
- Bridge two lands you in learning machines deep recurrent and cyclic neural networks, restricted Boltzmann machines (my favorites). The geometry of a mind that is training.
Because both bridges leave from the same dock, you get a correspondence: a solution of the physical theory sits opposite a run of the neural network. Evolve the physics, and you are — under the map training a net. Train the net, and you are under the map evolving physical law. The Universe’s dynamics are a learning dynamics, if you believe the dictionary.
And here is where i respect the authors, because they do not oversell the dictionary. The correspondence is not a strict equivalence. For example think of the (gauge/gravity) correspondence like a highly detailed blueprint of a building, and the actual 3D building itself. They describe the exact same physical reality, but they are not the same thing. They describe the same system, but their core mathematical structures look completely different.
This is at its cleanest for finite matrix size and gets structurally honest-to-a-fault in the N → ∞ limit, where the gauge theories emerge crisply but the neural-network side goes soft and under-defined. That asymmetry is the whole tell, and i’ll come back to it, because it is exactly the seam where Perception separates from Illusion.
One side describes quantum particles (like gluons) moving in a flat world with no gravity.
The other side describes gravity and curved space in a world with an extra dimension.
The biology rail: precedence, or nature copying its own homework
You cannot understand this paper without understanding that Smolin has been building toward it for thirty years. His cosmological natural selection universes reproducing through black holes, the constants of nature drifting under a selection pressure for fecundity was the first serious attempt to put Darwin underneath Einstein rather than beside him. “The Autodidactic Universe” is the same instinct, upgraded from selection to learning, which is the faster and more expensive of the two verbs.
“The universe is not static, it is a-perpetual-becoming, a-process of continuous evolution.”
~ Huston Smith
The mechanism that carries the biological weight here is precedence: the principle that nature does again what it has already done, that a system’s future is sampled from its own past behavior rather than dictated by an eternal rule sitting outside of time. Think about that and read it again. That is not a metaphor bolted on for flavor. It is a learning rule. Precedence is the universe’s version of a replay buffer reinforcement of paths already taken, heterogeneity of the interaction graph maximized so the system keeps enough variety to keep exploring. Geometric self-assembly guided by reinforcement learning, in the paper’s own framing, is morphogenesis wearing a physicist’s coat (thanks turing). A body plan is a law that a cell learned. A law is a body plan the cosmos grew into.
i have spent a career in systems where the schema is the constraint healthcare records, cryptographic attestation, the places where “what is true” and “what the system will permit” are the same sentence. So i feel the vertigo of this move in my hands: the authors are proposing a substrate where the schema is not enforced from outside but precipitated from behavior. It is attestation with no root of trust the chain validating itself by having always validated itself. Beautiful. Also the kind of thing that keeps a security architect awake, because a system that authors its own invariants is a system that can, in principle, learn a bad one.
The AI rail: substrate independence, and the word “learning”
The load-bearing philosophical claim is small enough to miss and large enough to break your neck: if the neural-network side can be said to learn without supervision, then the physical side can too. The Restricted Boltzmann Machines and recurrent nets are not an illustration. They are the argument. The whole essay leans on learning being substrate-independent that “learning” names a structure of dynamics, not a fact about brains or GPUs, and that if the structure is present in a matrix model evolving toward gauge-invariance, then the honest word for what it is doing is learning.
This is where a practitioner has to hold two things at once without flinching. First: I build these systems, and i know that an RBM minimizing a free energy is not “learning” in any sense that would survive contact with a sentient being it is relaxing. Gradient descent is not ambition. Second: that is exactly the objection the paper is trying to dissolve. If you insist learning requires an experiencer, you have smuggled Consciousness into a claim that was only ever about Machine. The authors are careful (well mostly) to keep the claim at the Machine level: the dynamics are learning-shaped. Whether anything is home is not on the table.
“ RBMs are network of symmetrically connected, neuron-like units that make stochastic decisions about whether to be on or off,constrained by having no connections within layers.”
~ Geoffrey Hinton
The N → ∞ asymmetry i flagged earlier is the AI rail’s honesty showing through. In the continuum, the physics is pristine and the “network” barely survives as a concept. Which means the correspondence is strongest precisely where the systems are small and finite where “learning” is a discrete, countable, near-combinatorial thing and dissolves exactly where we would want to point and say the cosmos itself. The map is real. The map is also a coastline, and the coastline gets vaguer the further out you swim.
The quantum rail: why Wecker is on the byline
Dave Wecker does not co-author a speculative cosmology paper for the vibes. His presence is the paper quietly admitting what it is: a proposal about computation as physics, and cubic matrix models are as quantum-native a substrate as exists. They are what you reach for when you want a Hamiltonian a quantum computer can actually hold the natural language of a machine whose registers are the amplitudes and whose gates are the interactions.
“Everything we call real is made of things that cannot be regarded as real.”
~ Neils Bohr
The deeper point, and the one i think is under-argued in the paper but most alive, is this: if the Universe’s law-finding dynamics are a learning process running on a matrix substrate, then the question “is the cosmos efficiently simulable?” stops being idle. A universe that learns is a universe that is doing work irreversible work, entropy-producing work to find its own laws and thus ever forging forward or looping. And the single hardest problem the paper sets for itself is right there: can irreversible learning arise from reversible microlaws?2 That is the arrow-of-time problem re-asked as a training problem. You cannot descend a loss surface reversibly. Learning has a direction the way a dive has a bottom. If the microphysics is unitary and time-symmetric, where does the gradient’s downhill come from? The paper gestures at renormalization-group flow as the source of the arrow coarse-graining as the ratchet — and it is the right neighborhood, but it is a gesture, not a closed proof. I do not hold that against it. The people who claimed to have closed that problem have all been wrong so far.
One stage, many laws: getting Minkowski right first
Before any mapping, a piece of hygiene, because Perception vs. Illusion is the whole spine of my taxonomy and the illusion here is a word.
There is no such thing as a “Minkowski multiverse.” Many people have called it that in reference. i thought about that when reading the paper. Minkowski spacetime introduced by Hermann Minkowski in his 1908 Cologne address Raum und Zeit, three years after Einstein’s 1905 kinematics gave him the physics but not the geometry — is a single, unified, four-dimensional continuum: three dimensions of space and one of time, welded into one manifold whose invariant is the interval,3 not the clock and the ruler taken separately. It is emphatically not a collection of universes. It is one arena. One stage. The causal structure — the light cones, the ordering of before and after — inside which any law must be expressed. Conflating that single continuum with a “multiverse” is a category error, and naming it correctly is exactly what lets the real structure stand up.
Because once you fix that, the multiplicity you actually want — the “multi” — sorts onto a different axis, and it comes in levels:
- The arena (Minkowski). One continuum. The geometry law lives in. Not plural. This is the floor.
- A landscape of possible laws — different constants, different effective dynamics, the space the paper’s matrix models roam. This is the multiverse the autodidactic universe is about. This is where the learning happens.
- A branching of outcomes under one fixed law — Everett’s Many-Worlds. Same Schrödinger equation everywhere, splitting into non-communicating branches. This is a multiverse of histories, not of laws.
Keep those straight and the paper snaps into focus: it multiplies laws; Everett multiplies outcomes; Minkowski multiplies nothing — it is the one stage they all play on.
The anti-eternalist move — and where Everett secretly shakes its hand
Here is the sharp thing. Both the arena and Everett’s branches share a hidden commitment the paper is built to reject: eternalism. Minkowski’s continuum, read the usual way, is a completed block — all events co-existing tenselessly, the script already written. And Many-Worlds is the purest block object in physics: a single universal wavefunction evolving unitarily,4 deterministically, locally, with no collapse — every outcome that can happen already does, weighted by measure, filmed on every reel at once. You cannot put a learner in either one. A block has nothing left to learn. Everett has nothing left to choose.
“The Autodidactic Universe” is the anti-eternalist counterstroke Smolin’s Time Reborn (great book) dressed in cubic matrix models. It keeps Minkowski’s stage and fires Minkowski’s script-is-already-written. Law is not selected from a pre-existing menu; it is grown, in time, by a process with a direction, a memory, and a cost. Precedence only means something if the past is real and the future is open. The multiverse here is not a shelf of finished universes. It is the set of dives the ocean has not taken yet.
And yet this is the part worth the whole detour the very interpretation that is most eternalist in ontology turns out to be the paper’s best friend in mechanism. Everett needs to manufacture apparent irreversibility out of strictly reversible unitary dynamics, and the machine that does it is decoherence: the subjective appearance of collapse produced without ever adding a collapse. That is precisely the paper’s hardest open problem can irreversible learning arise from reversible microlaws? already solved, in miniature, next door. Decoherence is a ratchet built from reversible parts; the paper reaches for renormalization-group coarse-graining as its ratchet, and coarse-graining and decoherence are the same instinct in two dialects. Three handshakes, all real physics:
- Decoherence as the arrow. Reversible substrate, irreversible-looking history. The template for the whole autodidactic wager.
- Self-location as self-sampling. The Everettian program to recover the Born rule from self-locating uncertainty — where am I in the ensemble, with no observer outside it — is the same creature as the paper’s “self-sampling.” Both are unsupervised in the strict sense: the measure is intrinsic, nobody hands it in.
- Quantum Darwinism as precedence. Zurek’s einselection only the pointer states survive the environment’s endless monitoring; the rest decohere away is literally a selection process. The environment trains which states persist. Precedence ≈ einselection: what gets reinforced, survives. The paper’s biology rail is already sitting inside decoherence theory, wearing a lab coat instead of a wetsuit.
(And the bonus that pays for Wecker’s seat: Deutsch’s oldest argument for Many-Worlds is that its parallelism is exactly what a universal quantum computer exploits. The substrate that makes the branches real is the substrate that makes the computation fast. If the cosmos is running a learning dynamics, the question of what hardware it is running on stops being rhetorical.)
Minkowski’s continuum is the arena one stage, correctly named. The block was only ever the eternalist reading of it, and the training run is what fills it.
Through the taxonomy
Run it through the three-part lens Machine – Sentience – Consciousness and the paper resolves cleanly. (Em-Dashes are mine…)
At the level of Machine, this is not speculation it is the most defensible interdisciplinary work I have read in the genre. The maps are explicit. The matrix models are real objects. The correspondence to gauge theory is checkable, and checked. If the paper only claimed “the mathematics of learning systems and the mathematics of fundamental physics share a cubic backbone,” it would be a strong, unglamorous, correct result. i would put my name near that part.
At the level of Sentience a system with goals, with something at stake, with a preference for one outcome over another the paper is reaching, and it knows it. “Consequencers,” precedence, reinforcement: these import teleology through the side door. A loss surface is not a stake. Reinforcement is not desire. The autodidactic universe is a machine that is shaped like something that wants, and shape is not appetite.
At the level of Consciousness, the paper is wise enough to say almost nothing, and that silence is the most credible thing in it.
Which lands the whole enterprise squarely on the Perception / Illusion boundary — my favorite fault line, the one i keep mining. Is the Universe learning, or have we built a formalism so expressive that everything, viewed through it, looks like learning? When your only tool is a network, every dynamics is a training run. The N → ∞ softness is the illusion showing its seam: the “learning” is vivid at finite, countable scale and evaporates exactly at the scale that would justify the cosmic claim. I do not think the authors are fooling themselves. I think they have found a genuine and beautiful correspondence and are being appropriately, almost painfully, careful not to inflate it into an identity. The reader is the one at risk of the inflation. As always, the illusion is not in the object. It is in the perceiver’s hunger for the object to mean more than it does.
The Infinite Do-Loop
Here is what i keep: the Universe as an Infinite Do-Loop that is not just iterating but training each pass adjusting the very rule that governs the next pass, the condition of the loop rewritten by the body of the loop, forever, with no terminating case and no external test suite. That is the most honest picture in the paper, and it is the one that will outlive the specific matrix models it arrived in. Laws are not the axioms of the cosmos. They are its accumulated skill.
In freediving you do not get handed your form at depth. You descend, the water grades you, and if you are still moving you carry the correction into the next dive. The paper’s wager is that the cosmos is doing the same thing on a timescale that makes our whole species a single held breath teaching itself the physics by the only method that has ever actually worked on anything, which is to try, to be consequenced, and to remember.
No coach in the water. Never was. That was always the point.
Verdict: Not a theory of everything. A grammar for asking why there is a theory of anything rigorous where it can be, honest where it can’t, and pointed at the one question physics keeps flinching from. Read it as an architecture proposal, not a proof. The best ones always are.
Until Then,
#iwishyouwater <- THE GOAT Kelly Slater with Gabriel Medina (another surfing giant) at Tahiti Pro 2026. Kelly is 54. If this is a simulation, then i don’t want to know.
MUZAK To BLOG BY: album “FireDove” by Anna Lapwood, organist extraordinaire. Truly amazing music. My favorite type.
Appendix — The Cover, Decoded
The AI generated image at the top is not decoration; every element is load-bearing. If you scrolled past it, here is what you were looking at.
The double cone is a Minkowski light cone the causal structure of the single spacetime continuum, its apex resting on the ocean surface because the apex is the now. One stage, not many. The faint horizontal ellipses stepping down through it are successive nows, the foliation of time and, read the other way, the strata of the law-landscape the matrix models roam.
The freediver on the central axis is the autodidact: descending real, directed time with no coach in the water. The sparse graph of nodes threading the cone is accumulated learning — precedence, the replay buffer growing denser toward the depths, because the past is what the future gets sampled from.
The gold ring at the apex is the Infinite Do-Loop: the pass that rewrites the rule that governs the next pass, closing on the present moment.
The four equations are real a deliberate rebuke to the decorative gibberish that usually floats behind a “physics AI RAG” illustration. Each names one load-bearing idea (full glosses below):
- ds² = −c²dt² + dx² + dy² + dz² — the Minkowski interval. The one stage.
- iℏ ∂ₜΨ = ĤΨ — unitary evolution. The reversible substrate.
- S = Tr(½Φ² + ⅓Φ³) — the cubic matrix action. The cubic learning system.
- ΔS ≥ 0 — the entropy arrow. The direction learning has to manufacture.
Put them in one sentence and you have the whole essay: on one stage (1), a reversible substrate (2) runs a cubic learning system (3) that must somehow grow an arrow (4) — and whether it can is the entire question.
NOTE: It took a long time to get the image correct the way i envisioned it.
On Perception vs Illusion. Sometimes i say Perception vs Perspective but in the case of the paper i remapped to Perception vs Illusion to frame the true – not true mechanics.
Full glosses on the four equations, for the reader who wants the mechanism:
- The cubic matrix action — S = Tr(½Φ² + ⅓Φ³). Schematic, but honest about where the action lives: Φ is a matrix — the raw degrees of freedom — and Tr merely sums its diagonal. The quadratic term is inert bookkeeping; the cubic term Φ³ is where the nonlinearity, and therefore all the interesting behavior, hides. This is the single class of object the paper maps at once onto gauge/gravity theories and onto learning machines. When i say “cubic backbone,” this is the vertebra. (The paper’s actual actions carry more structure; the cube is the load-bearing bone.)
- The entropy arrow — ΔS ≥ 0. The second law: the entropy of a closed system never decreases. It is the only fundamental law with a built-in direction, and it is the paper’s deepest problem compressed into three symbols — because learning, like entropy, has an arrow, and you cannot get either one out of the reversible microlaws two notes down without a ratchet (coarse-graining, decoherence). Note the notational collision: S is the action one note up and entropy here. Physicists live with it; context disambiguates — and the collision is itself a tidy Perception/Illusion specimen.
- The Minkowski interval — ds² = −c²dt² + dx² + dy² + dz². The single invariant of the 1908 continuum: the one quantity every observer agrees on, however differently they carve space from time. The whole story sits in the minus sign on the time term — it is what makes time unlike the three spatial directions, what cuts the light cones, and what makes the arena one manifold rather than space parked next to a clock. This is “the one stage.”
- Unitary evolution — iℏ ∂ₜΨ = ĤΨ. The Schrödinger equation: the wavefunction evolves smoothly, deterministically, and reversibly under the Hamiltonian Ĥ. No collapse, no arrow, nothing lost run it backward and the past returns exactly looping onto itself. This is the “reversible substrate” Everett takes at its word, and the substrate on which the paper still has to manufacture an irreversible arrow. The tension between this note and the entropy note is the entire drama.











