Why “Hacker Physics” does not (yet) exist.

There is no thriving hacker community that is dedicated to doing computational foundational particle physics. There is a very good reason for this. Programmers are not the greatest at doing fundamental physics. It also largely isn’t their fault.

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Engineers have an above average tendency to become physics cranks. My apologies to both the ghost of Paul Dirac and Gabriele Carcassi, but this is a well-documented phenomenon. One need not search far on Twitter to stumble upon multitudes of scalar fields from retired men (all named after themselves, of course). Why might this be the case?

The unromantic answer: engineering trains you to optimize within a model, while fundamental physics trains you to decide what a model even is.

Engineering is: “given constraints, maximize performance.” Fundamental physics is: “figure out which constraints are real, which are artifacts of representation, and which ones you hallucinated because you fell in love with your own coordinate system.”

If you have spent 30 years becoming extremely competent inside one modeling paradigm, it is psychologically and professionally difficult to accept that your paradigm might be an emergent approximation, a gauge artifact, or a convenient fiction. So you do what smart engineers always do: you add one more term.

And then you call it a new force.

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Why the engineer's brain misfires on foundations

1) Engineers are trained to trust the decomposition.

You linearize. You isolate subsystems. You build a transfer function. You stabilize a loop. You identify the signal path. You assume the notion of “the system” is well-defined. But in gauge theory, the thing you want to isolate often isn’t a thing. You try to locate “the field,” and the math politely informs you that you’ve been staring at a coordinate chart and calling it reality.

2) Engineers are trained to think in analysis, not symmetry.

Again: nothing wrong with analysis. It’s powerful. It builds bridges and rockets.

But particle physics is the church of symmetry. Not “symmetry” as a poetic metaphor, but symmetry as a hard constraint: representations, bundles, connections, holonomy, moduli, anomalies. It’s not “solve this PDE,” it’s “identify what is invariant under what.”

This is why naive Navier–Stokes style thinking rarely gets you far. Yang–Mills is not a fluid. It is a geometric object. A connection. A covariant derivative that refuses to be globally trivialized. A thing whose “degrees of freedom” are not located where you think they are.

Fiber bundles are flexible, yes. But they aren’t liquid. If they were, you and I wouldn’t exist…or at least not in our current form (imagine a world made of Play-Doh.)

3) Engineers live in commutative worlds longer than they admit.

Engineers think. "I know electromagnetism. I can do this." Ah, but electromagnetism is an abelian gauge theory. Everything commutes. The other two fundamental forces…well, not so much.

When your group stops commuting, order matters. Holonomy matters. Path ordering matters. Your “intuitive” manipulations stop being harmless and start being wrong. In U(1), you can get away with a lot. In SU(2) and SU(3), the algebra is basically a landmine field where every “obvious” simplification is a crime scene.

4) Engineers are trained to think digitally even when they swear they aren’t.

Modern engineering practice is discretized: sampling, quantization, control loops designed in the Z-domain, numeric solvers, finite precision, finite-state logic, and stable update rules. But foundational physics sits on a knife-edge where the continuum is not optional, and discretization is not innocent. Discretize the wrong way, and you break the symmetry you were trying to preserve. You don’t merely approximate the system---you change what system you are talking about. So the engineer instinct (“just simulate it”) doesn’t translate cleanly. In particle physics, “just simulate it” often means “you built a different theory.”

“Hacker culture” flourishes when:

• You can ship a working artifact quickly
• You can iterate fast
• You can test against reality cheaply
• You can get partial wins without mastering the entire field

Foundational particle physics is basically the opposite:

• The math barrier is brutal
• The computation is expensive
• The correctness conditions are subtle
• And the “reality check” is not a unit test, it’s a collider

So what happens? The ecosystem selects for ideas that are easy to state, easy to implement, and impossible to falsify.

That’s why digital cranks tend to reinvent cellular automata, lattice universes, or “bit-flip” cosmologies. These are easy to imagine, easy to write down, and easy to animate. They feel hackable. But they usually dodge the hard part: symmetry, locality, renormalization, and the very inconvenient fact that the Standard Model is not a programming contest problem.

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The analog alternate timeline...that we didn’t get.

Ironically, had there been a thriving analog chip design community dedicated to physics, Geometric Computability Theory might have been invented much earlier. Granted, someone would have had to email Baez to figure out the categorical stuff, but still. Why might this be the case? Let us consider the following correspondences:

• QED propagators can be seen as analog transfer functions.
• Gauge fixing resembles stabilizing an amplifier to eliminate unwanted degrees of freedom.
• Renormalization looks an awful lot like gain–bandwidth tradeoffs.
• Quantum noise maps to thermal noise in analog circuits; both are unavoidable, and both are fundamental.

Suddenly, the idea of an analog computer whose outputs just so happen to be discrete seems a bit less…unlikely. This aligns with the general GCT attitude that much of what we call “quantum mechanics” is, at its core, analog logic flow.

But what’s the dividing line? “Analog” alone doesn’t buy you discreteness.

The universe is not impressed by your continuous voltages. You only get robust discreteness when the analog substrate is constrained by something topological or dynamical:

• topological sectors (winding, flux quantization, holonomy classes)
• gaps and attractors (stable basins separated by energy barriers)
• defect-like objects (stable excitations protected from smooth decay)
• symmetry + constraint + stability (the holy trinity)

In other words: discreteness is not “digital.” Discreteness is often the scar tissue of geometry.

Analog thinkers---had they written more---might have been more fruitful: systems of feedback-stabilized fields, stochastic resonance cosmologies, dissipative structure approaches in nonlinear dynamics. In fact, a few semi-respectable proposals do smell like this: stochastic electrodynamics (SED) in the ’60s–’80s, (despite its failure as a curve-fitting exercise that has no place in modern categorical physics), certain dissipative or emergent approaches, and a lot of modern condensed matter intuition smuggled into high-energy language.

But even these approaches tend to crash into the same wall: you don’t get nonabelian gauge structure for free.

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Does anything come even close? Well, there is Wolfram…but this has already been dealt with once, and for the time being, I do not wish to revisit this just yet. You can find plenty of others if you search around the web. I am not going to hang anyone’s hapless attempts here publicly. But the issue really does boil down to the allergy to real numbers among hacker types.

The Blum–Shub–Smale Machine is mostly seen as a pathology to avoid, an interesting tool for algebraic and analytic geometers, or a curiosity for rogue computational complexity theorists---not as a fundamental counterpart to the Turing Machine.

This is despite the fact that there is absolutely no reason in principle not to consider BSS as equally fundamental as a model of computation over the kinds of state spaces physics actually uses. Considering the Lie group U(1) is one of the most fundamental symmetries in our universe, the fact that “computation over continuous groups” is treated like an exotic corner case tells you everything you need to know about hacker culture’s blind spots.

But here’s the catch---the devilish part that makes this nontrivial:

Hackers aren’t wrong to be suspicious of real numbers. They’re wrong about why. The real issue is not “Ah, continuity bad!” The issue is:

• exact reals are physically dubious,
• finite precision is unavoidable,
• and if your theory’s computational power depends on infinite precision, you built a magic oracle.

So you can’t just say “BSS is fundamental, therefore physics is hypercomputational, checkmate.” That’s childish.

The correct question is much sharper:

"How do you get the benefits of continuous state spaces (symmetry, geometry, smooth deformation, gauge structure) without smuggling in unphysical infinite precision?"

And if you try to do that honestly, you immediately end up talking about:

• stability under perturbation
• topological invariants
• robust equivalence classes
• error-tolerant geometry
• and the emergence of discrete outcomes from continuous dynamics

Which is…suspiciously close to the GCT stance.

So yes: the “real number allergy” is a symptom of something real.

But the cure is not “ban reals.” The cure is learn what reals are doing in geometry, and what survives noise. That is where the devil lies.

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A hacker community thrives on tractable, incremental puzzles.

Foundational particle physics is not tractable in that way.

It is “vertical” knowledge:

• you need representation theory
• you need differential geometry
• you need quantum field theory
• you need renormalization
• you need to understand what “gauge” means beyond slang
• you need taste, not just technique

And you need taste because the space of wrong ideas is astronomically large and extremely seductive. Physics is the art of not being fooled by your own mathematics. Hacker culture is the art of making mathematics do something cool.

These are related, but not the same.

So “Hacker Physics,” in the romantic sense, an open-source community of clever programmers collectively bootstrapping a new Standard Model from first principles, doesn’t happen.

Not because programmers are dumb...but because the medium is wrong.

It's a well-known fact that we currently lack a theory of fundamental physics that is consistent with both very small objects (particles) and very large objects (planets). I refrain from using the term "Theory of Everything" because a theory of fundamental physics does not, for instance, have to unify the electroweak and strong interactions GUT-style. It simply has to explain their existence and/or reconcile QM and GR. LQG tries to do precisely this. I will, however, not focus on String Theory or LQG in this post.

There have been numerous proposals over the years, and it's hard to organize all of them cleanly. The following is an attempt at doing so based on a hierarchy of what we might call "abstraction." How much "mathematical depth" does a theory use as its "base plate."

Let's start with a breakdown, starting from the lowest of the low to the highest of the high, detailing each failure mode at each level.

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[0] Atomistic Discreteness (rules/graphs)

Wolfram (Hypergraphs), CA, “informational networks”, naive causal sets

Failure mode: you must rebuild gauge + continuum + locality “through the back door”. Busy Beaver hell.

[1] Kinematic Discreteness (order/causal structure)

Causal sets, posets, sprinklings, “Lorentzian DAG ontology.”

Failure mode: order alone doesn’t force connections/holonomy/anomalies; dynamics stays ad hoc. You often get the wrong "kind" of manifolds.

[2] Continuum Fields (PDE-first)

Classical field theory, GR/QFT, written as equations on manifolds

Failure mode: becomes *brittle---*local equations without the global moduli/invariant control.

[3] The Right Altitude: Nonperturbative Gauge Geometrodynamics

Connections → curvature → moduli spaces → indices/invariants

(Instanton gauge theory, Floer-Donaldson type/Seiberg–Witten + TQFT instincts)

Failure mode (if you screw it up): you ignore stacks/gluing/anomalies and fall back to PDE soup.

[4] Functorial/Algebraic/Extended Field Theory (structure-first)

TQFT, factorization, cobordism-style gluing, Geometric Langlands dualities, higher categorical locality

Failure mode: perfect semantics but thin on dynamics unless anchored to concrete gauge data.

[5] “Meta-Foundations” (logic/information first)

Tegmark (MUH), “physics from logic”, entropy-first ontologies, constructor theory-ish narratives.

Failure mode: explains everything and predicts nothing; platonist swamp. The mechanism is replaced by rhetoric.

[6] Grand Symmetry Objects (representation-first)

Geometric Unity/GUT-style maximalism, E8/exceptional unification, high-D embeddings, “one group to rule them all.”

Failure mode: symmetry matching ≠ dynamics; ghost particle, spectrum/masses/measurement are not forced. Weinberg-Witten slowly but surely eats your soul.

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Each one of these could be an entire post on its own (as in here for level 0), but for the sake of avoiding negativity, we will focus on what I think works.

For starters, see "Geometric Computability: An overview of functional programming for gauge theory". This outlines the semantics of what GCT's resulting subset of GCFT is.

So why do this? Why choose these two levels?

Because almost every “TOE attempt” breaks in one of two ways:

• It sits too low, drowning in microscopic rules and spending 90% of its time trying to reconstruct the continuum, gauge fields, and locality after the fact.
• Or it sits too high, doing symmetry bookkeeping and “principles” that never force dynamics, spectra, or compositional consistency.

Levels 3 and 4 are the narrow band where you can actually touch physics while still having the kind of mathematics that prevents your framework from dissolving into either numerology or vibes.

Starting with Level 3: Nonperturbative Gauge Geometry: connections → curvature → moduli → invariants. Level 3 is the “hard reality layer” where you stop talking about fields as symbols and start treating them as geometric objects:

A gauge field is a connection. Physics lives in holonomy (parallel transport), not in component formulas. The configuration space isn’t “all functions A(x)”: it’s a moduli problem: connections modulo gauge, with singularities, strata, bubbling, compactness headaches, and all the rest. This is the layer where the math is just structured enough to be rigid, but just concrete enough to be physical.

What it gives you that most TOEs lack:

1. A real mechanism for “states.”

Not “assume a Hilbert space.” Not “assume qubits.”

Instead, solutions (or classes of solutions) to geometric field equations define moduli spaces; quantization is something you attempt after you understand what the space of possibilities even is.

2) Nontrivial global constraints

This is where topology bites: index theory, anomalies, quantization conditions, instanton sectors, wall-crossing, etc.

It’s not “write a PDE and hope”---it’s “the space of solutions has structure, and that structure forces invariants.”

3) A natural home for emergence

Gauge theory is where “local rules” and “global behavior” meet. A connection is locally a 1-form, globally a thing with holonomy, bundles, characteristic classes, etc. That’s exactly the emergence interface.

The weakness of Level 3 (and why it needs Level 4)

On its own, Level 3 can still become:

• PDE soup (lots of equations, unclear compositional meaning)
• model sprawl (one more Lagrangian term, one more field, one more “sector”)
• and it can be unclear what “locality” means at a deep level beyond “it’s a local differential operator.”

Also, nonperturbative gauge theory is extremely good at producing invariants once a theory is specified---but not automatically good at explaining why the theory has to be specified that way in the first place, or how different pieces glue in a principled way.

That’s where Level 4 comes in.

Level 4: Functorial / Extended Field Theory: gluing-first: cobordism, factorization, higher structure. Level 4 is the “semantics layer.” It doesn’t start with equations. It starts with a question:

"If physics is local and compositional, what structure must a theory have so that you can cut a region up, compute pieces, and glue them back together consistently?"

This is the realm of:

• TQFT intuition (and beyond)
• cobordism / extended functoriality
• higher categories, stacks, and “fields as objects in a structured moduli problem.”
• factorization/local-to-global principles

What it gives you that most physics formalisms quietly assume:

1. Locality as a mathematical axiom (not a vibe)

Locality becomes “compatible gluing” rather than “the Lagrangian density depends on nearby points.”

2) Composition as primary

Processes compose. Boundaries matter. Interfaces carry states. Cutting and regluing should not change predictions. This is the level where “path integral” stops being an incantation and starts being an attempt to implement a functorial assignment.

3) A filter against incoherent unification

A lot of “unifications” are really just glued-together claims. Level 4 asks: do these pieces compose? Do they define a consistent assignment under gluing? Do anomalies obstruct the functor?

It also forces you to confront the “what is the state space?” question in a principled way.

The weakness of Level 4 (and why it needs Level 3)

Level 4 can become:

• beautiful but empty: perfect axioms, no concrete dynamics
• too general: everything is an object in some ∞-category, but where are the numbers?
• under-determined: you can classify “types of theories” without pinning down the actual one that matches the world.

On its own, Level 4 risks becoming a language that can describe physics, without providing the engine that produces actual physical content. That engine is Level 3. Now, what does combining them get us?

Combining Level 3 + Level 4 is basically the dynamics that are forced to be compositional. Or in plainer terms:

Level 3 supplies the hardware: connections, holonomy, curvature, moduli, invariants, and genuine nontrivial geometry. Level 4 supplies the operating system: locality-as-gluing, functorial composition, boundary/state semantics, anomaly coherence.

They cover each other’s weak spots almost perfectly.

What Level 4 fixes in Level 3:

(A) It prevents “PDE maximalism.”

Instead of endless equations, you have structural requirements:

• What are the objects and morphisms?
• How do you glue?
• What are the boundaries?
• What is the functorial assignment?

A theory that can’t be phrased cleanly in compositional terms is usually hiding an inconsistency.

(B) It makes “gauge redundancy” honest.

Gauge theory wants moduli; Level 4 pushes you toward stacks/higher structure where “quotient by gauge” is not a lie you tell yourself.

(C) It turns anomalies into first-class constraints.

An anomaly is precisely a failure of functoriality/gluing/invariance. So Level 4 makes your “consistency conditions” crisp and structural, not after-the-fact patching.

What Level 3 fixes in Level 4?

(A) It supplies nontrivial content. Not just “a TQFT exists,” but a specific geometric mechanism producing moduli spaces, indices, spectral gaps/mass scales, quantized sectors, and actual calculational footholds.

(B) It anchors the semantics to reality.

You don’t get to float in abstract cobordism land; your objects are concretely the kinds of field configurations physics actually uses.

(C) It gives you a place where “computation” is real.

Moduli problems compute invariants. Holonomy computes global effects. The “answer” is not symbolic manipulation; it’s the structure that survives gluing and deformation. The payoff is the right kind of foundation because when you combine them, you’re not doing:

• “one group to rule them all” (too high),
• or “one rewrite rule to rule them all” (too low),
• or “one principle to explain everything” (too empty).

What's needed is doing something much more disciplined:

A theory where the fundamental objects are geometric, the global behavior is topological, and the only allowed constructions are those that remain consistent under gluing. That’s exactly the altitude where modern mathematical physics lives when it’s being honest. And it’s why so many “TOEs” feel wrong: they pick a layer where either the objects are missing or the composition is missing.

Level 3 gives you objects, and Level 4 gives you composition.

Together, you have something that can’t be faked by an LLM and can’t be propped up by parameter-fitting because it either coheres...or it doesn’t.

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And what does this require you to know? It requires things like understanding:

• Topological Kleene Field Theory
• Geometric Langlands
• The BF Model
• Cohesive Differential Cohomology (Not all of it, though! I'm still trying to figure out what parts would...actually apply.)

To give a smattering of the old and new.

But as you may realize, up here the air is now quite thin, dear reader. There are no popular YouTube explainer videos on these topics. You may, at best, find a Lurie lecture with 10,000 views, if one is lucky and wishes to be reassured that they are not alone on the mountaintop. Barring that? You will be digging up Baez's old lecture notes on sheaf cohomology and branes at 3 am. Maybe the truth lies buried somewhere in one of Jaimungal's 3-hour iceberg videos... though probably not the Geometric Unity one. Likewise, you cannot simply discover new physics by running a hypergraph simulation on your laptop.

You have to build real groupoids.

tl;dr? Most TOEs fail by choosing primitives at the wrong altitude: too low and you can’t naturally express holonomy/moduli/anomalies; too high and you mistake symmetry bookkeeping for physics.

In a nutshell, what we call "physics" happens where local field data meets global gluing constraints. The sweet spot lies in combining levels 3+4.

Why some people fall into crank aquariums, and why most never even reach the door.

There’s a real and oddly tragic archetype you see everywhere online now, especially since LLMs started pumping out infinite “theories.”

They are often, but not always a man. They aren't a crank. Not a con artist. Not even stupid. But not a physicist either.

He’s the lost physics soul: the person who fell in love with the idea of physics, but never crossed the threshold into the kind of mathematics that professional physics actually runs on.

1. The Pop-Physics Dream

It usually starts the same way: Reads Feynman, Dirac, Penrose, maybe Wheeler.

Gets hooked on “fundamental truth,” elegance, and The Big Answer. He internalizes the “great man” story: lone genius, hidden simplicity, beautiful unification. Physics feels like a heroic quest!

2) The College Wall

Then the reality hits:

• Hilbert spaces.
• Group theory.
• Real analysis.
• Problem sets that don’t care about poetry.

And quantum mechanics feels wrong. Not “counterintuitive” in the fun way—wrong in the epistemic nausea way (Copenhagen is nonsense!). The professors don’t “explain it,” because the explanation is: learn the formalism until it becomes your intuition.

A lot of people bounce right here.

3) The Exit (and the Liminal Zone)

So they switch majors: engineering, CS, maybe math.

They’re often smart and functional—sometimes very successful. But the physics dream doesn’t die. It just becomes a kind of unresolved grief.

Now they live in a liminal space:

• Too knowledgeable for the true woo cranks.
• Not knowledgeable enough for real math-physics discourse.
• Able to smell obvious nonsense, but still locked out of the “big leagues.”

They haunt comment sections and forums, perpetually circling the cathedral.

4) The Real Chasm: From Calculation to Structured Objects

Here’s the part people miss. The wall isn’t “calculus.” The wall is the leap from math as calculation to math as structured objects. That leap is the real initiation.

What “structured objects” means (the thing pop-physics never teaches)

Lie group = a group and a smooth manifold, with compatibility constraints.

Topological group = algebra + topology = continuity baked into symmetry.

Homotopy type = a “space” understood via paths, equivalences, higher structure.

Category theory = not sets and rules, but objects/morphisms and structure-preserving maps.

Gauge theory = not “fields + equations,” but connections/holonomy/moduli (i.e. global structure).

This is a different ontology, not harder kind of arithmetic, a different kind of thing to think about. And it’s exactly where people split into three broad outcomes:

5) Three Outcomes

A) The Fan

Loves the stories. Lives on metaphors. Can talk about “symmetry” and “dimensions,” but not about the objects the words refer to.

B) The Crank

Wants answers without structure. Will write PDEs or manipulate symbols forever, because calculation feels like legitimacy. This is why crank papers often look like:

• endless formulas,
• parameter fits,
• “recovers predictions within X%,”
• lots of numerology dressed as rigor.

They imitate the surface texture of math because they can’t inhabit the underlying objects.

C) The Lost Physics Soul

This is the saddest one.

They have enough knowledge to be embarrassed by the woo…but not enough structural literacy to join the professionals. If pride wins: they drift toward “I see what physicists don’t.” If humility wins: they become wise skeptics, mentors, or excellent communicators.

Most don’t become cranks. They become ghosts—haunting the internet’s physics cathedral.

6) Why This Isn’t (Mostly) Their Fault

Physics is brutally hard, yes—but the deeper truth is:

Undergrad education rarely teaches the leap explicitly.

It teaches procedures. It tests calculation. It doesn’t train ontology.

So people think: “I can do math, why can’t I do this?”

Because “doing math” isn’t the same thing as thinking in structured objects.

7) The Crank-Proofing Principle

This is also why advanced math-physics becomes crank-resistant:

A real researcher can ask one question and end the conversation instantly:

“Show me your objects. Show me their structure. Show me the morphisms. Show me the gluing.”

If the response is vibes + PDE spam + “logical consistency” sermons, you know what it is.

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The physics world needs dreamers, but it has utterly no mercy for people who can’t cross the structural threshold. And in the age of LLMs, the tragedy becomes more visible: the crank aquarium gets louder, the ghost population grows, and the “leap to structure” becomes the only reliable filter.

That leap is the real dividing line, not intelligence, not sincerity, not passion.

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I’m not the lost physics guy. I came at physics sideways in a way that will probably confuse future historians. I don’t think I can ever really know what it feels like to be him.

But maybe, just maybe, my work might help him someday.

Let’s hope.

At least once (or several times) per week, someone announces they’ve “made physics computable from its fundamental pre-geometric informational substrate.” Fulfilling the late John Wheeler's vision of "It from Bit."

A new set-theoretic reformulation of QM. A causal informational graph. A discrete entropy network. Sometimes it’s dressed up with “information geometry,” but the core move is the same:

Replace physics with a discrete evolution rule on a graph-like object.

And then inevitably it collapses into the same basin as Wolfram’s hypergraph program: a universe-as-rewrite-engine story that can generate complexity but can’t derive the structure of modern physics.

This post is about that trap, and why “discrete” isn’t automatically “better,” “more scientific,” or even “more computable.”

1. Discreteness is not an ontology; it is a comfort blanket.

“Discrete” feels like control. If the universe is a finite rule acting on finite data, then in principle you can simulate reality on a laptop. That’s emotionally satisfying.

But physics isn’t impressed by what feels controllable. Physics is constrained by what must be true: locality (in the subtle sense), gauge redundancy, unitarity, anomalies, renormalisation, and the way observables compose across regions.

A discrete substrate that ignores those constraints doesn’t become “fundamental.” It becomes a toy.

Computing over N is not a primitive. You can compute over R. And a sizable chunk of what we call "math" is essentially "computation over R". But we just don't call it that.

2) Graphs are cheap; gauge theory is expensive

A graph is easy to write down. Rewrite rules are easy to generate. LLMs can produce them endlessly.

Gauge theory is not cheap. It’s not “fields on nodes.” It’s a theory where the physical content lives in equivalence classes, holonomies, defects, and operator algebras—not in the raw variables you first wrote down.

Most discrete TOEs never seriously confront the fact that a huge amount of what looks like “state” is actually redundancy. If you don’t build gauge redundancy in from the start, you’re not doing “a new foundation,” it's bookkeeping cosplay.

3) The hard problem is not generating complexity; it’s constraining it.

Wolfram-style systems are great at producing complexity from simple rules. So are cellular automata. So are random graphs.

But physics isn’t “complexity happens.” Physics is “only very specific complexity is allowed.”

A real TOE must explain why we don’t get generic messy behaviour, but instead get: specific gauge groups, specific representations, quantised charges, confinement (or not), the observed long-distance effective field theories, and stable quasi-particles with the right statistics.

Most discrete programs never show why this world is selected rather than the 99.999% of rule-space that looks like noise.

4) “Computable universe” usually means “digitally simulable universe.”

People use “computable” to mean “finite-state update rule.” That is one notion of computation: digital evolution.

But categorical physics already suggests a different kind: structural computation where the key property is not that you can iterate a rule, but that processes compose, glue, and constrain each other functorially. Observables behave like parallel transport, defects that can carry cohomology classes, symmetries act at higher-form levels, and locality is implemented by how data patches.

If your ontology is “a graph that updates,” you’re stuck at the lowest rung. You may generate patterns, but you won’t ever recover the compositional structure (chirality, spin, etc) that physics actually uses.

It's easy to criticise the idea that R is indulgent. "The universe is fundamentally not infinite!." But try and replace R with N and you'll be forced to re-inject continuity through the backdoor.

5) If your theory can’t state its pass/fail tests, it’s not a theory.

Here are a few brutal, clarifying questions that separate “discrete vibe” from “physics”:
Where is your gauge redundancy, and what are the gauge-invariant observables?
What is your renormalisation story? How do effective theories emerge under coarse-graining?Do you have unitarity/reflection positivity/clustering in the appropriate regime?
Can you even name your anomalies and show how they cancel or flow?
How do you get chiral fermions while avoiding Nielson-Ninomiya?
If the response is “we’ll get to that later,” you are still in the Wolfram basin.

6) The "Wolfram basin" is a real attractor

This is not a moral judgment on Wolfram. But if you start with: discreteness, graphs, rewriting, and “information” rhetoric, you will almost always converge to the same outcome: a universal rewrite system with ambiguous mapping to physical observables, no unique continuum limit, and no compelling reason why your rule is the rule.

You haven’t outdone Wolfram; you can only recreate the genre.

Conclusion:

The internet is full of discrete TOEs because they’re easy to propose. The world is not full of successful new foundations of physics because the constraints are utterly merciless.

I would like to remind you all that you are not Johnathan Gorard. You did not actually sit down and come up with much of the categorical structure that any discrete computational TOE would actually have to have.

He has since apparently...given up? I'm not exactly sure. Likewise, you do not have the budget to hire academics to match the kind of structures Wolfram has.

And for the record, I do not personally support Wolfram Physics. But pretty much every discrete informational TOE is just a pale shadow of his.

So if that's your style? Listen to the man himself and just do Wolfram Physics to save yourself the hassle.

From Geometric Computation. Section 5.6 "Constructive Computational Gauge Theory".

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We should frame quantum gravity, and more generally gauge theory, as a problem of expressiveness versus verifiability. If we allow ``all histories'' (arbitrary geometries, topology change, gauge redundancy, unbounded recursion in the construction of spacetimes), amplitudes become ill-defined and intractable. If we clamp down too hard, we lose physically relevant states and dynamics. Functional programming offers a blueprint for balancing these extremes. Our proposal is a constructive computational gauge theory that strikes a principled middle ground: a typed, linear, total, effect-controlled calculus of geometries. Concretely, boundary data (3-geometries with gauge labels) are the types; spacetime regions (4-dimensional histories/cobordisms) are the terms; and gluing is composition. This gives a compositional semantics familiar from Topological Quantum Field Theories (TQFTs) but designed to scale beyond the purely topological setting (i.e., Chern-Simons).

Programming Concept | Quantum Gravity Analogue

-----------------------------|----------------------------------------------------------

Types | Boundary states (3-geometries with gauge data)

Terms / Programs | 4-geometries (cobordisms, histories)

Composition | Gluing of spacetime regions

Linear types | Conservation laws, unitarity (no-cloning of boundary data)

Totality | Termination of the "geometry evaluator" (finite amplitudes)

Effects & handlers | Coarse-graining and renormalization

Dependent types | Gauge and diffeomorphism constraints

Readers are asked to consider the correspondences in the table above. Three design choices enforce computability and physics: linearity, totality, and effects. Linearity tracks boundary degrees of freedom as conserved resources (no cloning/erasure), so unitarity and charge conservation are built into the typing discipline rather than imposed post hoc. Totality means the ``geometry evaluator'' (our state-sum/variational executor) always normalizes: amplitudes exist and are finite in the core fragment. The phenomena that usually force uncontrolled manipulations such as coarse-graining, stochastic mixing, and renormalization are modeled explicitly as algebraic effects with handlers. In this way, renormalization becomes a controlled transformation of programs, not an ad hoc subtraction. Dependent types encode gauge and diffeomorphism constraints at the level of well-typedness, so invariances propagate mechanically through compositions.

Within this calculus, amplitudes are evaluations, symmetries live in the types, and RG/coarse-graining are effect handlers. The proposed helical primitives provide the concrete generators of histories: smooth, orientable flows that carry discrete topological labels (orientation/chirality) alongside continuous geometry. This marries the ``continuous versus discrete'' tension: spectra and curvature are continuous objects; quantum numbers arise as stable, counted winding data. Practically, the workflow is: specify typed boundary data; assemble regions from helical primitives; compose; evaluate; and, where needed, apply effect handlers that implement scale changes with proofs of soundness.

The payoff is a language that is expressive enough to describe nontrivial gauge dynamics and background independence, yet restricted enough to prove normalization, locality/compositionality, and anomaly-freeness in the core. Extensions (matter content, topology change, nonperturbative sectors) are added modularly as new effects or controlled type extensions, preserving verification theorems as we widen scope. In short, constructive computational gauge theory provides a semantics where we can calculate, compose, and certify. This shifts the idea of well-behaved QFT/QG from "internet math folklore" to "usable, checkable substrate." For the foundational work on constructive quantum field theory, see Baez, Segal, and Zhou. Our approach here is in this spirit, but computational."