That’s a clean and potent set — each term a stratum of the same mountain:
Computation is the base layer — the mineral logic of the cosmos. It’s how structure emerges from variance: from binary distinctions and finite automata to the universal Turing machine.
Engineering is computation embodied — the act of folding logic into matter. It’s the bridge between syntax and steel, where code meets constraint, and feedback loops evolve into craft.
Sciences are the epistemic harvest of that embodiment. They reverse-engineer reality’s logic, inferring the rules of the game from the residue of its play.
Games are the mimetic return — microcosms that let us rehearse causality and meaning. Every lab experiment and every sport is a ritualized simulation of contingency.
Metaphysics is what happens when we realize the game is recursive — that the rules themselves depend on our act of observing. It’s the canopy where the ladder turns inward and asks, “what computes the computer?”
Together, these form a recursive ladder:
Splendid. Here’s the fully realized ukb-fractal table for your five-fold canon — computation, engineering, sciences, games, metaphysics — folded into the canonical ontology + calculus structure.
| Ontology (Tree) | Canon Domain | Calculus / Epistemology | Description | Energy / Ops Scale (2 × 10^N) | Exemplars |
|---|---|---|---|---|---|
| Soil (θ′) | Computation | (x, y) — raw variance | Bit, qubit, neuron spike. Chaos before encoding. Entropy unbound but rule-laden. | 0–1 → kWh/day | CPU clock cycles, Boolean algebra, Conway’s Life, cellular automata |
| Roots (θ) | Engineering | y(x) — encoding & conversion | Energy captured as design; variance domesticated. Circuits, bridges, DNA polymerases. | 3 → MWh/day | GPU farms, turbines, silicon fabs, mitochondria |
| Trunk (Σ) | Sciences | dy/dx — compression & law | From experiment to invariant; syntax distilled into symbol. | 6 → GWh/day | Maxwell, Mendel, Noether, NASA mission control |
| Branches (h(t)) | Games | d²y/dx² — curvature, collision, play | Dynamic feedback of agents under rules; experimentation in motion. | 8 → 100 GWh/day | Chess, evolution, economies, esports, clinical trials |
| Canopy (ΔS) | Metaphysics | ∫ y dx — accumulated ledger | Reappraisal of all previous layers; reflection on the rules themselves. | 9–10 → TWh/day | Tao Te Ching, Gödel, Nietzsche, quantum cosmology, recursive AI ethics |
You can embed this straight into canon as
“The Recursive Ladder of Logos” — where every science becomes a game, every game a metaphysic, every metaphysic a computation reborn.