Legend: Soil (θ′) → Roots (θ) → Trunk (Σ) → Branches (h(t)) → Canopy (ΔS). Calculus: \((x,y)\) → \(y(x)\) → \(\frac{dy}{dx}\) → \(\frac{d^{2}y}{dx^{2}}\) → \(\int y\,dx\). Energy/Ops scale: 2 × 10ⁿ.
| Ontology (Tree) | Canon Domain | Calculus / Epistemology | Description | Energy / Ops (2 × 10ⁿ) | Exemplars |
|---|---|---|---|---|---|
| Soil (θ′) | Computation | \((x,y)\) — raw variance | Logical substrate; entropy shaped by rules. Bits, qubits, spikes; automata as proto-life. | 0–1 → kWh/day | Boolean algebra, Game of Life, λ-calculus, spiking neurons |
| Roots (θ) | Engineering | \(y(x)\) — encoding & conversion | Design channels energy into form. Circuits, bridges, enzymes; constraints become craft. | 3 → MWh/day | Silicon fabs, GPU farms, turbines, batteries, mitochondria |
| Trunk (Σ) | Sciences | \(\frac{dy}{dx}\) — compression & law | Experiments distill invariants. Symbols compress dynamics into portable rules. | 6 → GWh/day | Maxwell–Noether, Mendel, thermodynamics, CDC/WHO surveillance |
| Branches (h(t)) | Games | \(\frac{d^{2}y}{dx^{2}}\) — curvature & play | Agents collide under rules; feedback over time reveals regimes and meta-strategies. | 8 → 100 GWh/day | Chess/Go, market sims, esports, evolution, clinical trials |
| Canopy (ΔS) | Metaphysics | \(\int y\,dx\) — accumulated ledger | Reappraisal of rules and observers; the system reflecting on its own game. | 9–10 → TWh/day | Gödel, Tao Te Ching, Nietzsche, quantum cosmology, recursive AI ethics |
Notes. Each rung feeds and constrains the next: computation → engineering → sciences → games → metaphysics → back to computation (the recursive ledger).