tabula geometrica — "the geometric blank slate." Train neural networks only on raw observations — never a metric, an interval, or Einstein's equations — and test whether geometry emerges as the cheapest internal explanation. The live experiments are in curvature/; the conceptual on-ramp is a step-by-step dimensional ladder (1+1 → 2+1 → 3+1 → 4+1) toward the real question:
how gravity curves spacetime — and whether that curvature "is" an extra dimension.
Every load-bearing claim (numbers, formulas, dimension-dependent facts) is verified against the literature before it goes in, with sources cited in each doc.
| Doc | What's in it |
|---|---|
| 3plus1_vs_2plus1.md | Our world vs Flatland, concept by concept: coordinates, rotation (axis vs plane), light cones, the wave "tail," 1/r² → 1/r forces, why 2+1 gravity is hollow, knots, chirality, trapping. |
| dimensional_ladder.md | The 1+1 bottom rung; the scaling laws (one master table of features vs dimension); shapes & measures (line/square/cube/tesseract; length/area/volume/hypervolume); black-hole horizons across the ladder; extrapolation to 4+1 with new vocabulary; the bridge to gravity-as-curvature. |
| nn_and_spacetime.md | A side-exploration: what really connects neural networks (embeddings, training, curvature) to spacetime physics. The metric tensor as the shared object; hyperbolic/Lorentz-model embeddings; PINNs; depth-as-emergent-dimension (holography reappearing in ML); the honest category errors; and toy experiments worth building. Confidence-tagged and cited. |
| emergent_dimension.md | "Is the extra dimension real?" The holographic emergent dimension explained CS-first (mipmap → RG → AdS/CFT → entanglement → Hashimoto's trainable network), the honest "is it real" verdict, and the three-way contrast (holographic-emergent vs Kaluza–Klein vs GR-curvature) that frames both finales. Ties S=A/4 back to the black-hole chat. |
| discovering_curvature_with_nn.md | The ambitious one: can an NN discover that spacetime is curved — unsupervised, from adjacent observables, never told the law? Names the paradigm (SciNet bottleneck), the precedent (a net already discovered the Minkowski interval), the honest feasibility verdict (pure dream impossible; equivalence-principle variant buildable), a concrete 2+1 experiment, and the genuinely novel angle (let the minus sign emerge; make geometry-vs-force compete). |
| JOURNAL.md | 📓 The activity log — one dated entry per working session. |
| writeups/emergent_geometry.md | ⭐ The shareable note, now complete: five acts — interval → light cone → gravity well → why gravity geometrizes (0 vs ~10 bits/body) → the Kaluza ending (charge migrates into an internal coordinate, r = 0.9998). With methods, failed-probe corrections, and honest limits. Start here. |
| writeups/curvature_field_guide.md | 🧰 The workshop version — every phase A→E + the generalist arc (G/H/I/J) + all side quests: setups, mechanisms, numbers, corrections, recurring patterns, and the explicit list of threads never pulled. The document to think and argue with. |
| writeups/legibility_law.md | 🔑 The crystallized result — the project's most novel finding as a standalone, three-part claim: a learned per-object code is legible when it's inferred, not stored; generic evolution re-scrambles it; invariant-preserving structure restores it. Backed by three controlled experiments; the through-line that explains the whole project. |
| curvature/ | 🧠 The main thread (the whole repo now): can a network invent spacetime geometry from raw observations? Phases A → E all passed + the Kaluza move (charge → internal coordinate, r = 0.9998) + the Gaussian curvature read out coordinate-free (corr 0.99). Phase G — one generalist across all world families: its internal world-summary space clusters into a physics taxonomy (ARI 0.82) with electromagnetism as its own region (EM-kinship z=27). Phase H — which particle labels become hidden "lanes": two-charge knee at exactly 2; Wong color charge marks the boundary (static labels geometrize, the dynamic rotation doesn't). Phase I — the legibility law: a per-object code is legible iff it's amortized (inferred by a shared encoder), not stored as free parameters. |
Black-hole LIGO projects moved out (2026-06-13):
echoes/(GW-echo search),ringdown_spectroscopy/(no-hair test via SBI), andprimordial_blackhole_search/(subsolar-mass merger search) now live in../BlackHole/. This repo is the neural-network / curvature work only.
- ✅ 3+1 vs 2+1 concept map
- ✅ 1+1 rung + scaling laws + 4+1 extrapolation (incl. shapes, measures, horizons)
- ⬜ Gravity is curvature — mass → Ricci curvature → geodesics that look like "falling"; intrinsic vs extrinsic curvature (Theorema Egregium)
- ⬜ The finale — "is curvature another dimension?" The intrinsic answer (no), then the genuine exception: Kaluza–Klein, where adding a real 5th dimension produces electromagnetism. Saved as the payoff.
Two recurring conventions:
n= space dimensions;D = n + 1= total spacetime dimensions.- Verdict tags when comparing worlds: ✅ clean parity (just fewer/more numbers) ·
⚠️ degenerate / vanishes · 🔀 qualitatively different.
Each doc ends with open threads — pick one and we extend it. The docs are living documents.