John Smart's Transcension Hypothesis quantified: at what synchronisation overhead does a compact ergosphere computer outperform an equivalent-mass Dyson swarm?
This tool quantifies the core claim of John Smart's Transcension Hypothesis: that past a critical threshold, inward compression of computation (near a black hole) becomes more efficient than outward expansion (a Dyson swarm). It compares two architectures of equal total mass, using the Lloyd limit as the shared baseline computation rate.
Compact system: all compute mass concentrated near the ISCO of an IMBH. Gravitational time dilation at radius r gives a subjective clock speedup of γ = 1/√(1 − r_s/r). Every unit of external coordinate time, the compact system completes γ × Lloyd(M) subjective operations. Communication latency is r/c (nanoseconds — negligible).
Distributed system: same total mass spread over a Dyson swarm of radius R_D. Total Lloyd limit is equal. But a fraction f_sync of all operations require global coordination — synchronised steps that can only proceed at the rate set by the round-trip light travel time 2R_D/c. Effective operations per coordinate second = Lloyd × (1 − f_sync) + f_sync × Lloyd × (r_compact/R_D).
Advantage ratio: (compact subjective ops) / (distributed effective ops) = γ / [1 − f_sync × (1 − r_compact/R_D)]. When advantage > 1, compact wins.
Crossover condition: compact wins when γ > 1 − f_sync × (1 − r_compact/R_D). For R_D >> r_compact this simplifies to: compact wins when f_sync > 1 − 1/γ. Equivalently, the minimum synchronisation fraction for compact to win is f_sync_min = 1 − 1/γ. At γ = 1.5, any f_sync > 33% makes compact better. At γ = 10, any f_sync > 90% tips to compact.
The Lloyd limit is 🔬 established physics (Lloyd 2000). The time dilation formula is 🔬 GR (Schwarzschild metric). The civilisational architecture comparison is ✦ engineering fiction — it assumes the compute hardware can actually function near the horizon (tidal forces, Hawking radiation flux, and accretion plasma are lethal at all realistic scales). The synchronisation fraction f_sync is a free parameter with no observational grounding; the result is only as meaningful as your estimate of it.
The compact system's time dilation advantage is computed in detail in the Time Dilation Comparator. The Lloyd limit is the output of the Bekenstein-Landauer Explorer Panel 2. The STEM compression trajectory toward this endpoint is in the STEM Compression Explorer.
v1.0 — 2026-06-02 · Tool content may be revised as scientific knowledge evolves.