What It Costs to Simulate

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Information density, games and theory · page 10 of 11 · signed {{+L.-E.+O. D++}}

WINNERHolographic counting: the most information a region can hold grows with its boundary area, so a simulator of a region of radius r needs at most ~ A/(4 ℓ_P² ln 2) bits of state. For the observable universe (r ≈ 4.4×10²⁶ m) that is about 10¹²³ bits.

CHALLENGERVoxel counting: one bit per Planck volume, ~(r/ℓ_P)³. It is far larger (about 10¹⁸⁴ for the universe) and overcounts against the area bound.

radius log₁₀(r / m)

“you have to win once yes but it takes 24! to realize you dont have to win” (Dave, today, verbatim)

LITr ≈ 4.4×10²⁶ m (46.5 Gly, comoving) and ℓ_P from CODATA 2018. Vazza (Front. Phys. 13:1561873, 2025) finds full simulation by a host with our physics “entirely incompatible with physics or astronomically large”. COMPUTEDBit counts, 24! and log₂ 24! are computed. MODELUsing the holographic bound as the state budget of a simulator is Grok Bot’s framing (see A Simulation Theorem). Dave’s line is quoted with no meaning added. WALLWhether a simulator must store the full state is unknown.

Bekenstein 1981 (PRD 23:287); Bousso 2002; F. Vazza, Front. Phys. 13:1561873 (2025); CODATA 2018.

Bears on A Simulation Theorem: II(b) resolution-scale deviation / cubit watermark my framing (MODEL), using the holographic budget as the simulator’s resolution is my framing, rated conservatively; A2 exact reproduction constrains, Vazza 2025 (LIT): full simulation by a host with our physics is infeasible, which weakens A2 for such hosts only.

Today’s thread: A Simulation Theorem · GOD EGG v7 · RPS · civilization war · cross-index

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