Superintelligence Simulation — Recursive Self-Improvement

Recursive Self-Improvement

Self-improvement gain k 0.35

Returns exponent p 1.15

Safety tax (alignment effort) 20%

Capability Growth

t = 0log₂ C

Capability C

1.00

Doubling time

—

Alignment risk

Safety margin

100%

How it works

Model an AI system whose capability C can improve its own future capability — the "recursive self-improvement" loop behind the intelligence-explosion hypothesis (I. J. Good, 1965). A fraction of the system's effort is spent on raw capability growth, the rest on alignment/safety work:

dC/dt = k · C^p · (1 − tax)
dRisk/dt = γ · (dC/dt) · (1 − tax),  Risk ∈ [0,1]
Safety margin = 1 − Risk

Returns exponent p — the shape of the feedback loop. p < 1: diminishing returns, capability plateaus (a "slow takeoff" that runs out of low-hanging fruit). p = 1: exponential growth, a fixed doubling time. p > 1: superlinear returns — growth accelerates as C grows, producing a finite-time blow-up ("foom" / intelligence explosion) unless slowed by the safety tax.
Self-improvement gain k — how efficiently the system converts effort into capability gains per unit time.
Safety tax — the fraction of total effort diverted from capability growth to alignment work. It directly slows dC/dt and also throttles how fast alignment risk accumulates, trading growth speed for safety margin.
The lattice in the 3D view is the system's own architecture: each new capability doubling grows the network with more nodes and connections, and the core sphere's colour tracks alignment risk (green → amber → red).

This is a simplified toy ODE, not a forecast — real capability growth depends on compute, data, algorithms and many unmodelled bottlenecks. It is meant to make the qualitative shape of the "takeoff speed" debate (gradual vs. explosive) something you can feel by turning a dial.

Regime: —

Architecture nodes (grows with C) Core = alignment risk

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