Algorithmic Randomness: The Intrinsic Barrier to Causal AI

The transition from correlation to causation remains a fundamental barrier for artificial intelligence. Here we identify algorithmic randomness—the intrinsic variability of causal inference—as an unavoidable mathematical property rather than mere implementation noise. Analyzing 102 real-world causal relationships across medicine, physics, economics and engineering (201881 samples), we demonstrate its universal presence (102/102 pairs), statistical definitiveness (p < 10⁻¹⁸), and precise power-law scaling with sample size (standard deviation σₙ ∝ n⁻¹.⁴⁰⁰, R² = 0.894). This randomness quantifies system determinism, spanning four orders of magnitude from 10⁻⁷ to 10⁻³. Our framework for the first time transforms algorithmic variability from an overlooked artifact into a measurable scientific phenomenon, enabling uncertainty-aware causal AI for trustworthy decision-making.