Links between Entropy, Complexity, and the Technological Singularity

Abstract: Entropy always increases monotonically in a closed system but complexity increases at first and then decreases as equilibrium is approached. Commonsense information-related definitions for entropy and complexity demonstrate that complexity behaves like the time derivative of entropy, which is proposed here as a new definition for complexity. A 20-year-old study had attempted to quantify complexity (in arbitrary units) for the entire Universe in terms of 28 milestones, breaks in historical perspective, and had concluded that complexity will soon begin decreasing. That conclusion is now corroborated by other researchers. In addition, the exponential runaway technology trend advocated by supporters of the singularity hypothesis, which was in part based on the trend of the very 28 milestones mentioned above, would have anticipated five new such milestones by now, but none have been observed. The conclusions of the 20-year-old study remain valid: we are at the maximum of complexity and we should expect the next two milestones at around 2033 and 2078.