Links between entropy, complexity, and the technological singularity

Abstract

• In a closed system complexity increases at first and then decreases as equilibrium is approached. • Complexity behaves like the time derivative of entropy. • We are presently at the maximum of complexity, which will soon begin decreasing. • The conclusions of my 20-year old study remain valid; we should expect the next two “milestones” at around 2033 and 2078. 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.