Links between Entropy, Complexity, and the Technological Singularity

TL;DR

This paper explores the relationship between entropy and complexity, proposing a new definition for complexity as the derivative of entropy, and discusses implications for the technological singularity and historical complexity milestones.

Contribution

It introduces a novel definition of complexity as the time derivative of entropy and revisits a 20-year-old study on universal complexity milestones, confirming the universe is at maximum complexity.

Findings

Complexity peaks and then decreases as equilibrium is approached.

No new milestones predicted by the exponential trend have been observed.

Maximum complexity is reached around the present, with future milestones expected in 2033 and 2078.

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.