Human wealth evolution is an accelerating expansion underpinned by a decelerating optimization process

Optimization and expansion are two modes of staged evolution of complex systems where macroscopic observables change at a decreasing, respectively increasing, rate. The number of microscopic variables and their interactions are fixed in the first case but change dynamically in the second. A prime example of evolutionary expansion, Gross Domestic Product (GDP) time series gauge economic activities in changing societal structures, and the accelerating trend of their growth probably reflects a manyfold increase of the human interactions that drive change. Naively, one could think of cultural evolution as the result of an optimization process, and then expect the associated GDP growth to have a decelerating trend. We show how optimization and expansion can coexist by replacing ‘wall clock time’ t as independent variable with a measure of human interactions intensity τ. The latter was introduced in a previous work and is computed using the GDP time series itself.