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 Tau. The latter was introduced in a previous work and is computed using the GDP time series itself. Our analysis of eight centuries of yearly GDP data from three regions of Western Europe, corresponding to present day UK, France and Sweden is carried out in two steps. First, a Monte Carlo algorithm is used to fit the GDP data to a piecewise continuous function comprising a sequence of exponentials with different exponents. These arguably correspond to social and technological stages of societal organization. In a second step, GDP data are plotted vs. Tau and shown to display two logarithmic regimes, both decelerating, that are joined by a power-law cross-over period. We connect the end of the first regime and the beginning of the second with the dawn of the Industrial Revolution and the societal impact of new transport, communication and production technologies that became widely available after World War I. We conclude that wealth evolution in terms of Tau is a decelerating process with the hallmarks of record dynamics optimization.