Aphorisms that "Rising tides raise all boats" or that material advances of the rich eventually "Trickle Down" to the poor are really maxims regarding the nature of stochastic processes that underlay the income/wellbeing paths of groups of individuals. This paper looks at the implications for the empirical analysis of wellbeing of conventional assumptions regarding such processes which are employed by both micro and macro economists in modeling economic behavior. The implications of attributing different processes to different groups in society following the club convergence literature are also discussed. Various forms of poverty, inequality, polarization and income mobility structures are considered and much of the conventional wisdom afforded us by such aphorisms is questioned. To exemplify these ideas the results are applied to the distribution of GDP per capita in the continent of Africa.