This paper develops a model describing how false paradigms may persist, hindering scientific progress. There are two paradigms, one describing reality better than the other. Tenured scientists display homophily: they favor tenure candidates belonging to their paradigm. As in statistics, power is the probability (absent any bias) of denying tenure to scientists adhering to the false paradigm. The model shows that because of homophily, when power is low, the false paradigm may prevail. Only an increase in power, coming from new data or empirical methods, can ignite convergence toward the true paradigm. Such an increase is the source of many scientific revolutions in history.