When Galileo wanted to study the heavens through his telescope, he got money from those legendary patrons of the Renaissance, the Medici. To win their favor, when he discovered the moons of Jupiter, he named them the Medicean Stars. Other scientists and inventors offered flashy gifts, such as Cornelis Drebbel’s perpetuum mobile (a sort of astronomical clock) given to King James, who made Drebbel court engineer in return. The other way to do research in those days was to be independently wealthy:...