As European society in the eleventh through the thirteenth centuries increased in population and expanded economically, it became increasingly diversified; more competitive in social, political, and economic contexts; and more specialized and professionalized in areas of administration, law, diplomacy, and teaching. In natural philosophy, the efforts in the twelfth and thirteenth centuries to bring order and even number into understanding the natural world are striking and broadly consistent with the increasing specialization and professionalization of medieval society. In the second half of the thirteenth century in particular, the impulse given to more technical endeavors contributed to the reestablishment of mathematical optics, statics, and kinematics; to the renewal of interest in mathematical astronomy; and to the application of such technical accomplishments to the solution of problems in medicine, particularly the explanation of the effects of compound medicines.

Scholars have also pointed to internal developments in philosophy and theology that...