That's So Second Millennium

As the emcee noted at a concert here in Lander, a Musical History Tour, the Renaissance--the period when Europe revived its intellectual life by re-evaluating the writings of the Hellenistic past--ends around the year 1600, give or take. By that time, the focus had shifted toward going beyond the ancients instead of merely revisiting their achievements. This shift in focus happened on a different schedule in different fields, to be certain. Music may have been well ahead of the ancients already in the high medieval period. The Scholastics, and indeed their Arabian predecessors, while firmly rooted in Aristotle and the Neoplatonists, were already progressing beyond those foundations in the thirteenth century. On the other hand, painting and sculpture may not have outstripped the Greeks and Romans until the nineteenth century. In any case, the seventeenth century would be the one in which Greek mathematics and Aristotelian natural philosophy gave way precipitously to new approaches. Algebra, lurking in the bac