Moreover, the works of della Francesca are of a piece with the passions and traditions of Sansepolcro. Its biggest festival involves men carrying banners attached to spears, like his rising Christ. So it's not just one flash of genius against a bland "dark ages." There's a lot going on, and not just in Sansepolcro. Piero della Francesco died in one of the most momentous years in modern history: 1492, the same year Lorenzo the Magnificent died in Florence, and a visionary explorer unexpectedly landed in the New World.
Years ago a very smart man I met on an airplane to California bragged that he and his colleagues at the Rand Corporation were looking into such profound questions as "Why is there a history of art?" It was a way of getting at the fact that artists represented things differently at different moments of history, or in different cultures at the same moments. Is that due to changes in our vision, or changes in our capacity and desire to portray our world, or what?
Whatever the answer to that one, it seems pretty clear that there have been "schools" of painting and sculpture, and that the artists therein more or less agreed with how the world should be portrayed. That warrior Christ has the sort of physical strength you can find in those strong men Michelangelo liberated from the marble in the Accademia in Florence, the ones you see as you walk down toward the David.
OK, we knew that. But look at della Francesca's Christ or at his Madonna, and you see something apprently totally outside the world-view of the time.
The same time Leonardo was doing things that neither art historians nor historians of science can fully explain. One of my favorite science fiction authors suggested that Leonardo had invented time travel, and brought back future inventions to his own world.
Well maybe Piero della Franesca was on those jaunts with Leonardo.
Just get yourself to Sansepulcro and immerse yourself...off the beaten path.