Post-apocalyptic fiction is full of scenarios where survivors sift through the bones and dust to uncover high-tech treasures they don't really understand. In "Beneath the Planet of the Apes," it was an atom bomb worshiped as a god. In "The Prince of Nothing" trilogy it was a laser weapon regarded as a magical spear.
Recently I posted about the union of science and theology in Dante's 14th century classic "Inferno" (you can read it here) and it got me thinking: Is Western medieval mathematics analogous to the dusted-off super technology in our bleaker works of sci-fi?
In "The Geometry of Paradise" Mark A. Peterson points out that Dante could easily have excelled as a mathematician had he been born into a time when geometry was more fashionable. Instead Dante lived in an age of languishing mathematics between the Hellenistic period and the 17th century.
"Medieval cultures were in the peculiar condition of being un-mathematical cultures in possession of sophisticated mathematics. They possessed it in the sense of having the books, studying them and translating them, and even doing some mathematics, but they had no clear indication where this rich subject had come from or what it would be good for. They did not know, in our terms at least, what it was." -- Peterson
I can't help but read that and imagine some vagabond in a "Mad Max" or "Dying Earth" scenario picking up an iPad-like device with a puzzled look on his or her face. What is this? "Oh, you can use it to crack nuts." Or maybe the person actually powers it up enough to marvel at its informational contents, but fails to realize they could look up how to prevent cholera on it.
With mathematics, residents of the Middle Ages had the language of God at their fingertips but couldn't use it to their advantage. They'd inherited the craft, but not the causes that provoked its development.* Peterson really drives home the point writing:
The Romans believed, and therefore later civilizations also believed, that the origin of Greek mathematics was a love of abstraction. If the medieval period attempted to see whether mathematics could flourish without earthly applications, the answer seems to be a resounding no.
Certain geometrical construction practices continued during this stretch with little or no innovation. Methods and notations changed. Algebra advanced in commercial applications while geometry, according to Peterson's words, became all but a dead subject.
So here comes Dante, a man fascinated by just about everything -- including mathematics. He applied the science's glittering abstractions to theology, in the same way a post-apocalyptic civilization might, say, create a cycle of myths about a crashed airplane or create a beautiful sculpture out of old computer hard drives.
It's math as a forgotten sorcery, math as the lost craft of the ancients. The fall of Mycenaean Greece as apocalypse. For my money, it's pretty fascinating food for thought.
* Peterson singles out Lucio Russo's "The Forgotten Revolution" as fine additional reading on the issue.