And now for something completely different.
I originally planned to title this blog The Monoenergetic Heresy. I’d learned about the heresy from the online lectures on the Early Middle Ages by my friend Paul Freedman. Then I decided I wanted something more descriptive of the math focus of the blog.
Even so, the monoenergetic heresy has led me down a rabbit hole or two over the years, so I decided it was about time I posted about my adventures.
First off, I want to put in a plug for the lectures. I may have started watching it because of our friendship, but I was immediately hooked. Here’s a sample:
Certainly, the Renaissance artists regarded everything that came before them as the Dark Ages. And it is they who call medieval architecture “Gothic”, by which they don’t mean a complimentary term…. [F]or Vasari and people like this—Italian Renaissance writers—all this was just junk. It was just junk of the past. It’s just the Dark Ages. The sun rose in Florence sometime after Dante, is what most people continue to believe.
And as a medievalist I long ago gave up fighting this and embraced it. The Dark Ages are cool. I know Halloween is over but, nevertheless, we all know that the Middle Ages is far more fun than the Renaissance. Who wants proportion and logic and severe classical lines, when you can have gargoyles and weird stuff? I’m preaching to the converted, right? You’re in this class….
So I’m trying to argue that this period is more than just a long nap for people just waiting for something like the Italian Renaissance. There’s a book … called The Long Morning of the Early Middle Ages … By “long morning” they don’t mean brunch.
That’s what I would have called it, The Long Brunch of the Early Middle Ages.
The monoenergetic heresy belongs to the branch of theology called Christology, all about the nature of Christ. The Byzantine Emperor Heraclius (c.575–641) tried to foist this doctrine on feuding theologians as a compromise between monophysitism and dyophysitism. (Didn’t work; that’s why it’s called a heresy.) The mono/dyo-physitism controversy dates back to the 400s CE. Monophysitism teaches that Christ has just one φύσις (physis), nature; dyophysitism opts for two. Monoenergism proposes that Christ may have two natures, but he has only one energy (ενέργεια, energeia).
With my preoccupations, the moment I heard the word monoenergetic I sat up straight and said, “Wait a minute, ‘energy’ didn’t enter the physics lexicon until the 19th century! How come they were talking about it over a thousand years earlier?”
Of course you know the answer: Aristotle. More on that in Part 2.
Recently I ran across another example of crossover appeal from theology, this time to mathematical logic. Here’s the very first exercise in Wilfred Hodges’ A Shorter Model Theory:
According to Thomas Aquinas, God is a structure G with three elements ‘pater‘, ‘filius‘, and ‘spiritus sanctus‘, in a signature consisting of one asymmetric binary relation (‘relatio opposita‘) R, read as ‘relatio originis‘. Aquinas asserts also that the three elements can be uniquely identified in terms of RG. Deduce—as Aquinas did—that if the pairs (pater, filius) and (pater, spiritus sanctus) lie in RG, then exactly one of the pairs (filius, spiritus sanctus) and (spiritus sanctus, filius) lies in RG.
Next stop: Aristotelian philosophy!