Order! Order!

It appears that the best efforts of the people of the United States have decided on two candidates that they don’t like; no pair of candidates in the history of modern polling have had such high unfavorables. The fascinating and disturbing political circus this year got me thinking a few weeks ago, “I wonder if any statesman is out there who wants to identify the world’s problems thoughtfully and then intelligently provide all the answers.” My search quickly uncovered World Order by Henry Kissinger. Seen as either the greatest Secretary of State of the last fifty years or a war criminal, Kissinger at least knows what he’s talking about, and his latest book shows great knowledge and wisdom. He covers North Korea, nukes, terrorism, communism, ISIL, and the internet, and, yes, he offers hopeful advice on how to deal with all of it.

The main problem, as Kissinger points out, is that the different peoples of the world don’t all have the same vision of world order that we do. The notion that the U.S. and Europe hold to is represented by the Treaty of Westphalia of 1648. (If you don’t pay attention during the first explanation in the book, you’ll be confused by the many subsequent references to “Westphalian Order.”) The Peace of Westphalia recognized the legitimacy and borders of the various German principalities and favored peace above subjugation and forced unity. For most of the book, Kissinger travels the globe and examines the views of all the major players on the topics of legitimacy, borders, peace, and unity, and as it turns out, other places don’t see things the same way at all.

Most of the analyses depend on history hat goes back much farther then even Westphalia. From the beginning of the Chinese Empire, the emperor saw himself as the loftiest human under Heaven. The Chinese didn’t much care about borders or other countries as long as anyone coming in to the court paid homage to the emperor as Lord of All Under Heaven. The Japanese believed the same thing about their emperor, but they said what the Chinese wanted to hear and got along fairly well for centuries. Twice the Chinese have been conquered, and each time they shrugged their collective shoulders and waited as the Mongols and Manchus discovered that they had to become Chinese in order to rule hundreds of millions of people confident in their cultural superiority. India on the other hand has welcomed diversity and incorporated many of the cultural aspects of their successive invaders. The Russians have centuries of experience expecting that they will one day pave the way to world peace but must suffer in order to earn the honor. Muslim governments typically wish to see the world united as one people worshiping Allah, but they have had many different policies on how to deal with others who don’t see things their way: some policies peaceful and some not so much. And the Americans? The Americans can’t figure out why everyone else can’t just agree to disagree.

As I read, I kept wondering what life in my old dysfunctional workplace would have been like had I looked at things China’s way or India’s or Japan’s. If there had been more professors like me, I could have waited like the Chinese as the parade of administrators slowly but surely became one of us. But as part of a minority, maybe I could have adopted the Indian policy and just thought, “OK, this madness is part of who we are now.” Almost certainly I should have acted like Japan, given the bosses what they wanted to hear, and then gone on to do what I was hired to do.

Hillary Clinton has contributed a small blurb of praise to the cover of World Order. Bernie Sanders has said that he is proud not to be a friend of Henry Kissinger and wouldn’t ever wish to seek his advice. These two disagree on the topic of Kissinger, as on so many things, but at least they’ve both heard of him and have an opinion, which is more than I believe of Trump.

The Probability of Aquinas

A short post today while I’m enjoying Ireland. Just before the trip, I read some of Thomas Aquinas’s views on the end times, and it struck me how often he used the word “probably.” All will probably know the hearts of everyone else, so that everyone can appreciate God’s judgment and mercy. God will probably judge everyone mentally in an instant rather than literally reading aloud from the books of judgment. (Considering the fact that the Last Judgment marks the beginning of Eternity, I don’t understand Aquinas’s concern that a verbal Judgment Day would last too long.) Christ will probably descend near Mount Olivet, since He ascended from there. I wish current Christian discourse on eschatology showed as much intellectual humility.

I Didn't Think It Possible

Having included a category on my Ten-Year Plan for eighteenth-century novels, naturally I made a place for Richardson’s Pamela, one of the biggest sellers of the time. But it grossly disappointed me. I supposed that it did me some good to have read the book that caused all the fuss. But its writing was clunky, its characters flat and unbelievable, and its plot absurd. For half the book, Pamela is relentlessly pursued by a sexual predator, yet maintains her virtue. Then the creep sees what a rare jewel he has found and repents his base treatment of her. The two marry, and he becomes the best husband possible. I’ve never heard of Stockholm Syndrome actually paying off in the real world.

This year, that eighteenth-century category took me to Henry Fielding’s Joseph Andrews. I had originally intended to reread Tom Jones but just decided to try out another of the author’s offerings. Not only is JA interesting and funny, it did something I didn’t think possible. I had seen Tom Jones fall well below Pamela’s virtuous mark, and I knew that Fielding wrote a parody of Richardson’s novel called Shamela. So I figured that Fielding somewhat shared my assessment of Richardson. But I didn’t realize that Joseph Andrews was Pamela’s brother and that his account followed his attempts to live up to his sister’s standard. I would have enjoyed Joseph Andrews without having read the earlier novel, but not as much. And so, just as Ewan McGregor and Renée Zellweger’s Down with Love made me glad I had suffered through the dreadful Pillow Talk, Joseph Andrews actually made me glad I had read Pamela.

Euclid’s Mysteries

Following a proof in Euclid feels a lot like watching Holmes or Poirot solve a murder. If the sum of the squares on AB and CD are equal to the value of the gold cufflinks, then the line from the library door at Gaveston House to the dock is greater than EF. And therefore Miss Emily Ross committed the crime with a regular pentagon inscribed in circle GHI. Like many a good mystery, each proof of Euclid’s puts all the facts before the reader, who, nevertheless, hasn’t the ability to see all the connections until the final reveal.

OK, I exaggerate. I’ve usually jumped on Euclid’s Orient Express of thought a bit before the very end. I love the moment, usually about three-fourths of the way through the proof, when I finally see the predestined conclusion coming. I still follow the clues through to the last deduction, though, and the Q.E.D. announcement never fails to overwhelm me.

And it is a deduction in the proper sense. Euclid unfolds a picture of spatial relationships every detail of which is absolutely certain given his very few postulates and the rules of logic. This makes Euclid more like Poirot than Holmes. For all of his famous talk about eliminating the impossible, Sherlock makes an abductive leap in just about every story that would make Agent Mulder proud.

The experience of enjoying Euclid’s trails of inevitable bread crumbs was especially interesting this year after I had just finished reading Kant’s Critique of Teleological Reason. I learned for instance that length of the side of a hexagon and that of a decagon inscribed in the same circle exhibit the Golden Ratio (what Euclid calls “extreme-and-mean ratio”), the greater segment being the side of the hexagon. The properties of the irrational phi are mind-bogglingly beautiful to begin with. But to think that inserting something as clear and comprehensible as a figure with six equal sides and a figure with ten equal sides inside a circle, itself formed by another wonderful and mysterious irrational, brings about the Golden Ratio makes one ponder if we’re seeing Proverbs 25:2 being demonstrated before our eyes. Did God conceal this beautiful network of mental constructs in order for Euclid, surely one of the glorious kings of human history, to discover it?

Boccaccio’s Generosity

It being year 10 of my ten-year reading plan, I find myself often experiencing a sense of accomplishment these days. In January I finished reading all of Plato and all the extant works of ancient Greek theater. In February I finished rereading all of Dickens’s novels. In April, I finished reading Orlando Furioso, the title that started my quest for a self-earned liberal education.

May brought two journeys to completion: rereading all the major works of Immanuel Kant, and reading (for the first time) all of Giovanni Boccaccio’s Decameron. Going over Kant again worked exactly the way I had hoped it would. The margin notes I took the first time through helped me actually understand what I was reading the second time. Kant makes five times more sense to me now than he did a decade ago. He would probably make at least twice as much sense if I read it all again in the next ten years, but I’ve decided to forego that experiment.

Boccaccio having arranged the one-hundred stories of the Decameron in ten days of ten stories each, and my reading plan being ten years long, I decided a decade ago to read one set of ten stories per year, so, according to the delicate rules of mathematics, I read the novellae of day 10 this year, that last day of Boccaccio’s collection centering on the theme of generosity. The plague refugees who tell each other these stories put in every effort to outdo each other on this last fling. The magnanimity of the heroes of their tales inflates past all human capability. They freely give up lands, treasures, thrones, dignity, wives, and lives. They have no Christian right to donate their wives, of course, and since the character who offers his life does so with no thought of any benefit that might result other than the display of willingness, his example doesn’t inspire me, either. But the other examples did, I suppose, what their authors (under which umbrella term I include the original producers, Boccaccio’s fictional narrators, and Boccaccio himself) intended; that is, they afforded the reader with examples of humility and sacrifice.

The greatest display of generosity in the Decameron, though, is the book itself. One-hundred stories: most of them interesting, some of them extremely good. With his tales of fools and princes, judges and thieves, wives and monks, Boccaccio lifts up a picture of humanity as a whole: the good and the bad, the high and the low, the selfish and the heroic come together to fill his pages. He gives all sorts and conditions the dignity of a reader’s attention and takes from no class of people the potential for either greatness or ridicule. And that equalizing treatment of humanity was one of the hallmarks of the Renaissance. The Encyclopedia Britannica goes so far as to say, “Without Boccaccio, the literary culmination of the Italian Renaissance would be historically incomprehensible.”

I’ve read that Boccaccio’s language did for Italian prose what Dante had done for Italian poetry. Consider this opening sentence from the randomly chosen story 7 on day 10:

When Fiammetta was come to the end of her story, and not a little praise had been accorded to the virile magnificence of King Charles, albeit one there was of the ladies, who, being a Ghibelline, joined not therein, Pampinea, having received the king's command, thus began.

The complexity far surpasses anything required for a language of the streets. Just take the words “being a Ghibelline.” It begins with a participle (itself a thing of wondrous beauty fast disappearing from our own vernacular) – a participle modifying “who.” That word, in turn begins a relative clause saying more about “one of the ladies.” That lovely group’s own subordinate clause starts a long parenthesis decorating the main action of Fiammetta yielding the floor to Pampinea. So at “being a Ghibelline,” we’re three whole levels below the surface.

Then there’s the whole influencing-Chaucer-and-Shakespeare thing. Yeah, Boccaccio gave us a lot.

The Fortituous End of Kant

In grad school I took a class that surveyed Renaissance music history. In one of the few actual seminars I ever took, we sat around one large table and discussed all the readings and music in question. One day as we went through some score by Josquin des Prez (I think it was Josquin), I made a remark about some pattern in the counterpoint that I thought was especially interesting and elegant. One of my classmates, however, felt very strongly that the composer should take no credit for the combination, that the pattern was the result of pure happenstance. “You can’t say that,” he urgently argued in my direction. “That’s just fortituous.” Not fortuitous, mind you: fortituous. He was so adamant about my being wrong that he pressed his point for another minute or so and repeated his unintentional neologism at least four more times. Fortituous! Fortituous! Fortituous! The word has stuck with me ever since as one of the fortituous benefits of an otherwise rather dull class.

Kant’s Critique of Teleological Reason is, if I understand him correctly (although I think there’s only about a 50% chance that I understand him at even 50% capacity), a book about whether elements of nature exist by design or fortituously. (Yes, the new beautiful new word comes in adverbial form as well.) The punch line of the book is that God can only be proven in human thinking by examining the moral law. But along the way to that point, Kant examines how to tell if a given thing in nature exists for some further end. Rivers bring us food, for instance. So are they there because of us? Are we the purpose of rivers? In Aristotelian terms, are we the final cause of rivers? In theological terms, did God create rivers for humankind’s benefit? Kant denies it by pointing out that nothing says any humans have to live by any given river. The river’s benefits are, to call on my old colleague’s linguistic turn once more, merely fortituous.

Kant’s other examples resonated a lot with other things I’ve been thinking about lately. He says that the mathematical structure known as a parabola has uses (describing the effect of gravity on a cannonball, for instance) that have nothing to do with its existence. We can have no possible justification, says Kant, in claiming that God made math and parabolas so that one day warriors would use their arcane properties to launch projectiles accurately. I’ve been studying calculus lately (and actually learning it this time!), and I had been thinking something along the very same lines. The way a derivative comes about is stunning. But derivatives weren’t created by God in order to describe the way water drains from a cone. (Or at least it would be presumptuous to say so.) In the same light, their way of torturing middle-aged, independent scholars whose multi-page calculations lead to something completely different from the answer in the back of the book is just a fortituous by-product; they don’t exist for the purpose of my self-educational pursuits.

Here’s another example from my recent real life. The ancient Greeks had several ways of locating a number between two other numbers in some mathematically meaningful or beautiful relationship. They called these middle numbers “means.” (Or I should say that translators indicate that the ancient Greeks would have called them “means” if those ancient Greeks had spoken modern English.) Calculating the average (adding the two original numbers and dividing by 2) is only one of the means they studied: the arithmetic mean. They also recognized what they called a harmonic mean. When a harmonic mean is interpolated between two other numbers, the differences between mean and extremes have the same ratio as the two original numbers. For example, 12 is the harmonic mean of 10 and 15. 10:12:15. The difference between 12 and 10 is 2; the difference between 12 and 15 is 3. So the differences show a 2:3 ratio, as do the two extremes, 10 and 15.

The crazy thing is, where numbers represent string lengths, these two patterns – the harmonic mean and the arithmetic mean – when applied to two numbers in a 2:3 ratio, produce major and minor chords, respectively. Now the Greeks had no interest in three-part harmony from two thousand years in the future. And the English composers of the late fourteenth century who popularized using thirds in harmonies had little chance of being experts in ancient mathematics (although not zero chance). In any case, it seems absurd to say that they started writing major and minor triads because of their knowledge of Greek means. Somehow it seems more reasonable to think that arithmetic and harmonic means came to the ken of ancient humanity so that one glorious day, western composers would begin to favor harmonies that display those relationships. But Kant reigns in my Platonic predestinarianism.

Just the other day, I learned that the periods of the orbits of Venus and Earth have a ratio very nearly 13 to 8, and that a regular tracing of the line between the two planets creates a picture of a five-petaled flower. So is that beautiful picture the reason for the relationship between the orbits? Kant would say it was presumptuous to believe so.

On the other hand, he says it would be presumptuous to believe it definitely wasn’t the reason, either.

I wonder how that student would pronounce “presumptuous”?