Tuesday, June 30, 2015

Consuming Aquinas

Let me say once again before I start that I’m not protesting anything, so don’t read too much into the word “Protestant.” I’m only using “Catholic” and “Protestant” here to indicate churches of today designated by those terms and tenets of doctrine typically found today in those respective churches.

I’ve said a time or two in earlier posts that little of Thomas Aquinas’s work sounds specifically Catholic to me. But the treatise titled “Before the Resurrection” gets into things that most Protestants would be uncomfortable with: Purgatory and prayers to saints, for example. Protestantism isn’t truly all that opposed to these doctrines. Protestants believe in a process of purging for Christians after death; it’s in I Corinthians 3:12-13. And C. S. Lewis made prayers to saints very palatable when he pointed out simply that asking Christians in Heaven to pray for us isn’t that different from asking the Christians who are living on earth. On the other hand, I don’t know any Protestant who would follow Aquinas’s lead by praying for the elect in Purgatory.

In any case, this section hasn’t helped strengthen and build my own beliefs as much as it has merely clarified the beliefs of fellow Christians. He certainly hasn’t concinced me of an ongoing Purgatory running in time parallel to ours. I’m not sure he’s trying to convince anyone to change his mind on these things, though. It may just be the way it looks to a non-Roman, broad-minded as I may be, but Aquinas here seems far from trying to prove anything and is instead simply laying out the order of a scheme. And the scheme, being a medieval scheme, is orderly indeed. There are two categories of sin: original sin and actual committed sin. Each can either plague a given person or not. Therefore, a departed soul can be in one of four states, and there’s a place for each of them: Hell is for those with both original sin and actual, Limbo for those with original sin only (i.e. unbaptized babies), Purgatory for actual only (the laborers in Purgatory having accepted Christ, they are free from the bondage of orignal sin), and Heaven for the Blessed who are completely cleansed of both. Well, OK, the neat, symmetrical scheme is spoiled by one last place for the dead: the Limbo of the Fathers held those destined for glory who died before the Resurrection of Christ.

Aquinas’s theory of end times also especially intrigued me. As a man of his era, he says nothing about various times at which the Rapture might occur and doesn’t mention the word “Millennium,” two issues that distinguish prominent eschatological views of today. He does refer to Antichrist and the persecution (or Tribulation), but only in passing. Of more urgency to Aquinas are the signs preceding the Day of Judgment and the nature of the fire that will consume the world (“the Final Conflagration”). Will the fire be an earthly fire? (Yes.) Will it cleanse all the elements? (Yes.) WIll it cleanse the heavenly bodies? (No.) In fact, the question of the fire takes up nine articles, far more than any others in this section, so we could say Thomas is in his own way consumed by the consuming fire.

All of “Before the Resurrection” was interesting to me, especially the parts trying to fit in Biblical prophecy with the Aristotelian theory of physics, but the most helpful for me were passages on prayer. On the surface, Aquinas talks about puzzles involving prayers by saints in Heaven, but most of the enigmas apply to prayers by Christians on Earth, as well. Why does God use prayer if He can simply do what He wills? How do predestination and prayer work together? Or in other words, can prayer change God’s mind? Aquinas cuts through the Gordian knot by showing these to be false dichotomies. God does do what He wants, and what He wants is to achieve his purposes through the means of his people’s prayers.

Friday, June 26, 2015

Increase Your Word Power with Patrick O’Brian – 2015

I always get a good response to Patrick O’Brian vocabulary quizzes. So to mark my completion of the last finished book in the series, I offer this matching quiz on words and phrases from Blue at the Mizzen. Some terms are nautical, some medical. Some pertain to flora and fauna, and some are just interesting and not quite common general words. As usual, try not to scroll down too far until you’re ready to check your answers. Good luck!

1. anhinga
2. bateleur
3. carboy
4. celerity
5. churr
6. distraint
7. drogue
8. euphroe
9. fid
10. fritillary
11. futtock
12. glabrous
13. gravid
14. kedge
15. languid
16. lobscouse
17. maroon
18. megrims
19. pawl
20. pintle
21. sanguine
22. scarper
23. skua
24. taffrail
25. tittivate
26. wigeon

a. a Eurasian plant of the lily family
b. seizure of property
c. to run away
d. smooth, free from hair
e. a curved piece of timber forming part of a ship’s frame
f. a thick peg
g. a brown and gray duck
h. a medium-sized eagle
i. to make a low trilling sound
j. slow and relaxed
k. optimistic
l. a stew of meat, vegetables, and hardtack
m. ornamentation around a ship’s stern
n. a curved bar that engages with a gear’s cogs so that it can turn only one way
o. a firework
p. depression, low spirits
q. a globular bottle with a narrow neck
r. a pin supporting the rudder of a ship
s. a fish-eating bird related to the cormorant
t. a predatory bird related to the gull
u. to move a ship by hauling in the hawser attached to a dropped anchor
v. a conical device towed behind a ship to reduce speed
w. speed
x. pregnant
y. to make small enhancing alterations
z. a long wooden slat that holds up an awning




1-s, 2-h, 3-q, 4-w, 5-i, 6-b, 7-v, 8-z, 9-f, 10-a, 11-e, 12-d, 13-x, 14-u, 15-j, 16-l, 17-o, 18-p, 19-n, 20-r, 21-k, 22-c, 23-t, 24-m, 25-y, 26-g

Friday, June 19, 2015

Trying to Summarize Euclid

It is impossible to summarize Euclid. You could simply list the propositions (i.e. theorems) that he goes through, but doing that wouldn’t convey the actual point of the book, which is the rational proof of the propositions. But I have to try something. In reading book XII of the Elements this year, I was most moved by the four-page proof of proposition 10. To explain what impressed me about it, though, I have to try to get into the details, and I don’t want to just reproduce the whole proof. So I’m going to try the impossible and summarize the proof. If you really want to follow it, you can find it online easily enough (although I hope you have better luck with your Java than I did just now).

By this point in the work, Euclid has proven that a polygonal pyramid has a volume equal to 1/3 that of the prism set up on the same base. Imagine any polygon you like: a square, a pentagon, or some crazy eleven-sided lopsided star-shaped thing. Then imagine each of the sides of your polygon extending straight up like so many walls and put a ceiling on your weirdly-shaped room. There’s your polygonal prism. Now go back to the original polygon – in other words, the floor of your hypothetical room – and imagine just one spot on the ceiling. Run lines from each corner up to that one point, and you have your polygonal pyramid. Euclid can show you that the volume of that pyramid is exactly 1/3 the volume of the whole prism. Basically, each of these shapes can be divided up into smaller shapes with triangles for sides, and geometry has a whole lot of useful things to say about triangles. So the relationship between the pyramid and the prism is pretty easy to demonstrate.

But in proposition 10, Euclid’s task is to show that a cone has a volume 1/3 of that of the cylinder built on the same circle and carried to the same height. No triangles here. Just circles and curved walls. I think Newton could have proven this proposition using his calculus, but Euclid didn’t have the mathematics of limits and infinitesimals. So what does he do? He uses a reductio ad absurdum: suppose the proposition is not true, and then see what contradiction you run into.

First, suppose that the cone’s volume is more than 1/3 the volume of the cylinder. Then inscribe a polygon in the circular base and imagine the pyramid starting at that base and extending up to the point of the cone. Now you have a pyramid tucked snugly inside your cone. Remember, the cone is larger than 1/3 of the cylinder in this supposition, so now increase the number of sides on your inscribed polygon, thereby increasing the size of the pyramid above it, until the pyramid is also larger than 1/3 of the cylinder. Well, that pyramid has a volume 1/3 the size of the prism on that same base. And if the pyramid is greater than 1/3 of the cylinder, the whole prism must be greater than the size of the whole cylinder. But its base is inscribed inside the circle, so the prism is actually smaller than the cylinder. And you’ve reached your contradiction: the prism can’t be both smaller than and larger than the cylinder, so the supposition must be incorrect.

So Euclid has proven that the cone is not greater than a third of the cylinder. Now all he has to do is turn the whole process around backwards to prove that the cone isn’t less than a third of the cylinder. And if its volume isn’t either greater than a third of the cylinder or less than a third of the cylinder, it must be exactly equal to a third of the cylinder.

I think the proof of proposition 10 is the longest proof of the whole book. It’s wonderful to see how brilliant Euclid is – how much he can prove with a few suppositions, a good grasp of logic, and a lot of creative imagination – even in the short, simple proofs. So this long proof was simply astonishing to me. If I, in turn, was unable to astonish you with my poor summary, go read it for yourself. Of course you have make it through eleven books plus nine more propositions in order to understand proposition 10 of book XII. So start reading now!

Monday, June 15, 2015

I’ve Changed My Mind

Blogging about reading means, among other things, coming up with something to say about a book while I’m in the middle of it. And sometimes I decide by the end of the book that what I said in the middle wasn’t exactly right. And that’s just what happened with The Romance of the Rose.

In an earlier post, I said that I thought second author Jean de Meun disapproved of the lover’s pursuit of the rose. But in the end, the lover gets his way, and I think Jean does, too. But then why does Jean bring in Reason with a long sermon against getting swept away by passion? And why does he make Friend offer advice so wanton that even the young man in love thinks he’s gone too far?

The key for me lay in the characters False Seeming and Nature. False Seeming (or Hypocrisy) defends himself to the God of Love (i.e. Cupid), who reluctantly agrees to ally with him. And in this apologia, he concentrates on the advantages religious hypocrites have. In fact, sometimes it sounds like False Seeming works with no one who isn’t a monk, nun, or priest. And the hypocrisy he works in these people all goes to hide the sexual activities of people who have taken vows of celibacy. Nature’s long (all the monologues in Jean’s part are long) speech basically says that God gave sex to Nature as her way of perpetuating the species, so where would the human race be if everyone took the vow of celibacy?

Now, remembering that Jean, in order to have the knowledge of classical works that he does, must have been trained in a monastery or cathedral school, I saw the pieces fall into place. He takes (or is ready to take, or has contemplated taking) the vow of celibacy, and then he reads Guillaume de Lorris’s aborted poem, its lovely verses singing the beauty of the passion of love. And then he experiences a debate. Perhaps he actually argues with his superior, or perhaps the conflict of ideas is all in his mind. One way or another, like my hero Mortimer Adler, he came to see the authors he had studied facing off against each other in a Great Conversation. And in the grand debate he witnesses, it soon becomes clear that the answer can’t be as simple as yes or no. The arguments on both sides are too good. So Jean must find a way to reconcile the rationale for virginity that he receives from the Church and from Reason, with Nature’s lesson that sex is God’s good gift to the world. On the negative side, he has to find the golden mean between the excess of Friend’s promiscuity and the defect of Hypocrisy’s call for total abstinence from everyone. The protagonist may land a little on the excessive side in my view, but at least he gives us noncelibates a model of enjoying a rose as a blessing of God.

Thursday, June 11, 2015

They’ve Killed Pippin!

I just finished Patrick O’Brian’s The Hundred Days, the nineteenth book in the only series of books Ron Swanson will read. Over nineteen volumes, stories change, the heroes now in one of the Seven Seas, now in another. But some things you can count on. Jack Aubrey and Stephen Maturin, of course, are always there. Their music is always there. Jack may get assigned to different ships now and then, but Surprise always has a way of coming back to him. Yep, no matter where fate, stock prices, Napoleon, and the Admiralty take the captain and his friend, you know anytime you pick up a Master and Commander book you’re going to encounter some familiar elements.

But in book 19, O’Brian suddenly kills off one of Jack’s loyal crewmembers, a favorite minor character who’s been there from the very beginning. I don’t want to give too much away, but the actor who played him in the movie also played a hobbit in The Lord of the Rings. What?! How can you kill Pippin?!
Well, the novel does deal with the end of the Napoleonic wars. The title refers to Napoleon’s brief escape before his final defeat at Waterloo. So once the historical plot motivator ran its course, the series had to start moving toward its inevitable end, and I suppose that means some characters have to die. At least the hobbit dies in action before the reader’s eyes, though; another prominent secondary character dies in a second-hand report. I guess that’s the old-fashioned Greek way, but still it’s not satisfying. I’m reading the twentieth installment (the last complete book in the series) next week, so I should probably prepare for more sudden deaths. Oh! I hope Killick isn’t in for a violent end!

Tuesday, June 9, 2015


As I began to read The Romance of the Rose with its poetic, allegorical depiction of a young heart pierced by Cupid’s arrow, I often imagined myself a thirteenth-century scholar discovering the book. I would have to have lived in a monastery to be able to read, but my training would have made me much more able to read Latin than French, even if French were my first spoken language. The books I would have read in Latin would mostly concern the Christian faith: the Vulgate Bible, the prayers and texts of the mass and offices, devotionals, theological works, and so on. I would also have read Latin treatises on the mathematical arts; perhaps I would have learned music from Guido of Arezzo. And I might have read some of the orations of Cicero or some other classical authors.

But then I come across a poem in French – the language of cooking and cleaning, the language I argued with my brother in while we were growing up – and this French poem speaks of a passion that consumes the thoughts, overthrows reason, and brings both the best and the worst possible emotions. What do I make of it? I might be tempted to forsake my vows. I might scoff at it as so much nonsense. But either way, I’m sure I would be fascinated.

Then the real me realized that my imagined scenario was exactly that of Jean de Meun. Original poet Guillaume de Lorris never finished his romance, so Jean undertook to complete it about forty years after it was begun. And Jean was clearly educated in Latin classics. (See the previous post.) So then I thought about a reader from the next century coming across the dual-authored work and what he might have made of it. Guillaume’s part would have led him to Jean, and Jean’s part might have sent him back to Boethius’ Consolation of Philosophy or to Ovid or Homer.

Or maybe I’m Shakespeare reading the work three hundred years later. I come across these lines from Reason:
Love is hostile peace and loving hatred, disloyal loyalty and loyal disloyalty; it is confident fear and desperate hope, demented reason and reasonable madness. . . . It is a most healthful sickness and a most sickly health.
I might then decide to write a play (based on yet other sources) in which I give the male lead these lines about love:
Why then, O brawling love! O loving hate!
O any thing, of nothing first create!
O heavy lightness, serious vanity,
Misshapen chaos of well-seeming forms,
Feather of lead, bright smoke, cold fire, sick health,
Still-waking sleep, that is not what it is!
Or maybe I’m a twenty-first century reader trying to work his way back through historical patterns of thought by reading the classics, and peel back the onion skins one by one: Shakespeare, Jean De Meun, Boethius, the Bible, Cicero, Plato. This would make a good book itself: the story of an archeologist of literature who uncovers past civilizations by digging through layer upon layer, each later culture built on the ruined foundations of the one prior.

Or maybe you are the protagonist of the story. If any of my poor accounts lead you to a good book, then your journey of archeological discovery has begun.

Friday, June 5, 2015

Romancing the Rose

I first learned about The Romance of the Rose in music history class back in college. And so now of course I’m reading it. It only took me thirty-eight years to get around to it.

This long allegorical poem was begun by Guillaume de Lorris in the early 1200s. A half a century or so later, a fellow named Jean de Meun picked it up and did something like finish it. The plot, which runs seamlessly from one author to another, concerns a first-person, male narrator who wanders to the Garden of Pleasure and falls in love there with a rosebud that he wishes to pluck. Both authors promise to explain what it all means, and neither ever follows through, but we all know that deflowering represents deflowering.

In her preface, the editor proffers the puzzle of whether the two authors approve of the lover’s pursuit of his goal, disapprove of the young man’s quest, or disagree on the commendability of their joint protagonist’s obsession with the rose. As she points out, the narrator’s voice, which always at least partially masks an author’s, is in turn mostly hidden by still other voices in this book. Each author brings in several allegorical characters who speak quite a bit and occupy almost all of the poem’s lines. So which character or characters does each author identify with? Which presents the point of view to which the authors are sympathetic?

Well, I don’t know the answer. I’m no trained expert in medieval hermeneutics, and I’m only halfway through the book. But I have an opinion, and of course I’m going to share it. In other words, I’m not a medieval scholar, but I play one on the internet.

My extremely interesting, well-founded, and highly plausible hypothesis begins with a clear distinction of style between the two poets. If the plot flows seamlessly and the authors’ sympathies lie hidden in the Pleasure Garden’s grass, their respective tones are clearly differentiated. Guillaume is concerned with the psychological dynamic of wooing a rose, while Jean spends his efforts intellectually exploring the ethical issues involved. The former author introduces a parade of allegorical figures representing the feelings and thoughts of a young man and woman as their acquaintance, shall we say, develops: Love and Reason, Fair Welcome and Rebuff, Courtesy and Shame all step apace into and out of the dance of courtship. The latter, on the other hand, gives a handful of the characters one long chapter each in which, one by one, they present their advice to the young lover. And Jean fills these sermons with classical allusions, revealing even more clearly his scholarly approach.

Jean de Meun’s bookish, philosophical view of the matter suggests to me that he disapproves of the romance. Reason, for instance, gives the young lover a long lesson on the perils of passion and the necessity of basing a relationship between a man and a woman on piety and purpose. It is so convincing, so full of good arguments drawn from Plato, Boethius, and others, that Jean must have believed it all when he learned it in the first place. Two details seal the deal for me. First, Reason mentions that someone ought to translate Boethius’ Consolation of Philosophy into French so modern laypersons can benefit from it, and the editor tells us that Jean himself executed that translation a few years later. So surely Reason speaks for Jean. And second, when Friend gives his advice simply to bribe and lie to the rose and everyone surrounding her until the young man gets what he wants, the lover himself balks and calls for rational, virtuous discourse with both humans and plants.

So at this point I have an idea what this classic poem is about, what it might mean, and what the authors thought readers should get out of it. Now I just have to go back and reread that chapter in my old textbook to see what any of it has to do with medieval music.