Six Great Schoolmasters: Curriculum

It’s been a while since I posted on the uneven but interesting Six Great Schoolmasters.  I only read a few pages before bed and not all that consistently, so I am limping my way through.  But a while back I read a passage which completely poleaxed me.  I’ve been ruminating on it ever since.

Here’s what a Great Schoolmaster, Dr. Moberly, thought of an over-stuffed curriculum:

“In my judgment…you cannot bring French in as a co-ordinate subject of instruction with the two chief subjects of education, classics and divinity, or even with the third, mathematics.  We can neither find the time in the week, nor the teachers…”

Wait, did he just say they only teach three subjects? Continue reading Six Great Schoolmasters: Curriculum

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Teaching Badly: Pons Asinorum

Lately I’ve had the experience of trying to drag someone across the Pons Asinorum.  It has put me in mind of teaching and the nature of child development.

Pons_asinorum_dzmanto

Pons Asinorum (Bridge of Asses) is an ancient, colloquial name for Euclid’s second triangle proposition.  There are some disagreements about why it is called this, but I don’t really see why.  Elements I.5 is the first proposition that requires the student to really see some things for the first time.  You can’t drag someone through it anymore than you can drag a recalcitrant donkey across a bridge.  Either give them the answer to memorize or wait for them to get older.

So having gone through the proposition once without success, I have to take stock of what to do next.  The “answer” to I.5 is quite simple: in an isosceles triangle, the angles opposite the equal sides are themselves equal.  Should I hand that over as a definition and move on? Continue reading Teaching Badly: Pons Asinorum

Orlando Furioso Canto XII: Ares vs. Death

The end of this canto has my favorite Orlando scene, hands down.  He’s wrapped up the Ariadne/Olympia quest line and escaped the magical villa (I’ll come back to that another day).  The following spring, after some anonymous winter feats, he gets intercepted by two squadrons of Saracen knights.  What happens next is not terribly surprising, considering a cannon only pissed him off a few cantos back.  But once you’ve compared a guy to the god of war and then ramped it up to Jupiter, where do you go for the next superlative?  How do you top that?

Easy:

Grim Reaper
Ares.  Move or I close your eyes too.

No, we’re not going to compare Orlando to Death.  Don’t be silly.  We’re going to make Death jealous of him (XII.80):

Death roams the field in strange variety
Of horrid forms, and all inspiring dread;
And says, “For hundreds of my scythes may stand
His Durindana in Orlando’s hand.”

Hold on.  I got ahead of myself. Continue reading Orlando Furioso Canto XII: Ares vs. Death

Read More: City of God

St. Augustine’s City of God is my white whale.  I have tried and tried and tried to finish this book, which I love and which I happily declare a masterpiece.  But. It’s. So. Long.  Every few months to a year I pick it up again and have to go back to the beginning to get back into it because I completely forget where I have left off.  I think I’ve read Book I maybe 12-15 times now.  I’ve read a lot of books of not-inconsequential length before, but this one somehow just slays me every time.

One of my enduring delights about City of God–despite being trapped in it like Groundhog Day–is St. Augustine’s ambivalent approach to the Roman gods.  It’s an ambivalence that I’ve shared for a long time, primarily thanks to reading a lot of fantasy literature as a kid.  Reading classics and especially medieval stuff like Ariosto has strongly reinforced it.  We may summarize the whole problem by taking a sharp left turn and considering a dinner-table conversation in my house.

“Dad,” sayeth the heir.  “Are the Greek gods real?”

Respondit the father, “Uh….” Continue reading Read More: City of God

Cool Math: Lucas Numbers

I was torn between posting a video explanation of how they found the recent super-massive Mersenne Prime and this shorter bit on Lucas Numbers, which is how they found it.  Since this video has more explanation–and some very cool commentary on the nature of mathematics toward the end–I went with it.  I’ll save the super-Mersenne for another day.

Lucas Numbers are related to the Fibonacci Sequence.  Both are related to the Golden Ratio, which I definitely need to post on at some point.  Like many Numberphile videos, this one does a good job conveying infectious love of numbers.  Enjoy! Continue reading Cool Math: Lucas Numbers

Requiem

The priest who baptized my son ten years ago is a good man.  He’s not a pastor of any local parishes; possessed of many gifts of intellect, he works for the diocese.  By a twist of providence he has started helping out in our parish from time to time, largely because of his impeccable Latin.  It’s a delight to see him again after ten years.

His father passed away recently.  I have not seen him since, although I hope to do so in the near future so as to pass along my condolences.  I never met his father, nor have we ever spoken of him before.  As a priest in the Catholic Church it is not easy for him to do so. Continue reading Requiem

Bernard on Benedict on Pride

I posted a bit on St. Benedict’s 12-step program for humility–the daunting Jacob’s Ladder in chapter seven of his rule.  For some comments on the harrowing final rungs of that ladder, see the earlier post.  Now I want to turn to how another Benedictine saint riffed on that chapter.

Saint_Bernard_of_Clairvaux

St. Bernard of Clairvaux is a criminally underrated spiritual author.  Or at least I criminally underrated him; reading him in college was a chore and I only came back to him in small, infrequent doses.  But again, getting inside the Rule a little bit changed me for the better.  Getting older probably helped.  When I re-read St. Bernard two years ago, he absolutely lit me on fire.  He has a profound insight into human nature similar to that for which St. Augustine is justly famous.  I was so stupid when I was nineteen!  I try to remember that when I’m teaching. Continue reading Bernard on Benedict on Pride

Lent 2016

Courtesy of St. Bernard of Clairvaux.  Expect to see more of him in this space over the next few weeks/months.  This is his introduction to the steps of pride, his exposition on St. Benedict’s ladder of humility:

[O]ne does not fall to the depths of evil all at once, anymore than one leaps to the heights of virtue in a single bound, but only  by climbing step by step.  So too the way down is followed step by step…

There is a way down, then, as well as a way up.  There is a way to good and a way to evil.  Avoid the evil way and choose the good.  If you cannot do it by yourself, pray with the prophet and say, “Keep me from the way of sin” (Psalm 119:29).  How?  “Show me the mercy of your law” (Psalm 119:29).  That is, that law which you have given to those who go astray on the way, those who desert the truth, of whom I am one, for I have truly fallen from the truth.

But surely if a man falls he will rise again?  Yes.  It is in that hope that I have chosen the path of truth by which I shall ascend in humility back whence I fell through being proud.  I shall ascend, I say, singing “Lord, it is good for me that you have humbled me.  The law of your mouth is better for me than a thousand pieces of gold or silver” (Psalm 119:72).

David seems to offer you the choice of two ways.  There is only one, as you know; but there is a distinction to be made.  We can use different names for the way of sin, by which those who are going down travel, and the way of truth, by which those who are going up journey.  It is the same way which goes up to the throne and down from it, the same way to the city and back.  One door lets people both into and out of a house.  The angels appeared to Jacob going up and down by the same ladder.

What is the relevance of this?  That if you desire to return to the truth you do not need to search for the road.  You know it.  You came down that way.  Retrace your footsteps.  Go up by the same steps by which you came down in your pride…Identify the step of pride you have reached and you will not need to strive to find the way of humility.

On Humility and Pride IX

Action/Contemplation

It’s been a murder week, between a massive investment of energy at work, the ongoing war against entropy at home, and the ramped-up preparations for Benedict’s arrival on March 17th.  New beds were constructed, enormous amounts of trash were hauled up and down and out and away, children demanded to know what else I was planning on doing for them.  It’s been immensely gratifying.

What all that work hasn’t left any time for (in addition to blogging) is reading and thinking.  One of the great perks of my job is that I have time between classes to decompress and meditate on…well, just about anything.  A lot of Ovid, Benedict, or Ariosto happens in there!  And when I ride the train home, that’s 45 minutes of uninterrupted rest and contemplation.  But lately, I’ve been feeling the loss.

Time isn’t the right word for the problem, though.  It’s not quite energy either, although I have been doing a lot more sleeping on the train.  Even when I am up and about, or sitting at a desk with no parent, student, administrator, or child demanding my attention, I simply cannot concentrate on words and ideas.  And while it’s amusing to tell people that I have pregnancy hormones, and the stupid television blaring in the background doesn’t help, it’s really just another first-hand look at the irreducible tension between the active life and the contemplative life. Continue reading Action/Contemplation