Wednesday, March 21, 2018

Out of the mouths of babes

Once when my sister, Anne Marie, was two or three years old, we were out driving when a particularly low quality song came on the radio. When it was over, she remarked, “That song isn’t real. Somebody just made it up.”

Naturally I DID NOT LAUGH when she said it, even though I laugh every time I remember or retell it.

But I have remembered it and retold it regularly, not just because it was funny, but because I think there’s real truth in there.

I was reminded of it again this morning while reading Stratford Caldecott’s Beauty for Truth’s Sake. In his chapter on music he quotes the English composer John Tavener, who says that, “all music already exists. When God created the world he created everything. It’s up to us as artists to find the music.”

He goes on to say:

Music just is. It exists. If you have ears to hear, you’ll hear it! . . . I believe we are incarnated in the image of God in this world in order for us to re-find that heavenly celestial music from which we have been seperated. Our whole life is a continuing return to the “source.”
(p. 96)

Saturday, September 2, 2017


My morning walks are something like a meditation time. When I first starting walking regularly I would bring along an audio book or my French lessons and I found that I hated it — I couldn’t focus on the walk or the book. Instead I focus on the walk itself, and it’s much more pleasurable and relaxing that way.

First I focus on my feet, how I’m placing them. This will sound silly but it’s actually necessary for me. A couple of years ago the pain in my right foot became so bad that I finally went to a doctor and he put me in physical therapy for a few months. Turns out that the weeks I spent walking in a cast after breaking my foot when I was five years old caused me to develop bad habits, and the years of that gait caused damage to my foot, my ankle, my knees, hips, back, and neck! So the first thing I do is make sure that I’m planting that foot the way I should be and pushing off correctly.

Then I spend a bit of time noticing my hips and lower back, checking for correct posture and muscle usage. Then I move up to my upper back, neck, and shoulders, making sure they’re correct and relaxed, so that my chest is open and relaxed and I’m breathing properly. Then I cycle through again to make sure I haven’t lost anything along the way.

CS Lewis said, “When you put the feet right, everything else comes right.” 😀

This sounds time-consuming, and it was at first, but while I’m concentrating on my gait, posture, and breathing, I’m also taking in the look of the ground and noticing whether it shows signs of recent rain or wind. I’m smelling the air and feeling the temperatures. I’m listening to the birds and other animals and to the sound of the wind in the trees. I’m looking up at the sky and noticing the color and whether there are any clouds and what they’re like.

Nowadays focusing on my own body has become easy enough that it doesn’t take much attention or energy, so I have more of that for simply noticing the creation and letting my thoughts wander to whatever I want to think about.

There’s a specific technique that I had learned before all of this came up, and I think it’s why focusing on all those things came fairly easily for me. It’s counting your breaths. This sounds dumb, but it’s actually pretty hard.

Go sit or lie someplace quiet with no distractions. Then breathe in to a slow 3-count and out the same way. Count in your head, if possible, so you can keep your body as quiet and relaxed as possible. At the end of each cycle, count that as 1 breath (keeping count on my fingers works best for me). Try to get all the way to 10 without thinking of anything else. If any other thought intrudes itself, push it out and start over counting.

The goal is to be able to count to 100 (ten 10s) while maintaining that level of focus. It took me weeks and weeks to get there, but it’s worth it! Especially if you have an annoying dental procedure coming up and don’t like using the laughing gas. 😉

~*~ ~*~ ~*~

(This post was originally a comment at Joy’s blog.)

Tuesday, June 27, 2017

Reading The Faerie Queen with children: handling allegory

The many generations who have read and re-read The Faerie Queene with delight paid very little attention to the historical allegory; the modern student, at his first reading, will be well advised to pay it none at all.
~C.S. Lewis’s essay “Edmund Spenser 1552-99,” in Studies in Medieval and Renaissance Literature

I’ve been very grateful to have Lewis as a mentor on our journey through The Faerie Queene, especially as we read Canto IX of Book V this morning. In the canto, Duessa, the arch-villainess through much of the story, has finally been captured and brought to trial at the court of the great queen Mercilla. In her defense come Pity, Regard of womanhood, Nobility, and Grief, among others, who plead her case so well that Prince Arthur is moved to feel sorry for her. But then the prosecutor, Zeal, makes his case and brings Strife, Murder, Sedition, Incontinence, Adultery, and Impiety to testify against her.

All which when as the Prince had heard and seen,
    His former fancy’s ruth he gan repent,
    And from her party eftsoons was drawn clean.
    But Artegall with constant firm intent,
    For zeal of Justice was against her bent.
    So was she guilty deemed of them all.
    Then Zeal began to urge her punishment,
    And to their Queen for judgement loudly call,
Unto Mercilla mild for Justice gainst the thrall.

But she, whose Princely breast was touched near
    With piteous ruth of her so wretched plight,
    Though plain she saw by all that she did hear,
    That she of death was guilty found by right,
    Yet would not let just vengeance on her light;
    But rather let in stead thereof to fall
    Few pearling drops from her fair lamps of light;
    The which she covering with her purple pall
Would have the passion hid, and up arose withall.

[Spellings updated]

The notes at the back of my copy of the book go to great lengths to describe the historical background – all the conflicts between Catholic and Protestant during the Reformation in England – and explain that in this scene Duessa is Mary Queen of Scots, and Mercilla is Queen Elizabeth.

I usually keep Lewis’s admonition in mind, but even though this is technically our first reading, we’ve already met this scene in a children’s version that we read before approaching Spenser himself, given my children’s ages – 14 and 16 – after we finished the canto I decided to address the historical background just a little. Mainly I pointed out that though there are historical parallels, this shouldn’t be taken as plain allegory. I thought it would be a good idea to start letting them know about literary criticism and analysis of the kind that might kill the joy of the piece if we take it too much to heart.

I can’t tell you how much we’re loving reading The Faerie Queene. I wish I’d read it with my older kids when they were still at home.

If you’re interested, here’s another post I wrote a few years ago with quotes from the same Lewis book I quoted above: C. S. Lewis on Spenser’s Faerie Queene.

Wednesday, March 1, 2017

Dear March, come in!

~Emily Dickinson (1830-1886)

Dear March, come in!
How glad I am!
I looked for you before.
Put down your hat—
You must have walked—
How out of breath you are!
Dear March, how are you?
And the rest?
Did you leave Nature well?
Oh, March, come right upstairs with me,
I have so much to tell!

I got your letter, and the birds’—
The maples never knew
That you were coming—I declare,
How red their faces grew!
But, March, forgive me—
And all those hills
You left for me to hue—
There was no purple suitable,
You took it all with you.

Who knocks? That April!
Lock the door!
I will not be pursued!
He stayed away a year, to call
When I am occupied.
But trifles look so trivial
As soon as you have come,
That blame is just as dear as praise
And praise as mere as blame.

Monday, July 11, 2016

Literature as Logos

This, so far as I can see, is the specific value or good of literature considered as Logos; it admits us to experiences other than our own. . . . it may be the typical (and we say ‘How true!’) or the abnormal (and we say ‘How strange!’); it may be the beautiful, the terrible, the awe-inspiring, the exhilarating, the pathetic, the comic, or the merely piquant. Literature gives the entrée to them all. Those of us who have been true readers all our life seldom fully realise the enormous extension of our being which we owe to authors. We realise it best when we talk with an unliterary friend. He may be full of goodness and good sense but he inhabits a tiny world. In it, we should be suffocated. The man who is contented to be only himself, and therefore less a self, is in prison. My own eyes are not enough for me, I will see through those of others. Reality, even seen through the eyes of many, is not enough. I will see what others have invented. Even the eyes of all humanity are not enough. I regret that the brutes cannot write books. Very gladly would I learn what face things present to a mouse or a bee; more gladly still would I perceive the olfactory world charged with all the information and emotion it carries to a dog.

This is the next-to-last paragraph of C.S. Lewis’ Experiment in Criticism. How does he do this? How does he put into words everything I’m feeling?

When I read that, I put the book down and sat there for a moment, sobbing.

Why does it hurt so much to be human?

The next paragraph says:

“Literary experience heals the wound, without undermining the privilege, of individuality.”

Yes. That’s it. “The wound of individuality.” I didn’t know what that feeling was before, but now I do. (This is why I love you so much, dear saint! More than anyone, you help me understand what I’m feeling and thinking.)

But in reading great literature I become a thousand men and yet remain myself. Like the night sky in the Greek poem, I see with a myriad eyes, but it is still I who see. Here, as in worship, in love, in moral action, and in knowing, I transcend myself; and am never more myself than when I do.

Friday, March 25, 2016

Cyphering books

In my casual research on mathematics and its teaching I came across something interesting -- I'm just sharing it here in order to keep track of it myself, and to offer it up to anyone else who may be interested.

I found the latest fragment in a book called Rewriting the History of School Mathematics in North America 1607-1861: The Central Role of Cyphering Books, which I will probably never buy because it costs over $100. 


A cyphering book is something like a copy book, only for rules of computation and examples of how each rule works, plus exercises which the student solved himself. Each student wrote out his own cyphers in his own notebook, copied from work the teacher gave him. The cypher book was intended to serve him the rest of his life as a reference manual.

A page from Abraham Lincoln's cyphering book

Back to Rewriting the History . . . . It turns out that something I had been suspecting is true -- which is not surprising, because there's nothing at all revolutionary about it, but it's always fun to find actual proof -- and that is this: The way we teach arithmetic today has more to do with book-keeping than with mathematics.

Remember last summer when I mentioned that the ancient Greeks made a distinction between arithmetic and logistics? Logistics is skill in computation for practical purposes. There is nothing at all wrong with teaching logistics. After all, we want our kids to be able to function in our society, so of course they need to know how to keep a budget, how to double or halve a recipe, how to buy enough paint or carpet or lumber for a project, how to figure out what kind of insurance they need, or whether they can afford a mortgage, and all those things. Many of our kids will need more complicated math for programming computers or analyzing data. So I'm not saying we classical/CM educators shouldn't teach our kids that kind of math.

But I do think it's lopsided for that kind of math to make up the bulk of our curriculum.

The bit of Rewriting History that's available for viewing on Google gives a rough of idea of the development of the modern situation.

Beginning in the 1200s, trade between city-states and republics proliferated to the extent that successful merchants needed to hire skilled "reckoners" to calculate profits, predict risks and control losses, figure weights and measures, deal with simple and compounding interest, keep track of partnerships, and all kinds of complicated things. 

As demand for this skill increased, reckoning schools sprang up around Europe. But get this. Boys of ten or eleven years of age would be sent there for a two-year course which prepared them for work in the actual business. And they didn't have calculators.

Of course, the universities were still concerned with the mathematics as liberal arts, and the book goes on to describe the changing attitudes there, but that's the extent of what I can read online for free.

Maybe I should as for this book for Christmas.


Thursday, March 10, 2016

My blog is now a teenager

Remember when
I used to update the blog's theme
to go with the seasons?
I've never had a teen-aged blog before. I wonder how it will behave? I have a blog post brewing that I'm strongly tempted to call "Charlotte Mason was wrong about math," just to see what kind of reaction it elicits. Can't decide whether to squelch that or roll with it. ;-)

Sunday, October 25, 2015

Saint Crispin's Day festivities

Last night we had our annual bash -- a bonfire/cookout/St Crispin's Day feast/Henry V/Medieval everything party. Some guests come in costumes and we give a prize to the crowd's favorite. We set up an archery range and take turns shooting. We play Medieval music, several of the menfolk put on the first part of Act IV, Scene II of Shakespeare's Henry V, the part with The Famous Speech, and this year we sang Non nobis Domine at the suggestion of one of our guests.

But the highlight of the festivities is always the dragon tail we serve.

We neglected to take a prettied-up picture of it

Creepy, isn't it?

Work in progress

Eldest Daughter has made it for us every year and I usually decorate it, but this year my youngest son asked to be in charge of decorating, so we bought him some fondant and told him to go to YouTube and figure out how to work with it, since we've never used it before.

I think it turned out really well.

Monday, September 14, 2015

Arithmetic for young children, classical style

This summer I visited the Parthenon in Nashville. While there I bought a book by Jacob Klein, entitled Greek Mathematical Thought and the Origin of Algebra (translated by Eva Brann). I’ve only read a little of the beginning of it, but it’s given me another piece of the puzzle I’ve been trying to put together for the last couple of years—how was math taught to children prior to the revolutionary changes that were made in the 1800s?

Since the fall of 2014 I’ve been slowly (ever so slowly!) working my way through the Introduction to Arithmetic written by Nicomachus of Gerasa, who was born in the first century after Christ, and along the way I’ve also been reading through the supplemental materials that are available in this PDF version of Nicomachus, where I found the following passage:

Arithmetic is fundamentally associated by modern readers, particularly by scientists and mathematicians, with the art of computation. For the ancient Greeks after Pythagoras, however, arithmetic was primarily a philosophical study, having no necessary connection with practical affairs. Indeed the Greeks gave a separate name to the arithmetic of business, λογιστικη [logistic, or calculation]; of this division of the science no Greek treatise has been transmitted to us. In general the philosophers and mathematicians of Greece undoubtedly considered it beneath their dignity to treat of this branch, which probably formed a part of the elementary instruction of children.

“Studies in Greek Mathematics” by Frank Egleston Robbins and Louis Charles Karpinski

This was my first clue that what we call arithmetic today isn’t necessarily the same thing as what Plato called arithmetic, and that brings me to chapter two of the Klein book, which summarizes the very few references in classical literature to teaching arithmetic—excuse me, calculation—to children. One of the books mentioned was Plato’s Laws, so I looked up the passage in my copy of the book:

All freemen I conceive, should learn as much of these branches of knowledge as every child in Egypt is taught when he learns the alphabet. In that country arithmetical games have been invented for the use of mere children, which they learn as a pleasure and amusement. They have to distribute apples and garlands, using the same number sometimes for a larger and sometimes for a lesser number of persons; and they arrange pugilists and wrestlers as they pair together by lot or remain over, and show how their turns come in natural order. Another mode of amusing them is to distribute vessels, sometimes of gold, brass, silver, and the like, intermixed with one another, sometimes of one metal only; as I was saying they adapt to their amusement the numbers in common use, and in this way make more intelligible to their pupils the arrangements and movements of armies and expeditions, and in the management of a household they make people more useful to themselves, and more wide awake; and again in measurements of things which have length, and breadth, and depth, they free us from that natural ignorance of all these things which is so ludicrous and disgraceful.

Plato, Laws, Book VII [819] (emphasis added)

The second chapter of Klein also quotes a passage from a commentary on Plato’s Gorgias by Olympiodorus the Younger (c. 495-570) where he says in passing that “even little children know how to multiply.” And in chapter three Klein reiterates that children must be taught calculation through play, “thus making it possible for children to acquire correctness in counting and in combining numbers painlessly.”

This is such an exciting line of inquiry! I wish all my kids were babies again so I could start over.