Rogationtide: Praying for mercy and for fruitful seasons

 

Everything is burgeoning! The dogwoods, irises, and peonies have finished blooming, but the clematis and pinks are going wild and the lavender shooting out bloom stalks. I love this time of year.

My youngest daughter has started two bed in a sunny spot in our back yard that are modelled after the traditional “three sisters” way of planting. First she planted corn and sunflowers. Now that they’re coming up nicely she’s going to plant beans, which will twine up the stalks of the taller plants, then in a few weeks she’ll plant squashes, which will flourish on the ground below the other plants.

This coming Sunday will be the sixth Sunday of the Easter season. Up until fairly recently the Gospel reading for this Sunday was John 16:23-33, which begins, “Verily, verily, I say unto you, Whatsoever ye shall ask the Father in my name, he will give it you.” The Latin word for ask is rogare, and so this Sunday is known in liturgical churches as “Rogation Sunday.”

One of the traditional prayers for this brief season is the prayer for fruitful seasons:

Almighty God, Lord of heaven and earth: We humbly pray that thy gracious providence may give and preserve to our use the harvests of the land and of the seas, and may prosper all who labor to gather them that we, who constantly receive good things from thy had, may always give thee thanks; through Jesus Christ our Lord, who liveth and reigneth with thee and the Holy Spirit, one God, for ever and ever. Amen.

I have written before about some of the festive ways Christians have kept the days between Rogation Sunday and Ascension Thursday, but this week something new struck me and I wanted to mention it here.

Over the last year I’ve been dipping into Eleanor Parker’s delightful book, Winters in the World: A Journey Through the Anglo-Saxon Year, and last night I read her section called “Holy and Healthy Days,” which is on the origins of Rogationtide and the ways the early medieval English Christians kept this season. She mentions one of Aelfric’s sermons for Rogationtide and describes how the season was a penitential season as well as a festive one. Aelfric says that during this season, “we should pray for abundance of our earthly fruits, and for health and peace for ourselves, and, what is still greater, for the forgiveness of our sins” (pp. 157-158).

So, on the Rogation Days (the three days between Rogation Sunday and Ascension Day), the priests and parishioners would walk around the parish boundaries not only praying for fruitful seasons, but also praying for the forgiveness of their own sins and for the Lord’s mercy on their city. In his History, Bede quotes a chant from the Gallican Rogation Litany:

We pray Thee, O Lord, in all Thy mercy, that Thy wrath and anger may be turned away from this city and from Thy holy house, for we are sinners. Amen.

As Parker puts it so beautifully, “The Rogation Days seek physical and spiritual health for the individual, the community and the natural world; all are connected, one harmonious whole” (p. 162).

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For more on Aelfric’s sermon and the medieval traditions, see Eleanor Parker’s blog post at The Clerk of Oxford.

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Rogationtide, part two: Traditional prayers

"... angry passion yields to wisdom and Ares stands in awe of the Muses"

 "Not only during peacetime but also in war, the Gauls obey with great care these Druids and singing poets, both friend and enemy alike. Often when the two armies have come together with swords drawn these men have stepped between the battle-lines and stopped the conflict, as if they held wild animals spell-bound. Thus even among the most brutal barbarians angry passion yields to wisdom and Ares stands in awe of the Muses."

~ Diodorus Siculus (fl. c. 60-c. 30 BC)
Bibliotheca Historica, Book V.31

Of knights and snails

One the funnest parts of looking at medieval art is running across an illustration of a knight fighting a snail. 

There are many theories as to what these snails are doing in the art, but not a one of them matches my own, which I came up with this year while reading through the Psalms with my family. Take a look at this:

Psalm 58

1 Do ye indeed speak righteousness, O congregation? do ye judge uprightly, O ye sons of men?
2 Yea, in heart ye work wickedness; ye weigh the violence of your hands in the earth.
3 The wicked are estranged from the womb: they go astray as soon as they be born, speaking lies.
4 Their poison is like the poison of a serpent: they are like the deaf adder that stoppeth her ear;
5 Which will not hearken to the voice of charmers, charming never so wisely.
6 Break their teeth, O God, in their mouth: break out the great teeth of the young lions, O Lord.
7 Let them melt away as waters which run continually: when he bendeth his bow to shoot his arrows, let them be as cut in pieces.
8 As a snail which melteth, let every one of them pass away: like the untimely birth of a woman, that they may not see the sun.
9 Before your pots can feel the thorns, he shall take them away as with a whirlwind, both living, and in his wrath.
10 The righteous shall rejoice when he seeth the vengeance: he shall wash his feet in the blood of the wicked.
11 So that a man shall say, Verily there is a reward for the righteous: verily he is a God that judgeth in the earth.

 

The psalmist is describing how ferocious and dangerous the enemies of God appear, but then in verse 8 he says, "As a snail which melteth, let every one of them pass away."

In other words, they appear unconquerable, but they really aren't. 

The popular idea about this image is that the knight has given up and is begging mercy of the victorious snail, but I believe he has recognized that this is spiritual warfare, so he has laid down his sword and is praying to God for deliverance.

What's your favorite theory?

Alfred the Great

Photo credit: Odejea
Wikimedia Commons

 "O God, who didst call thy servant Alfred to an earthly throne that he might advance thy heavenly kingdom, and didst give him zeal for thy church and love for thy people: Grant that we, inspired by his example and prayers, may remain steadfast in the work thou hast given us to do for the building up of thy reign of love; through Jesus Christ our Lord, who liveth and reigneth with thee and the Holy Spirit, one God, for ever and ever. Amen."

 On this day in the year of our Lord 899, Alfred King of the Anglo-Saxons passed into glory. He was a good man -- a poet, a scholar, a warrior, a lawgiver, and above all a devout Christian.

This month I've been reading aloud on Zoom G.K. Chesterton's magnificent Ballad of the White Horse, which is about Alfred's fight against the pagan invaders. Here's the link to the read-aloud on YouTube, if you'd like to listen. I've read it aloud to my kids nearly every October for over a decade and they've all graduated and I'm having my Morning Time alone these days, so that's why I decided to read the Ballad on Zoom. I'm glad I did -- it was a lot of fun. You know, I didn't even think about mentioning it here ahead of time!

You can read more about Alfred at this Lectionary page. It includes the Collect I've quoted above, plus Scripture readings for the day, and brief history of Alfred. 

This article from the University of Oxford has more information, including excerpts from some of his writings.

And here's an interesting article from a few years ago about the coin known as the Alfred coin

Enjoy!

 

“Goblin Feet”

“The Meeting of Oberon and Titania,” Arthur Rackham (1908)
Wikimedia Commons

 

“Goblin Feet”
~ J.R.R. Tolkien (1892–1973)

I am off down the road
Where the fairy lanterns glowed
And the little pretty flitter-mice are flying:
A slender band of gray
It runs creepily away
And the hedges and the grasses are a-sighing.
The air is full of wings,
And of blundery beetle-things
That warn you with their whirring and their humming.
O! I hear the tiny horns
Of enchanted leprechauns
And the padded feet of many gnomes a-coming!

O! the lights! O! the gleams! O! the little tinkly sounds!
O! the rustle of their noiseless little robes!
O! the echo of their feet—of their happy little feet!
O! their swinging lamps in little starlit globes.
I must follow in their train
Down the crooked fairy lane
Where the coney-rabbits long ago have gone,
And where silvery they sing
In a moving moonlit ring
All a-twinkle with the jewels they have on.
They are fading round the turn
Where the glow-worms palely burn
And the echo of their padding feet is dying!
O! it’s knocking at my heart—
Let me go! O! let me start!
For the little magic hours are all a-flying.

O! the warmth! O! the hum! O! the colours in the dark!
O! the gauzy wings of golden honey-flies!
O! the music of their feet—of their dancing goblin feet!
O! the magic! O! the sorrow when it dies.


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Written on 27-28 April 1915, shortly before leaving for the War, for his future wife who “loved tales of ‘spring and flowers and trees, and little elfin people.’”

Obviously this is nothing like his portrayal of elves and goblins that fans of The Lord of the Rings are familiar with and Tolkien himself later tried to distance himself from this very Victorian painting of the little people — in 1971 when he was asked permission to include “Goblin Feet” in an anthology, he said, “I wish the unhappy little thing, representing all that I came (so soon after) to fervently dislike, could be buried for ever.”

Tolkien’s first encounter with fighting was in France, in the Battle of the Somme, which is remembered as the bloodiest battle ever fought in history. On the first day of the battle nineteen weeks before Tolkien arrived, nineteen thousand British troops were killed. By the time the battle was over more than eight hundred thousand of the British had been killed.

[…]

Tolkien never forgot the brutality and horror of the battle. Many years later he drew on these memories to create his own lands. The blackened landscape of Mordor, and the Battle of Helm’s Deep were both based on The Battle of Somme.

(Information and quotes found at the Tolkien Library.)

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This post first published April 17, 2008.

We watched 1917 (such a good movie!) a few days ago and it has me thinking about that war and especially how it changed the men who fought it. Tolkien was a very different man after the Great War, wasn’t he?

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. 

O.o

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.

:-D

Recipe from Cookery and Dining in Ancient Rome

I know that since reading about the Romans' habit of eating stuffed dormice a few years ago y'all have all been dying to try it for yourselves. Well, today I came across an authentic Roman recipe.

STUFFED DORMOUSE

IS STUFFED WITH A FORCEMEAT OF PORK AND SMALL PIECES OF DORMOUSE MEAT TRIMMINGS, ALL POUNDED WITH PEPPER, NUTS, LASER, BROTH. PUT THE DORMOUSE THUS STUFFED IN AN EARTHEN CASSEROLE, ROAST IT IN THE OVEN, OR BOIL IT IN THE STOCK POT.

From the aforementioned cookbook by Apicius, Book VIII, Chapter IX.

The translator adds this helpful note:

Glis, dormouse, a special favorite of the ancients, has nothing to do with mice. The fat dormouse of the South of Europe is the size of a rat, arboreal rodent, living in trees.

Galen, III, de Alim.; Plinius, VIII, 57/82; Varro, III, describing the glirarium, place where the dormouse was raised for the table.

Petronius, Cap. 31, describes another way of preparing dormouse. Nonnus, Diæteticon, p. 194/5, says that Fluvius Hirpinus was the first man to raise dormouse in the glirarium.

Dormouse, as an article of diet, should not astonish Americans who relish squirrel, opossum, muskrat, “coon,” etc.

You're welcome.

:-D

Sleepers Awake

Sleepers Awake (also known as Wachet auf, ruft uns die Stimme, BWV 645) is a chorale cantata J.S. Bach composed in 1731 for the 27th Sunday after Trinity, which fell on the 25th of November that year.  That was a year when Easter came unusually early, because it's not often the calendar has twenty-seven Sundays after Trinity, so thankfully this piece has become a popular part of Advent.

Many hymnals have a version of it. The the 1940 Episcopal hymnal, the OPC's Trinity Hymnal, the LCMS's Lutheran Worship, and the UMC's 1989 hymnal all share Catherine Winkworth's 1858 translation, called "Wake, Awake, for Night Is Flying."

The Cyber Hymnal provides an 1864 translation by Frances E. Cox called "'Sleepers, Wake!' The Watch Cry Pealeth," and in 1982 Carl P. Daw, Jr, translated it anew, calling it "'Sleepers, Wake!' A Voice Astounds Us," for the hymnal that was published that year.

I had always assumed that the cantata was written first and the hymn was taken from it, but it turns out that it's exactly the other way around!

Philipp Nicolai was a Lutheran minister and hymnwriter who lived through an outbreak of the plague in the late 1500s.  He lost 170 of his parishioners in one week alone, and in 1598, to comfort those who remained, he wrote a series of meditations called  The Mirror of Joy, which contained this hymn.

I believe this is the original version of it:

Image source:
http://imslp.org/wiki/Wachet_auf,_ruft_uns_die_Stimme_%28Nicolai,_Philipp%29

I've been all over YouTube the last couple of days listening to dozens of lovely renditions of this hymn and of the cantata -- far too many to put into one blog post -- so I will post a few more of my favorites as the week goes on.  In the meantime I'll leave you with this, a congration singing it in Lituanian to the melody as originally composed by Philipp Nicolai.

CiRCE Conference 2014 -- some tidbits

Pre-conference session with John Mark Reynolds

Worry less about the condition of your child's soul and more about yours -- he's going to imitate you, you know.

Your calling is towards your own relationship with Christ.

“The important thing is to prepare your kids to die well.  That’s the only thing they are all going to do.”

Find a good teacher and you'll find a place where they "waste time."

The only way to teach math is the Platonic way -- you poke them.

The 1940s and 50s changed the way math was taught -- didn't need kids to understand it, just be able DO it efficiently so that they could become scientists and engineers and help us beat the Russians.

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Teaching is leading the student from the known to the unknown according to the student's nature. (Andrew Kern)

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I could listen to John Hodges quote Shakespeare and Scripture and talk about music all day long.  Y'all have to listen to the Brahms' requiem Ein Deutsche Requiem (op 45), especially if you're familiar with traditional requiems.

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Piety, Imitation, and Art:  A Circle of Paideia -- Ravi Jain

Gymnastic (training the body) and Music (tuning the heart) are the foundation of education.  By "Music" he means the nine Muses, so practically everything I've been accustomed to think of as an education (literature, history, and the rest) are actually the foundation, not the education itself!

In teaching math, you should recapitulate with your students the narrative and discoveries of mathematics, so that they're as close as possible to the wonder, awe, and mystery of Math.

Math is concerned with proofs -- this is the Logos, the unifying principle of math.

Let your students come up with their own proofs.

Textbooks help mediate the conversation [i.e. don't abandon them, but don't follow them slavishly].

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The Three Paths to Wisdom -- Paula Flint

"By three methods we may learn wisdom; first by reflection which is the noblest, second by imitation which is the easiest, and third by experience which is the most bitter." (Confucius)

Nature is the first classroom.

Reflection comes after experience and imitation -- it's a harder level and takes time.

In imitation we benefit from past accomplishments.

As teachers and parents we need to think in terms of building good habits.  Good habits make life easier, freer.  It's not about punishment -- it's about helping children live a good life.

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St. Augustine and the Dialectic of Desire -- Wes Callihan

Cicero had a daughter named Hortensia who was a famous orator -- she spoke before the Senate!  Cicero wrote a book named after her, Hortensio.  It was an encouragement to philosophy, and sadly, is lost.

Practically everything you know and believe, you believe by faith. If you had to prove everything you'd never get anywhere. We are finite beings, so it's our nature to live by faith.

"Beatrice" is not the thing the soul is made for -- she is the reminder of the thing the soul is made for.  [This reminds me of CS Lewis's Surprised by Joy.]

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With Hobbits on the Road to Wisdom -- Andrew Seely

Homer wrote great works that are for his time -- we have to educate ourselves for them to have a real affect on us.  But Tolkien is for our time -- we don't have to do any groundwork before coming to his work.

All the stories told during The Lord of the Rings were Frodo's education, to that he could make the right decision at Parth Galen.  Frodo has a new heart which is trustworthy.  When he pities Gollum, he is able to follow his heart instead of his old ideas of justice.

The temptation for anyone who has made their home life beautiful is to cut themselves off from the rest of the world.

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[More later.  I'm tired now.]

Squaring the Circle, part 2 -- the Mesopotamians

Plimpton 322
Image via Wikipedia

Reading about mathematics in Mesopotamia has been pretty interesting.  They seem to have done a lot of math just for the fun of it.  They were fond of tables comparing numbers and their relationships to one another – multiplication tables, tables of reciprocals, squares, cubes, and square and cube roots.  Algebra was their specialty. 

They had a base 60 system, apparently because sixty can be divided so nicely in so many different ways – into halves, thirds, fourths, fifths, sixths, tenths, twelfths, fifteenths, twentieths, and thirtieths (did I miss any?).  We still use base-60 for telling time and for measuring angles, which is interesting because it doesn’t seem that the Babylonians had the concept of measuring an angle.

For numbers above 59 they used a place value system which worked the way ours does.  The first place to the right is “ones,” the numbers from 1 to 59 in their case.  The place to the left of that is for the base units – 10 in our case, 60 in theirs.  To the left of that is the base squared – 100 for us, 3600 for them.  (This looks like x(60)² + x(60) + x in Math-ese, but I prefer English.)  They eventually developed a zero which they used as a place holder in the middle of long numbers, but they didn’t use it in the far right position if it was needed there, so 1, 60, and 3600 look like the same thing and have to be guessed from context.

This place value system was also used for fractions and is the reason for the unfamiliar notation I mentioned last week.  In the example quoted, the first number is the whole number.  The semi-colon serves the way a decimal point does for us – to separate the whole number from the “less than one” part to the right.  The commas are needed to distinguish the places since each place might have anything from a 1 to a 59 in it.

Those are some of the basics of math in Mesopotamia, but this is supposed to be about finding the area of a circle, right?

Remember all those tables and lists I mentioned in the first paragraph?  The clay tablet pictured at the top of this post is a table that describes the relationship of the squares drawn on the sides of a triangle, sort of like this:

This is such a handy way of understanding shapes that the Mesopotamian mathematicians noted this kind of relationship with all the regular (equilateral) polygons with three to seven sides, comparing the area of each shape to the square that could be made along its side.  One tablet lists all these relationships and gives very accurate ratios describing the relationships.

The ratio of the area of the pentagon, for example, to the square on the side of the pentagon, is given as 1;40, a value that is correct to two significant figures. For the hexagon and the heptagon, the ratios are expressed as 2;37,30 and 3;41, respectively.  In the same table, the scribe gives 0;57,36 as the ratio of the perimeter of the regular hexagon to the circumference of the circumscribed circle, and from this, we can readily conclude that the Babylonian scribe had adopted 3;7,30, or 3 1/8, as an approximation for π.
[Merzbach and Boyer, p. 35]

Whew!

Me, trying to learn Math.
And yes, that does mean a hexagon with a circle drawn around it.
I checked.  :-)

So it turns out that there’s a good reason for comparing various shapes to squares, and circles to various regular polygons – it helps us understand the relationships between different shapes, which helps us understand the shapes themselves.  And noting these relationships gave the Babylonians, like the Egyptians before them, a fairly accurate way of figuring out the area of any circle.

But one thing that confused me in A History of Mathematics’ chapters on the Ancient Greeks and Mesopotamians was the phrase “an approximation for π,” which the authors use several times.  They make it sound like π is a thing that everyone knows about and only needs to be clearly defined or standardized, the way a “foot” was eventually standardized as a unit of measure.  It was pretty exciting when I finally realized why they keep saying this, but that will be in the next post.

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Click here for Part 1, which is about the Egyptians

Squaring the Circle, part 1

Fragment of the Ahmes Papyrus
Image via Wikipedia

Have you heard that phrase before?  I have and I didn’t know it referred to anything other than trying to do something that’s impossible, and also rather silly, right?  I mean, why would anyone try to turn a circle into in a square?

Turns out there was actually a good reason for it.  Back in the days when the best tools mathematicians had were the compass and straightedge, they needed a fairly simple way of determining the area of a circle, which is devilishly hard to do.  It’s very easy to find the area of a square, so one solution they thought of was to figure out a simple way to draw a square that had the same area as a given circle. 

This endeavor went on for millennia and turned out to be futile.

In the mean time they did a pretty good job of estimating the area of a circle.  Here’s what they did, and how we know about it.

Back around 450 B.C. the Greek historian Herodotus traveled around Egypt interviewing priests and observing all the great work that went on there, from building monuments to farming along the Nile.  He said that geometry was invented in Egypt in part because the land had to be resurveyed every year after the Nile’s flood waters receded.  (Aristotle disagreed with him – he said that it was the priestly leisure class who did all the cool math in Egypt.  I don’t see why they can’t both be right – I guess it’s the age-old rivalry between engineers, who have practical problems to solve, and mathematicians, who are frequently philosophers and deal in the purely abstract realm.)

A piece of evidence on Herodotus’s side of the story, is the Ahmes Papyrus, which resides in the British Museum.  This papyrus was named for the scribe who around 1650 B.C. wrote it, using material from about 2000 to 1800 B.C.  In the papyrus, Ahmes says that the area of a circular field with a diameter of 9 units is the same as the area of square that’s 8 units on each side.

A little earlier on he had worked a problem that shows how this relationship was discovered.

First, you draw a circle with a diameter of 9 units.  Then you draw a square around it.  This square is 9 units on each side.

 

Then you cut off an isosceles triangle from each corner . . .  

. . . which gives you an octagon with an area of 63 units that has roughly the same area as the circle, though it’s not clear whether Ahmes thought it was exactly the same, or “close enough for practical purposes.”

From this they came up with the rule that “the ratio of the area of a circle to the circumference is the same as the ratio of the area of the circumscribed square to its perimeter [A History of Mathematics, Mertzbach and Boyer, page 15].”  Apparently this works out to a mathematical constant, 4(8/9)², which they used the way we use π, but I don’t really understand that part of the story.  Mertzbach and Boyer say that it’s “a commendably close approximation” of π and I’m taking their word for it.

The Ancient Babylonians also had a method, but I’ll have to tell y’all about that another time.

Have you heard of Coursera?

Another new term you might have seen is MOOC:  Massively Open Online Course, which is what Coursera offers.

From the website:  “Coursera is an education platform that partners with top universities and organizations worldwide, to offer courses online for anyone to take, for free.”

I’ve taken three classes over the last couple of years, Introduction to Mathematical Thinking, The Ancient Greeks, and Reason and Persuasion: Thinking Through Three Dialogues by Plato.

The format for each is similar.  There are lecture videos to watch and homework assignments and tests.  There are discussions forums available.  Most classes have some standard you have to meet in order to receive certification. You get out of it what you put into it, and that will vary according to your goals, how much time and effort is demanded by the class, and how much time and effort you can afford to devote to it.

Once you’ve taken a course you’ll always have access to the archives so you don’t have to finish by the deadline, and you can listen to the lectures over again if you like.

The only class for which I met the standard for certification was The Ancient Greeks.  My goal for this class was to get a solid overview of the period – the flow of events and ideas.  Of course, we’ve touched on Ancient Greece over the years in our home school, reading Plutarch’s Lives together and Rosemary Sutcliff’s adaptations of The Illiad and the Odyssey.  I cut my teeth on Edith Hamilton’s Mythology, and I’ve read some of her other books, like The Echo of Greece, but I lacked a cohesive understanding of this period, and that’s what this course offered.  I did not have time to read everything on the syllabus, but I feel like I’ve gotten a decent start on the topic, a foundation to build on in the future, which is what I wanted.

My goals for the Reason and Persuasion course were to read The Meno at a deeper level than my previous effort, to learn more about Socrates and the Socratic Method, and to be introduced to philosophy.  Since the class covered three of Plato’s dialogues and spent two weeks covering recent developments in philosphy, a lot of what was taught was outside the scope of my interest.  I watched all the introductory material, read The Meno and The Euthyphro and listened to their lectures, and listened to the lectures on The Republic. 

I did not write the paper, or listen to the later lectures, and I only took two tests, but I feel the course was a success because I met my own goals.  Near the end of the course, I even decided to buy the textbook.  I really like the translation and I want to reread the dialogues regularly in the future, especially The Meno, since it’s the one that sets the standard for interacting with a student.  Also, I really appreciated the instructor’s style and insight and wanted to finish reading his commentary.  (The textbook was available online for free in PDF format, but I find that a difficult format to get much use out of.  I want a book I can curl up in bed with or carry with me when running errands.  I want to be able to underline and write notes, and flip quickly through pages to find things.  My brain simply has not adapted to e-readers – not for a purpose like this, anyway.)

The one class where I did not meet my own goal was Introduction to Mathematical Thinking.  That class was brutal.  The pace was too rapid for me.  It took me ages to do my homework and the only way I could understand what was going on was by asking the members of my study group to walk me through things.  They were very kind, and one in particular, Denise Gaskins of Let’s Play Math, was very patient and helpful with her clear explanations, but I was falling farther and farther behind everyone else, and I finally gave up. 

I’m not completely discouraged though – I believe that the time I spent in that class won’t go to waste, even it just sits in my mind and turns to compost.  When I took it in the fall of 2012, it was seven weeks long but since then they’ve reformatted it into a ten-week class and have offered it twice more.  I’m interested in trying it again in the future, but that will depend on... well, life.

“What do you DO with your kids if they don’t learn to read before age 10 or so?” Part 2

(Here is Part 1:  What I did with my older kids, and the post that sparked this series, Different children learn to read at different ages, and that's okay.)

I'm sorry it took me so long to get to part 2 of this series.  I pretty much hibernate in the winter, and my brain is just starting to shake off the winter fuzziness.  Has it actually been five months!?!  Golly, I'm sorry!

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Part 2: What I'm doing with my younger children

Last time I wrote about these basic elements that made up my older children's school year:

• plenty of outside play time
• Nature Study
• Bible, history, and literature
• talking about what we're reading
• math
• classical music
• hymns

I'll run through them in the same order so you can see how things have changed over the years.

Probably the biggest change involves their time spent out of doors and Nature Study.  In 2005, my husband retired from the military and got a job in rural Virginia.  We bought a house on a little over three mostly-wooded acres.  Over the years we've accumulated goats, chickens, geese, ducks, guinea fowl, cats, and a dog, so my younger children have outside chores that my older children never had -- we never even had a pet while Mike was active duty (except for a tankful of fish for a few years) because of moving so often, and having babies regularly, and my husband being out of town for a week or more at a time on occasion, including one time when he was gone for a year, and I just didn't want the added responsibility of looking after an animal.

Having the animals has been a good thing in many ways, besides the obvious benefit of having fresh, raw goat milk, fresh eggs, and meat we've raised ourselves.  The biggest benefit is giving meaningful work to my second son, who is nineteen years old and profoundly delayed in many ways.  He'll never be able to read, to live on his own, to drive, or to do most of the things that an adult needs to do in order to fit into our society.  I doubt he'd be able to hold down any kind of a job, and anyway I wouldn't really want him working away from home unless it were with a family member since his ability to communicate is so limited -- if he were ever mistreated he'd have a hard time letting us know about it, and he wouldn't be able to defend himself.

Second Son has faithfully milked the goats every day for two or three years.  We bred the does last fall and they're expecting in another few weeks and we dried them off (that is, quit milking them) last month, so he's getting a break right now, but he loves this work.  He also collects the eggs each day, makes sure all the animals have food and water, and just generally keeps an eye on them.  If they get out of the pasture the other children have to round them up for him because he doesn't have the speed or dexterity to handle them when they're on the loose.  Mike and two of the other younger children keep the goats' hooves trimmed, and doctor them if they need it, but Second Son is the one who looks after the animals' daily needs.

Whenever we butcher animals (which hasn't been very often this past year) most of the children help their daddy with the processing, and he's good about letting them do a lot of the work themselves, and teaching them the names of the organs and pointing out other interesting things.

Hopefully, learning to pay attention to the animals and anticipate their various needs will help them grow into the righteous man of Proverbs 12:10, who "regardeth the life of his beast."

I still occasionally ask them to describe something they've seen, and we've been in the habit of watching the song birds that visit the birdbath and the feeders ever since Ambleside Year 1.  We've even added Nature notebooks, though checking them just now I see that they've only got one entry each.  One August day I put a pretty little bird's nest that my youngest daughter had found that morning on a dish and sat it in the middle of the table and had them sketch it.  A pleasant activity, and I don't know why we haven't done anything more like that.  Always room for improvement.  :-D

Bible, history, and literature have been very much influenced by our use of AmblesideOnline.  I used Years 1 through 3, and by then had gotten over the rough patch I was going through with my health, so I'm mostly branching out on my own, while bringing with me what I learned from AO and still using some of the suggestions.

Our Bible readings are included in our Morning Prayers, which I've blogged about here and here.  In a nutshell, we start off with the greeting and response:  "The Lord be with you."  "And with thy spirit." "Let us pray."  This is followed by a selection from Psalm 51 ("Open my lips, O Lord / And my mouth shall proclaim your praise. . ." ).  Then we read the passages for the day.  Some years we follow the lectionary, but lately we've being going straight through the Psalms, reading a passage from Luke, and a chapter of Galatians.  Then we say the Apostles' Creed, the Lord's Prayer, and finish with a benediction, followed by "Go in peace to love and serve the Lord."  "Thanks be to God."  We say this even though they're going to be sitting down and starting school, not actually going anywhere.  When the older kids are home, they join us for prayers and stay if they have time, or leave if they need to.  Eldest Daughter particularly likes to stay when it's a Plutarch day.

Next on the agenda is poetry.  I read one selection and then we talk about it.  The conversation is always better when Eldest Daughter joins us.

These two things we do each school day.  The next three items we do once or twice a week, depending on how much time we have.  My third daughter's violin lessons have been moved from Tuesday afternoon to Monday morning and I haven't really adjusted to the change yet.

Plutarch -- we're using Anne White's study guide from AmblesideOnline as we read the Life of Nicias.  I have to stop often to let someone narrate.  Generally I ask, "What's he talking about here?" or "What just happened?"  Stopping often while reading Plutarch is necessary because the sentences are long and complex.

Then we move to Homer.  We're about half way through The Wanderings of Odysseus.  At the end of the chapter I ask, "Who would like to tell this part of this part of the story?"  Usually someone volunteers, but if needed I'll just tell someone to do it.  After the narration I'll usually ask whether anyone else wants to add anything.

I don't really know how to categorize this next item -- history, music, art. . .  It's all that.  We're studying through Professor Carol's Early Sacred Music course.  If #1 Son is home, this is what he's most interested in.  Much of the early part was filmed in Jerusalem and describes the worship at the Temple during the time of Christ.

Next is math.  I think I will need to write a post just on this subject since we're doing a lot of different things.  I've been learning a lot about teaching math and I'm pretty excited about it.  But one of the things I'm doing with my two youngest and with Second Son, is reading through the Life of Fred books.  There are math games that I play with the two youngest, together or one on one.  Also, the two youngest do a lesson from the Teaching Textbooks most days.

Something new we're doing is oral composition, using James Selby's Classical Composition series, which isn't meant to be done orally, but I don't see why delayed reading and handwriting skills should stop a child from thinking about stories and composing variations in his head.  So far I'm following his order fairly closely -- I'll write a separate post on how it works if anyone's interested.  When it's time to "write" the assignment, my eleven year old daughter wants to type it on the computer, and my thirteen year old son wants to recite the story into an audio file which I then transcribe. So far I like the way it's working.

What we're missing -- we haven't been singing hymns much lately and that's a shame.

Also, I've been using the cursive handwriting program from The Logic of English, but we haven't picked it back up yet since Christmas break.  This doubles as reading lessons because phonics instruction is built in to and I can easily add more phonics practice to this time if needed.  Obviously, as we progress with the program, it also serves as spelling lessons.

I mentioned in the "Different children read at different times" post that my then-twelve year old son had suddenly started reading, and over Christmas break, my daughter turned eleven, and started reading too.  Youngest Son has been reading several books for school on his own, but Youngest Daughter isn't to that point yet.

Wednesday with Words: A word from the Father of History

Marble bust of Herodotus
photo by Marie-Lan Nguyen
Wikimedia Commons

Herodotus of Halicarnassus here displays his inquiry, so that human achievements may not become forgotten in time, and great and marvellous deeds — some displayed by Greeks, some by barbarians — may not be without their glory; and especially to show why the two peoples fought with each other.

[Herodotus, The Histories, translated by Aubrey de Sélincourt, revised by John Marincola.]


Herodotus (c. 484–425 BC) was born at Halicarnassus, which is on the Aegean coast of modern day Turkey.  Cicero called him the Father of History because he is the first person we know of who systematically inquired into events of the past and tried to make sure that they had actually happened before creating his own narrative.

That seems obvious to us, but compare his book's opening lines with the usual way of telling of memorable deeds of the past:

Sing, O Goddess, the anger of Achilles son of Peleus, that brought countless ills upon the Achaeans. (The Illiad. tr. Butler)

and:

Speak to me, Muse, of the adventurous man who wandered long after he sacked the sacred citadel of Troy.  (The Odyssey, tr. Palmer)

Homer appeals to the goddess for inspiration, and then tells how the gods' actions led to the events following.

But Herodotus begins by saying that he's going to tell about great things people have done and then gives a lengthy account of the Persian's version of what caused the war:  Io was kidnapped by a group of Phoenecian sailors and then in retaliation Europa was kidnapped by a group of Greeks followed by the abduction of Medea which inspired Paris to kidnap Helen.  Evidently the Persians thought all this kidnapping was no big deal, but "the Greeks, merely on account of a girl from Sparta, raised a big army, invaded Asia and destroyed the empire of Priam."

All of this caused the eternal enmity between the Greeks and the Persians.  No mention at all of gods, but simply the actions of men — things that can be verified by inquiry.

Just for fun, here's the original Greek text:

Ἡροδότου Ἁλικαρνησσέος ἱστορίης ἀπόδεξις ἥδε, ὡς μήτε τὰ γενόμενα ἐξ ἀνθρώπων τῷ χρόνῳ ἐξίτηλα γένηται, μήτε ἔργα μεγάλα τε καὶ θωμαστά, τὰ μὲν Ἕλλησι τὰ δὲ βαρβάροισι ἀποδεχθέντα, ἀκλεᾶ γένηται, τά τε ἄλλα καὶ δι᾽ ἣν αἰτίην ἐπολέμησαν ἀλλήλοισι.

[Source:  Sacred Texts]

Oh, and the "word" from Herodotus?  The third word in Greek is ἱστορίης, which means inquiry.  It is pronounced something like istoria, and gives us our word history.

And there you have the history of History.

Wednesday with Words: The power of a poet

We all know what it means to be spartan – stern, austere, brave, frugal – but Sparta, the home of Menelaus and Helen, was not always “spartan.”  During the Dark Age and the early Archaic Age of Greece she was not so different from other Greek cities like Athens.  Sparta’s merchants traveled to other cities to trade, her poets wrote lyric verse, her craftsmen and artisans flourished.

In the eighth and seventh centuries B.C. the Spartans fought two wars with neighboring Messenia. During the First Messenia War, Lycurgus gave his famous laws to Sparta, but scholars see the warrior-poet Tyrtaeus, who lived during the Second Messenian War, as the man who first envisioned the true Spartan – the people they became and whom we think of as Classical Spartans.

“Spartan Soldier”

~Tyrtaeus of Sparta (c. 620 B.C.)

It is beautiful when a brave man of the front ranks,

falls and dies, battling for his homeland,

and ghastly when a man flees planted fields and city

and wanders begging with his dear mother,

aging father, little children and true wife.

He will be scorned in every new village,

reduced to want and loathsome poverty; and shame

will brand his family line, his noble

figure. Derision and disaster will hound him.

A turncoat gets no respect or pity;

so let us battle for our country and freely give

our lives to save our darling children.

Young men, fight shield to shield and never succumb

to panic or miserable flight,

but steel the heart in your chests with magnificence

and courage. Forget your own life

when you grapple with the enemy. Never run

and let an old soldier collapse

whose legs have lost their power. It is shocking when

an old man lies on the front line

before a youth: an old warrior whose head is white

and beard gray, exhaling his strong soul

into the dust, clutching his bloody genitals

into his hands: an abominable vision,

foul to see: his flesh naked. But in a young man

all is beautiful when he still

possesses the shining flower of lovely youth.

Alive he is adored by men,

desired by women, and finest to look upon

when he falls dead in the forward clash.

Let each man spread his legs, rooting them in the ground,

bite his teeth into his lips, and hold.

Content source:  http://uts.cc.utexas.edu/~sparta/topics/articles/academic/poetry.htm#tyrtaeus

Wednesday with Words: "House and wife and an ox for the plough"

This semester I’m taking a seven week-long class from Coursera on The Ancient Greeks. Check out the syllabus – it’s brutal.

This quote is from one of my assigned readings this week, a selection from Aristotle’s Politics, on the polis.  I’ve deleted a longish section because I wanted to focus on Aristotle’s description of the oikos, the household or family.

He who thus considers things in their first growth and origin, whether a state or anything else, will obtain the clearest view of them. In the first place there must be a union of those who cannot exist without each other; namely, of male and female, that the race may continue (and this is a union which is formed, not of deliberate purpose, but because, in common with other animals and with plants, mankind have a natural desire to leave behind them an image of themselves), and of natural ruler and subject, that both may be preserved…. 

Out of these two relationships between man and woman, master and slave, the first thing to arise is the family, and Hesiod is right when he says, 

        ‘First house and wife and an ox for the plough,’ 

for the ox is the poor man’s slave. The family is the association established by nature for the supply of men’s everyday wants, and the members of it are called by Charondas ‘companions of the cupboard,’ and by Epimenides the Cretan, ‘companions of the manger.’

Source:  http://www.fordham.edu/halsall/ancient/Aristotle-politics-polis.asp

Greatness

It’s October and that means I’m thinking about Alfred the Great whose feast day is on the 26th.  We’re enjoying our tradition of reading Chesterton’s The Ballad of the White Horse, my favorite long poetic work, which is about Alfred – the only English king to be called “the Great” – and his struggle to stop the Danish invaders. This is not a retelling of historical events in verse, but an epic poem of the legendary Alfred, portraying the eternal conflict between Christian faith and pagan nihilism.

It is layer upon layer of truth and beauty, and greatness. I think this is our fifth time to read it, and every time I find a new gem, which is one reason it’s so important to be deeply familiar with a few great works.

The passage that stands out the most to me this time is from Book II: The Gathering of the Chiefs. In Book I, Alfred had a vision of Mary in which he asked whether he would succeed in driving out the pagan invaders. She refused to answer him, saying only that it would get worse and he must be brave. In Book II, Alfred has been to Eldred, a chief who is of Saxon descent, and Mark, of Roman blood. He now comes to Colan, who is Welsh and Irish, representing the pre-Roman Britons. I’ve shared before the passage where Colan is introduced to us. Here is Alfred’s encounter with him:

Lifting the great green ivy
    And the great spear lowering,
One said, “I am Alfred of Wessex,
    And I am a conquered king.”

And the man of the cave made answer,
    And his eyes were stars of scorn,
“And better kings were conquered
    Or ever your sires were born.

“What goddess was your mother,
    What fay your breed begot,
That you should not die with Uther
    And Arthur and Lancelot?

“But when you win you brag and blow,
    And when you lose you rail,
Army of eastland yokels
    Not strong enough to fail.”

“I bring not boast or railing,”
    Spake Alfred not in ire,
“I bring of Our Lady a lesson set,
This—that the sky grows darker yet
    And the sea rises higher.”

Then Colan of the Sacred Tree
    Tossed his black mane on high,
And cried, as rigidly he rose,
“And if the sea and sky be foes,
    We will tame the sea and sky.”

~*~ ~*~ ~*~

Look at that again:

“But when you win you brag and blow,
    And when you lose you rail,
Army of eastland yokels
    Not strong enough to fail.”

After we finished reading Book Two, I went back and read that passage over again to my children. It is said that if you want to know what something is, one thing you should do is learn what it is not. Alfred does not respond in anger, but humbly accepts the rebuke and proves proves his greatness by stating that he’s planning on continuing the fight, even if it ultimately ends in defeat.

If you read yesterday’s post, you’ll know that I need these lessons myself as much as, if not more than, my children.


~*~ ~*~ ~*~ 


The Ballad of the White Horse is available online for free at Gutenberg.com and for Kindle, but I highly recommend the hardback by Ignatius Press, especially if you’re going to be reading it over and over again, which of course you should. This copy is elegantly laid out, uses a simple and beautiful font, and is generously illustrated with woodcuts by Robert Austin. The introduction gives a brief historical note on the events in the poem as well as some discussion of the poem itself, and contains a photograph of the actual white horse, which is cut into the turf on the side of a hill and filled with chalk – it’s nearly 400 feet long and its age is unknown. When the Romans asked the Britons about it, they said that when their people first arrived it was already there, and the people who were there before them did not know who had made it. This copy of the book also has a lot of end notes with helpful and interesting tidbits, but there are no notes in the text itself, so you’re not distracted by them while reading.

Also helpful is Benjamin Merkle's biography, The White Horse King (also available for Kindle).


~*~ ~*~ ~*~


Previous entries on Alfred the Great:

Alfred the Great post from the 26th of October, 2005; history, prayers, and lots of cool links; don’t miss it!

Three selections from Poetry Month 2008:
The Way of the Cross (Mary’s answer to Alfred, when he asked whether he would prevail over the enemy)
The Great Gaels of Ireland (where Colan is introduced)
The King’s Laughter (from the episode of the old woman and burnt cakes)

All my posts where he’s mentioned are filed under the Alfred the Great label

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I'm an Amazon Affiliate.  If you click through the links to The Ballad of the White Horse and buy it, I'll earn a little bit for advertising on my blog.

A Celtic monastery in Brittany

My friend Eleanor took these pictures recently and they're too beautiful not to pass on.

The early Celtic Christian monks were famous for their evangelism, and apparently thought nothing of taking Christianity to the "uttermost parts of the Earth". This abbey is a good example of a Celtic Christian monastic community that did just that. A group of them must have gotten into a boat, and crossed from Cornwall to Brittany, and proceeded to find the most remote spot they could get to. They did this so well that it wasn't even easy for us to find.

This abbey was first founded by a monk in the fifth century. From very rough and modest beginnings, it grew over the next 400 years to have a nice, classic Romanesque abbey church, which was (oh good grief, not again) destroyed by the Norsemen. Those would be my ancestors, argh. After the Norsemen had had their fun, the monks rebuilt. In about another 400 years the place was again demolished, this time by the Normans. Bad Normans! Same folks, really, as the Norse. One stone higher, responded the monks and built yet another establishment which lasted about another 500 years, and was them abandoned. Today it is owned by the Benedictines, who have not restored it to use, but are conserving it and have established a museum collecting its artifacts and history.

Be sure to visit Eleanor's blog to see all the pictures and read her comments on them.

Thanks so much for sharing, Eleanor!