Reaching Back

Well, as of Monday vacation will be officially over over - although I've already been attending meetings and planning and preparing all week and throughout the break. Before getting back in the classroom I just want to look back at break - times of fellowship and gaming and celebrating - what a good break we had!!

For the first time since August I got to truly relax . . . ahh . . . so many books, so little time!!We had friends and family over and played lots and lots of games! I even played a game of solitaire Mah-jongh and won. Here's the proof (might not happen again for a while!).We had fun celebrating the season - decorating our new house for the first time - having everyone at our place for the Christmas day meal - getting cards, letters and pictures from friends and family near and far - good stuff!
I love this picture Sierra took of me at our family party!We celebrated at Mom and Dad's too! . . . and the guys opened gifts grom Grandma in Michigan!David and the boys were back at it a week ago - note the somber expressions - actually they've made a good transition back, and I trust I will too, but it's good to look back and remember the awesome (and much needed) break that we had!
Happy New Year everyone!

Lorelei

It is no night to drown in:
A full moon, river lapsing
Black beneath bland mirror-sheen,

The blue water-mists dropping
Scrim after scrim like fishnets
Though fishermen are sleeping,

The massive castle turrets
Doubling themselves in a glass
All stillness. Yet these shapes float

Up toward me, troubling the face
Of quiet. From the nadir
They rise, their limbs ponderous

With richness, hair heavier
Than sculptured marble. They sing
Of a world more full and clear

Than can be. Sisters, your song
Bears a burden too weighty
For the whorled ear's listening

Here, in a well-steered country,
Under a balanced ruler.
Deranging by harmony

Beyond the mundane order,
Your voices lay siege. You lodge
On the pitched reefs of nightmare,

Promising sure harborage;
By day, descant from borders
Of hebetude, from the ledge

Also of high windows. Worse
Even than your maddening
Song, your silence. At the source

Of your ice-hearted calling-
Drunkenness of the great depths.
O river, I see drifting

Deep in your flux of silver
Those great goddesses of peace.
Stone, stone, ferry me down there.

Sylvia Plath (1932-1963)

New Year Reminder

If we continue to do today
what we did yesterday,
we will not be ready for tomorrow.

- author unknown

Like a Bicycle

Life is like riding a bicycle. To keep your balance you must keep moving.

- Albert Einstein (1879-1955)

12 Days of Christmas Can-Can

For the Time Being

He is the Way.
Follow Him through the Land of Unlikeness;
You will see rare beasts, and have unique adventures.

He is the Truth.
Seek Him in the Kingdom of Anxiety;
You will come to a great city that has expected your return for years.

He is the Life.
Love Him in the World of the Flesh;
And at your marriage all its occasions shall dance for joy.

from: For the Time Being: A Christmas Oratorio
W. H. Auden (1942)

No Comment

Sets a Thing Significant

Death sets a Thing significant
The Eye had hurried by
Except a perished Creature
Entreat us tenderly

To ponder little Workmanships
In Crayon, or in Wool,
With "This was last Her fingers did"—
Industrious until—

The Thimble weighed too heavy—
The stitches stopped — by themselves—
And then 'twas put among the Dust
Upon the Closet shelves—

A Book I have — a friend gave—
Whose Pencil — here and there—
Had notched the place that pleased Him—
At Rest — His fingers are—

Now — when I read — I read not—
For interrupting Tears—
Obliterate the Etchings
Too Costly for Repairs.

Emily Dickinson (1830-1886)

Time

I love this quote and this comic, but somehow I think it applies more to my life than that of my teens!!

Weekend Edition Puzzle

While listening to NPR's Weekend Edition yesterday, I heard the following puzzle, which was created by Scott Kim:

Name five two-digit numbers that are evenly spaced out — like 32, 34, 36, 38 and 40 — in which all 10 digits from 0 to 9 are used once each. What numbers are these?

My son came up with one answer, which I thought was the only one, but when I gave it as extra credit to my students today as they were taking their exam I saw two other correct answers as well. Can you solve solve this puzzle? Can you come up with more than one answer?

After December 17 I will put the answers I am aware of in the comments section. No fair peeking until you've come up with a solution of your own! If you come up with one I do not have listed, please comment and let me know!

PS I've also posted this on my "Fun Math" blog. If you are interested in more things of this type, you might want to check it out at:

http://heidifunmath.blogspot.com/

BY THE WAY, if you are reading this before noon on Thursday, December 17, you can still enter. Go to Weekend Edition at http://www.npr.org/templates/story/story.php?storyId=121382258 for details.

Wingless

Though long (usually I have most appreciation for short poetry) this is one of my favorite poems. I find it very clever while at the same time very accessible, two characteristics I also like in poetry. Even if you, like me, are not a fan of long poetry, you might want to give this one a chance.

In my search for it online (so I didn't have to type it all out myself), I came across a wonderful post centered on this piece. It has some lovely positive thoughts on the ways in which we connect in our modern world - and it tells an interesting story that I enjoyed very much. How cool that as I looked for a poem to share on my blog I found a lovely story about connecting on someone else's site, which in itself was an interesting way to connect.

The Labyrinth

Anthropos apteros for days
Walked whistling round and round the Maze,
Relying happily upon
His temperament for getting on.

The hundredth time he sighted, though,
A bush he left an hour ago,
He halted where four alleys crossed,
And recognised that he was lost.

"Where am I? Metaphysics says
No question can be asked unless
It has an answer, so I can
Assume this maze has got a plan.

If theologians are correct,
A Plan implies an Architect:
A God-built maze would be, I'm sure,
The Universe in miniature.

Are data from the world of Sense,
In that case, valid evidence?
What in the universe I know
Can give directions how to go?

All Mathematics would suggest
A steady straight line as the best,
But left and right alternately
Is consonant with History.

Aesthetics, though, believes all Art
Intends to gratify the Heart:
Rejecting disciplines like these,
Must I, then, go the way I please?

Such reasoning is only true
If we accept the classic view,
Which we have no right to assert,
According to the Introvert.

His absolute pre-supposition
Is--Man creates his own condition:
This maze was not divinely built,
But is secreted by my guilt.

The centre that I cannot find
Is known to my Unconscious Mind;
I have no reason to despair
Because I am already there.

My problem is how not to will;
They move most quickly who stand still;
I'm only lost until I see
I'm lost because I want to be.

If this should fail, perhaps I should,
As certain educators would,
Content myself with the conclusion;
In theory there is no solution.

All statements about what I feel,
Like I-am-lost, are quite unreal:
My knowledge ends where it began;
A hedge is taller than a man."

Anthropos apteros, perplexed
To know which turning to take next,
Looked up and wished he were a bird
To whom such doubts must seem absurd.

W. H. Auden (1907-1973)

Quote of the Day

Nothing is foolproof to a sufficiently talented fool.

author unknown

A Day in the Life

We had a good day yesterday, and for some reason I was in the mood to capture it with images. It was a day of work and of fun, of getting things done and of enjoying each other.David made more progress in the garage by building MORE shelves to hold MORE stuff - a seemingly endless process!We got our first Christmas decorations put up for the year. For the first time ever we have a fireplace and mantle - a place to put stockings and a way for Santa to get in! :-)We even got our tree! YEA!! (I'm not sure when it will get decorated, but it's here and up at least!)I began preparing an extensive study guide for my calculus students to use as they prepare for the final exam in a week.The weather changed a lot over the course of the day, but was mostly cold and blustery . . . . . . but did cold, blustery weather stop the intrepid runners?!
No way!
Here they are warming up for their 5.75 mile run.Among other things Anthony took his SAT test today - here he is reading for relaxation after the SAT and before taking me on in Magic! And then some reading for school too! (Nice face Anthony!)Caleb and Jacob relaxing in their way.Time for dinner:Anthony preparing, happily, to take his first bite of his Dagwood-sized burger!We ended our day with a game of Life. I don't think I'd played this since I was a kid. What a hoot! All in all a good day - filled with many things!

A Place of Abundance

David shared the following passage with me tonight. It was part of his reading last night and really struck him as describing our life over recent years and where we are now. He read it to me without telling me why, and it came across the same way to me. We are so grateful for the blessings of the present and the protection through the past!

From Psalm 66:

8 Praise our God, O peoples,
let the sound of his praise be heard;

9 he has preserved our lives
and kept our feet from slipping.

10 For you, O God, tested us;
you refined us like silver.

11 You brought us into prison
and laid burdens on our backs.

12 You let men ride over our heads;
we went through fire and water,
but you brought us to a place of abundance.

Alone

It is not by driving away our brother that we can be alone with God.

George MacDonald (1824-1905)

Just Looking Round

We do not play on Graves—
Because there isn't Room—
Besides—it isn't even—it slants
And People come—

And put a Flower on it—
And hang their faces so—
We're fearing that their Hearts will drop—
And crush our pretty play—

And so we move as far
As Enemies—away—
Just looking round to see how far
It is—Occasionally—

Emily Dickinson 1830-1886

In a Flood of Remembrance

Piano

Softly, in the dusk, a woman is singing to me;
Taking me back down the vista of years, till I see
A child sitting under the piano, in the boom of the tingling strings
And pressing the small, poised feet of a mother who smiles as she sings.

In spite of myself, the insidious mastery of song
Betrays me back, till the heart of me weeps to belong
to the old Sunday evenings at home, with the winter outside
And hymns in the cosy parlour, the tinkling piano our guide.

So now it is vain for the singer to burst into clamour
With the great black piano appassionato. The glamour
Of childish days is upon me, my manhood is cast
Down in the flood of remembrance, I weep like a child for the past.

D. H. Lawerence (1885-1930)

Not Tall Enough for Me Today!

(CLICK TO ENLARGE)

Dinner Conversation at Our House

Dinner conversation Sunday, November 22,2009 (since family members don't always appreciate being identified in my blog, I have eliminated names.):

Speaker 1: It's nice that taking care of this big house isn't as time consuming as we feared it might be.

Speaker 2: Well, time is ALWAYS being consumed. The question is what are we choosing to have it consumed by?

Speaker 3: Time isn't consumed. Time is passing.

Speaker 4: What happens to time after it passes?

This is the environment by which I am surrounded!
(And I think it's cool :-)

From Generation to Generation, We Will Remember

Lord, you have been our dwelling place throughout all generations.

I just got the news that my great uncle Paul passed away this week. Now Grandpa is the only one left of the 10 siblings. It's hard to believe that nearly that whole generation has passed.Here are my Van Dyken Great Grandparents on their 45th anniversary. As I look at their eyes in this picture it just does seem hard to believe that they and 9 of their 10 kids have passed on to glory (though nearly all made it into their 90's, and Great Grandpa made it to 100).Here are Great Grandma and Great Grandpa just starting out with the first 4 of their ten kids: Anne, Dinah, Bert and Sadie. My grandpa was the next baby to come along.Here is the whole family - not sure of the year - in the 1950's maybe? Time like an ever rolling stream bears all her sons away --
-- very true, very true.

Psalm 90

Lord, you have been our dwelling place
throughout all generations.

Before the mountains were born
or you brought forth the earth and the world,
from everlasting to everlasting you are God.

You turn men back to dust,
saying, "Return to dust, O sons of men."

For a thousand years in your sight
are like a day that has just gone by,
or like a watch in the night.

You sweep men away in the sleep of death;
they are like the new grass of the morning-

though in the morning it springs up new,
by evening it is dry and withered.

The length of our days is seventy years—
or eighty, if we have the strength;
yet their span is but trouble and sorrow,
for they quickly pass, and we fly away.

Teach us to number our days aright,
that we may gain a heart of wisdom.

Relent, O LORD! How long will it be?
Have compassion on your servants.

Satisfy us in the morning with your unfailing love,
that we may sing for joy and be glad all our days.

Make us glad for as many days as you have afflicted us,
for as many years as we have seen trouble.

May your deeds be shown to your servants,
your splendor to their children.

May the favor of the Lord our God rest upon us;
establish the work of our hands for us—
yes, establish the work of our hands.

Long Time Coming

This is a milestone in my life, so, though it may be gauche I am going to post notes from my chalkboard today.
Today, for the first time in the 26 years since I learned it I had opportunity to teach
The Fundamental Theorem of Calculus.
Here is the proof (literally and figuratively!):TWENTY-SIX years later, I have FINALLY taught this!!

I usually use the overhead projector, but this called for the boards - ALL of them!

Plunge Downward

Grow not too high, grow not too far from home,
Green tree, whose roots are in the granite's face!
Taller than silver spire or golden dome
A tree may grow above its earthy place,
And taller than a cloud, but not so tall
The root may not be mother to the stem,
Lifting rich plenty, though the rivers fall,
To the cold sunny leaves to nourish them.
Have done with blossoms for a time, be bare;
Split rock; plunge downward; take heroic soil, ---
Deeper than bones, no pasture for you there:
Deeper than water, deeper than gold and oil:
Earth's fiery core alone can feed the bough
That blooms between Orion and the Plough.

Edna St. Vincent Millay (1892-1950)

Fallen Giant

One of the giants of twentieth century mathematics fell last month at the age of 96. He was called "one of the last of the greatest who worked in nearly every field of mathematics." He was called by one student, "very unpredictable and very wise," and a colleague considered him the most interesting person he had ever known.

Gefland never finished high school and never attended college as an undergraduate student. He went to Moscow at age 16 or 17 and worked odd jobs but was always interested in mathematics, attended seminars, and at the age of 19 was admitted directly to graduate school of Moscow State University. He worked in extremely abstract areas of mathematics, which most people do not even know exist, but much of his work has profound application as well, and some medical imaging tests that most of us benefit from at some time in our lives (such as 3D images created by MRIs and CAT scans) are possible due to his work. It is said that he sought not just to teach the rules of math but also the beauty and exactness of his field (my kind of guy!). He also had a sense of humor and was quoted in a 2003 interview with the New York times as saying:

“Mathematics is a way of thinking in everyday life. It is important not to separate mathematics from life. You can explain fractions even to heavy drinkers. If you ask them, ‘Which is larger, 2/3 or 3/5?’ it is likely they will not know. But if you ask, ‘Which is better, two bottles of vodka for three people, or three bottles of vodka for five people?’ they will answer you immediately. They will say two for three, of course.”

His obituary (from which I took the information above) can be found at
http://www.nytimes.com/2009/10/08/science/08gelfand.html

A Chainless Soul

Riches I hold in light esteem
And Love I laugh to scorn
And lust of Fame was but a dream
That vanished with the morn–

And if I pray, the only prayer
That moves my lips for me
Is–"Leave the heart that now I bear
And give me liberty."

Yes, as my swift days near their goal
'Tis all that I implore
Through life and death, a chainless soul
With courage to endure!

Emily Bronte (1818-1848)

His Own Words

David just let me know that he posted his reflections about being 2-years post-stroke on his website. I had posted mine below. If you'd like to check his out, click on DAVID at right.

Early Thanksgiving

We are so thankful to be where we are today and not where we were 2 years ago today.

Two years ago today I was sitting in the intensive care unit at David's side - not entirely sure he would make it through the night - and if he did, not sure whether or not he would ever walk again. He has come so far in these two years - not yet as far as he would like, but so far from where he was. We are so thankful!

(Here is the post I wrote that day asking for prayer, and I want to say "thank you" again to those who did and have upheld us in prayer. We have seen those prayers answered!)

Game Theory and National Policy

A friend sent me this link, and I found it to be one of the clearest explanations of The Prisoner's Dilemma I'd ever heard. As the speaker relates this to foreign policy and explains what it has to say about how we should most wisely interact with other nations, it seemed to me to be a piece of crystal clear logic. Who says you don't use math in everyday life?! Click here to go to the video you see pictured below.

Fall Stuff

I have a great new job, and I also now have no life, but although my vision is filled with the following nearly 24/7, I want to get some pictures up of fall activities for family and friends far away (and nearby too). There is a lot going on, and for now I'll let my family take it in, and I'll try to catch up over Christmas vacation.I move from one table to the other - to the floor - back to a table - keeps me from cramping up over long periods of time.We have a new house:Someday I hope to read some books in the new house.The boys (including David) are enjoying the pool.The boys are also enjoying the new experience of having a 2-story house.We continue to cheer on the Enochs cross-country team, and especially Anthony (who in this picture is hidden behind the second person from the left).We've had some weird - and beautiful - weather.Caleb has found his true identity as "ketchup boy" (aka "Chip" in his youth group).We are so thrilled that Mike and Amy and Sierra and newly arrived Ava live so near us now - in a home we can see from our new home! Another reason I'm eager for break is to have some time with them!We took a quick trip to one of our favorites - Knight's ferry:Here are my special guys at Knight's Ferry. I need to get back to my "task" and not lay it aside, but I need to record that life is going on in my near vicinity anyway, and I'm eager to rejoin it soon!