A Few For Now

We just got in from our annual Thanksgiving camping trip to Pismo Beach. We got some great pictures, but they sure don't show how cold it was! After sleeping in a tent I am more thankful than ever for central heat, indoor plumbing, and much else! A few photos for now and then off to bed for me! A real bed! Ahhhhhh!

Only in Mathematics

Only in mathematics was there that sense of moving through another dimension, one that didn't exist in time and place - that feeling of falling into and through a puzzle, of having it surround you in a physical way.

from The Eight by Katherine Neville

Hide and Seek

Here where the dead lie hidden
Too well ever to speak,
Three children unforbidden
Are playing hide-and-seek.

What if for such a hiding
These stones were not designed?
The dead are far from chiding;
The living need not mind.

Too soon the stones that hid them
Anonymously in play
Will earn their names and bid them
Come back and hide to stay.

Robert Francis (b. 1901)

Olber's Paradox

The heavens hold more stars than earth has grains
Of sand, and given time, each tiny sun
Combined should make a world where starlight stains
The sky bright white and dark would be undone.
And yet the night remains. the dim stars gleam
Their separate ways, and constellations drawn
Connect their dots, while under them we dream
And sleep, then wake to such a thing as dawn.
The universe, expanding since its birth,
Is larger, older than its light; sublime,
The force that keeps this constant day from earth
The same that measures out our years -- is time:
The limitation that provides us night
And saves us all from unremitting light.

Robert W. Crawford (2004)

Fall and Night Fall

It's finally fall in California (though you wouldn't have known it by the warm temps today!)


"Fossils" of a fall long ago!


Fall and summer fighting for dominance:


A certain slant of light . . .


Sunset through my home-office window . . .



. . . and nightfall:

At Arlington

Two dates carved in stone above his grave
tell us he was seventeen, not how
this soldier died, nor whether he was brave
or terrified, or both. No matter now:
the only life he had to give, he gave.

Wiley Clements 2004

Random Act of Culture

YouTube link:
http://www.youtube.com/watch?v=wp_RHnQ-jgU

In This Short Life

In this short Life
That only lasts an hour
How much -- how little -- is
Within our power

Emily Dickinson (1830-1886)

STEPHEN TO LAZARUS

But was I the first martyr, who
Gave up no more than life, while you,
Already free among the dead,
Your rags stripped off, your fetters shed,
Surrendered what all other men
Irrevocably keep, and when
Your battered ship at anchor lay
Seemingly safe in the dark bay
No ripple stirs, obediently
Put out a second time to sea
Well knowing that your death (in vain
Died once) must all be died again?

C. S. Lewis (1898-1963)

Status

On facebook I can post a status - in some sense that's what this post is - and the status is good!

I had such a busy day I didn't notice the date (Nov. 2) until now. It is 3 years since David's stroke. Whew! It seems both longer ago and shorter ago. Though things are still not as they were before that, we are thankful for the tremendous healing that has been granted by God's grace!

We are sure in a different spot three years ago today!

His Kingdom is Forever

I missed singing this today, so am posting it instead:

A mighty fortress is our God, a bulwark never failing;
Our helper He, amid the flood of mortal ills prevailing:
For still our ancient foe doth seek to work us woe;
His craft and power are great, and, armed with cruel hate,
On earth is not his equal.

Did we in our own strength confide, our striving would be losing;
Were not the right Man on our side, the Man of God’s own choosing:
Dost ask who that may be? Christ Jesus, it is He;
Lord Sabaoth, His Name, from age to age the same,
And He must win the battle.

And though this world, with devils filled, should threaten to undo us,
We will not fear, for God hath willed His truth to triumph through us:
The Prince of Darkness grim, we tremble not for him;
His rage we can endure, for lo, his doom is sure,
One little word shall fell him.

That word above all earthly powers, no thanks to them, abideth;
The Spirit and the gifts are ours through Him Who with us sideth:
Let goods and kindred go, this mortal life also;
The body they may kill: God’s truth abideth still,
His kingdom is forever.

Set Daily Puzzle

I just found one of my favorite games online in a solitaire version. The game is Set and is made up of cards having 4 attributes: color, shape, shading and number. There may be 1, 2, or 3 shapes on the card. The shapes may be diamonds, ovals or squiggles. The shading may be solid, lined or open. And the color may be green, red or purple.

The goal is to find sets of three cards that, for each characteristic are all the same or all different. For instance, the column on the left above contains a set because all three cards have the same color but all have a different number of items, a different shading, and a different shape. The second column from the left is not a set because although they all have the same color and the same number, there are two open figures and also two diamonds (not all three the same and not all three different with these last 2 attributes). Remember, for each attribute you must have three matches or three differences. How many sets can you find in this image?

There is a new game posted daily at:
http://www.setgame.com/
I know I'm going to be checking in on this!

A Bright Light Has Gone Out

A colleague approached me today and asked if I had heard that Mandelbrot had died. Though I only met him once I feel I've lost a friend. Benoit Mandelbrot was a French mathematician who founded the field of fractal geometry - one of my favorite branches of mathematics. The field is innovative, applicable and beautiful. He was often interviewed for science programs, and I am posting a link to a NOVA presentation in which his life and work are explored (click at bottom of post). Even if you are not a math person, this is a presentation I highly recommend. To me he was not just a great mathematician but a great person who got outside the box and looked beyond the received wisdom of his day to bring together something truly ground-breaking that enriches us all.


Click here to view video.

His obituary from the American Mathematical Society can be found at the following link:

http://www.ams.org/news?news_id=892

Flies

With all the flies in our area this autumn, and David swatting them left and right, I can't stop thinking about poetry involving flies!

SHAKESPEARE:

As flies to wanton boys are we to th' gods,
They kill us for their sport.

King Lear Act 4, scene 1

WILLIAM BLAKE:

Little Fly,
Thy summer's play
My thoughtless hand
Has brush'd away.

Am not I
A fly like thee?
Or art not thou
A man like me?

For I dance
And drink & sing:
Till some blind hand
Shall brush my wing.

If thought is life
And strength & breath
And the want
Of thought is death;

Then am I
A happy fly,
If I live,
Or if I die.

from Songs of Experience 1794

A Bit of Fall Stuff 2010

We've had some crazy weather out here in CA this year - kinda chilly this summer, which bummed me out because it's the first year we've had a pool - and rather hot this fall, now that I don't have time to swim! - but we've had some beautiful skies:
As of this month we've been in our "new" house for a year - really enjoying it and just thinking a lot right now of friends and family who helped us with that move at that very busy time last year!

It's very cozy...
...and very pretty......and our bulbs transplanted from the old house are finally making an initial showing......and our boys, more and more, are growing into young men! (Where's my baby?)
Last week something really amazing happened. People used to talk about "random acts of kindness." I hadn't seen that phrase recently, but I experienced not one but two of them in the same day! I was out for a quick walk - very short and totally on a whim - before going to work, and a woman waiting for her bus to take her to her day school struck up a conversation with me and then handed me a flower and wished me a good day! My whole heart was just smiling all day! (Oh, and her name was "Anjelica" - pronounced the Spanish way - halfway home I realized that's from the same root as "angel." I think she was.)And then I went to teach, and after my Math 10 class - last class of the day - I found two Hershey's Dark candy bars in my bag that a student had dropped in anonymously. Below is what remains. I feel inspired to go out and do random acts of kindness too now!
And I went and got prettied-up today - an unsual event for a tom-boy like me - threading (Ooo...ouch!) and a haircut.
So that's what's going on around here this fall (in my life anyway).

In the Connecting Tube

Parts of an Hourglass

Connecting Tube

A narrow tube connects the bulbs to allow the sand to flow between the bulbs. The tube is made of the same material as the bulbs, whatever it may be.

More to come (after more sand falls).

A bit more sand has fallen - though not enough to finish this yet, but a television commercial is right along the same lines:

What We Need

Geese appear high over us,
pass, and the sky closes. Abandon,
as in love or sleep, holds
them to their way, clear
in the ancient faith: what we need
is here. And we pray, not
for new earth or heaven, but to be
quiet in heart, and in eye,
clear. What we need is here.

Wendell Berry (b. 1934)

Better Spent

A REPROOF

Grook in answer to a long explanatory letter

In view of your manner
of spending your days
I hope you may learn,
before ending them,
that the effort you spend
on defending your ways
could be better spent on
amending them.

Piet Hein (1905-1996)

It Just Doesn't Get Any Better Than This!

Artprize - Shimmering Stones

I wish I could be in Grand Rapids right now to take in Artprize (September 22-October 10). In 192 venues in downtown GR the work of 1713 artists is displayed. The pubic votes on their favorites, and the winner is announced October 7. The photograph above, by Bill Vriesema, is part of one of the displays that caught my eye online. You can view others by clicking Artprize. All sorts of art - big and small - painting and sculpture - you name it - is part of this - and you can vote for your favorites online!

Made My Day

There is a YouTube TED presentation put on by math teacher Dan Meyer that describes in the opening sentences the plight in which math teachers often find themselves:

"Can I ask you to recall a time when you really loved something - a movie, an album, a song or a book? And you recommended it whole-heartedly to someone you also really liked, and you anticipated that reaction, you waited for it, and it came back and the person really hated it. So by way of introduction that is the same state in which I've spent every working day of the last 6 years. I teach high school math.

I SELL A PRODUCT TO A MARKET THAT DOESN'T WANT IT BUT IS FORCED BY LAW TO BUY IT."

That's a tough spot!

I shared a couple of posts ago how I try to work to "create wonder" in my classes. Given the above, it's a tough prospect, but when it works it is a joyful thing for me and my students.

Today, in two situations, I saw the wonder, and it was beautiful!

One of these things was a student coming to office hours today who is in my Math for Liberal Arts class - basically a Math Appreciation class - just as there are Music Appreciation classes and Art Appreciation classes. We do something similar, sampling a wide variety of topics. I try to bring in the topics that are the most beautiful (tessellations and fractals) and that are the most different from arithmetic and algebra but are very applicable (topology/graph theory and logic). It was so cool talking with this student today, because he saw how much of the purpose of class was to develop a new way of looking at things, a mathematical vision that lends itself to a bigger picture of life and also new problem solving techniques that stretch the brain to envision things and approach them in new and productive ways. YES!!

Another situation was with another Math 101 student. One aspect of this class is math history, and the students will be teaching that part. They each need to select a mathematician on whom to do a presentation. This student had interacted with me a bit, debating which one to choose. She finally decided on Piet Hein. That's a name that appears regularly on my blog because he is a poet as well as a mathematician (as well as a scientist, inventor, game creator, and designer). He created a type of poetry that is one of my favorites: Grooks. For example, one Grook that has come to my mind a lot lately (in the face of the dilemma described in the opening lines of this post) is one that I've posted before:

THE CURE FOR EXHAUSTION

Sometimes, exhausted
with toil and endeavour,
I wish I could sleep
for ever and ever;
but then this reflection
my longing allays:
I shall be doing it
one of these days.

In sending me her official request to have Piet Hein as her mathematician, this student wrote the following:

I'll speak of Hein's mathematical psalms,
Although, I must add this caveat:
I admit to having some qualms
About choosing the teacher's favorite!

KH

I've had a smile on my face all evening from these two interactions. Teaching math is not easy, but sometimes it has some pretty rewarding moments, and today I had not just one but TWO of them that made my day!

I Need More

I need more than a truth to believe
I need a truth that lives, moves, and breathes
To sweep me off my feet
It ought to be

More like falling in love
Than something to believe in
More like losing my heart
Than giving my allegiance
Caught up, called out...

...all religion ever made of me
Was just a sinner with a stone tied to my feet
It never set me free
It's gotta be

More like falling in love

(from More Like Falling in Love by Jason Gray)

Working to Create Wonder

Finally, can you not change the world through working to create wonder?

I came across this statement today on a student philosophy forum I am following. It caught my attention because of a recent NPR Science Friday program that touched on wonder (in math) - and because of a question I was asked this week by a fellow juror - and because of a conversation I had with a friend this morning in which we touched on topics of physics, faith, Beethoven and mathematics.

What was beautiful about that conversation was a sense of wonder.

What I try to convey in my teaching is a sense of wonder.

I'm often asked (not only by students but by acquaintances and even strangers) why people need to learn math and whether or not anyone EVER USES algebra.

Certainly we all have likes and dislikes. I'm a very picky eater and don't like or appreciate comestible delicacies that others savor and rave about. I would love to appreciate a wider variety of foods, because the ability to appreciate is a gift and enriches life.

I think the same is true of just about everything from sports to wine to academics to music to art to nature.

We can approach any of these things with a "What's it good for and how can I USE it?" attitude. But to only validate things for their USE to us seems to me to diminish the experience of the whole of life.

Yes, for most people math is intimidating or at least not inviting.

No, most people don't use algebraic formulas in their daily life or in their work.

EVER.

Though I would say, other than reading, math CAN BE one of the most readily applicable topics we learn in school and is useful in everyday life in everything from balancing checkbooks to determining gas mileage to cooking to splitting the bill at a restaurant to deciding on purchases to remodeling to making appropriate logical decisions after hearing political arguments. Of course you can avoid using math in this by not balancing your checkbook and by ignoring whether or not you get good gas mileage and by letting someone else figure out how to split the bill. So do you NEED math in your everyday life?

No.

It's also applicable through the technologies we have that people who understand math have figured out for us - computers, televisions, satellite dishes, airplanes, medical imaging technology, and so much more! But here too, we can just say, "I'll leave that to someone else who likes math and knows how to do it. I don't care how these things are made - just so they work."

OK.

But math isn't just about producing a product.

One other thing math (algebra and beyond) is about is training the mind to think. It's about logic and abstraction and strengthening that brain "muscle."

Another thing math is about is having a fuller understanding of the universe we live in, in all its aspects. Galileo said, "Mathematics is the alphabet with which God has created the universe." He also said that the universe "cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word." So if you want to go a little deeper in understanding how the world and universe hold together, you need to know a little math. You don't have to explore deeply the wonder of creation; you can take it or leave it, but here we are ALIVE and in the middle of an amazing world and universe, which is a really cool thing to explore and savor while in this short life we have the chance to do so!

Some people, including my favorite poet, Emily Dickinson, have expressed that mathematizing things makes them sterile and ruins the wonder. Dickinson says: "Arcturus is his other name. I'd rather call him 'Star.' It's very mean of science to go and interfere."

But does knowing the math or science of something really diminish it's wonder or beauty? I love Emily Dickinson, but I prefer Richard Feynman's view when approached by a friend who thought science diminished the beauty of a flower: "[There are] All kinds of interesting questions [for] which the science knowledge only adds to the excitement, the mystery and the awe of a flower. It only adds. I don't understand how it subtracts."

Another Feynman quote that gets to the heart of the matter, and for which I would insert "math" just as much as physics, is:

"Physics is like sex. Sure, it may give some practical results, but that's not why we do it."

When people ask me about learning math, they want to know how they can USE it, and I feel trapped in a corner because the question already presupposes that the only reason we might learn math is for how we will APPLY it in life or work. If we go about all our learning in this way - history, geography, chemistry, physics, math, literature, music - honestly, no one HAS TO USE any of these things in their everyday lives.

A third reason to learn math is because, just like music and art, it is (when viewed and presented properly) beautiful in its own right.

A significant part of education is to open eyes to see wonder.

I understand, not everybody is going to like math. I get that. I don't like blueberries - even though people think that's crazy. But I'd sure like to move the focus away from thinking EVERYTHING we learn has to be OF USE and on to at least trying to find the beauty and sense of wonder in things we encounter in life - whether they be Beethoven's Symphonies, food, galaxies, fine wines - or even - math!

The student comment I opened with was: "Finally, can you not change the world through working to create wonder?"

That is what I try to do with math in my classes and in my conversations. It is my hope that people will allow themselves to be open to the wonder - rather than shutting it down with the seeming coup-de-grace, "How am I ever going to USE it?"

And maybe I'll even give blueberries another try!

What Would You Do?

I got home today from a long day of jury duty (three week trial!!), office hours and then teaching a 3-hour-long night class. I was tired, and there were some frustrating things that happened today beyond that. So, as I was griping once I finally got home after 10pm, my husband said, "Tell me one good thing that happened today."

I had to think a bit.

But what I realized surprised me.

The good thing that happened today was reading my students' homework.

This is for a Math for Liberal Arts Class. We were discussing higher dimensional geometry - including time as the fourth dimension. One of their homework questions was:

"If a time machine were invented and you were allowed one round trip, would you travel to the past or the future? What would you do with this one chance, and why would you make that choice?"

I found some of the answers really intriguing. Here is a sampling:

1) I would go to the past and tell my self things not to do and then not do them.

2) I would go to the past, before this current recession, and put all my money in gold.

3) I would go to the past and prevent the Library of Alexandria from being destroyed; just think of where we could be now if we had not lost all that knowledge then.

4) I would go back and relive my good childhood memories.

5) I would go to the future to see my great-grandkids.

6) I would go to the future, about 200 years, and see what new technologies there were, especially in the health field.

7) I would go to the past and hear Jesus give the Sermon on the Mount.

8) I wouldn't travel in time to the past or the future, because I wouldn't want to mess anything up like can happen with the "butterfly effect."

So, now I leave you, reader, with the same question. If a time machine were invented, and you got to take one round trip to the past or the future, which direction would you go and what would you do?

Universal?

There are symbols that transcend language and can be understood by all (or nearly all) people. Often road signs are designed this way, allowing travelers who do not speak the language of the country they are in to drive safely nonetheless.

Here are a couple of examples of symbols that seem to work well universally:




Such "universal," language-free symbols are also included on products, on assembly instructions or on tags of products that are sold in a variety of countries.

Today I had to wash an item I had not washed before. I looked at the tag, and it only had symbols on it. I had no idea what they meant. Thank goodness for Google and the internet! I was able to cross-reference the symbols and find out if the item was supposed to be washed hot or cold or what. I'm curious. Do you know what the symbols below mean? I am posting the answers in the comment section. No fair peeking until you've taken the "quiz."

Do people other than, say, dry cleaners or other professional launderers really understand these symbols? How did you do on the quiz?

Hard Times, Holy Water

When through the deep waters I call thee to go,
The rivers of sorrow shall not overflow;
For I will be with thee thy trials to bless
And SANCTIFY to thee thy deepest distress.

When through fiery trials thy pathway shall lie,
My grace all-sufficient shall be thy supply;
The flame shall not hurt thee; I only design
Thy dross to consume and thy gold to REFINE.


So shall each fear, each fret, each care
Be turned into a song,
And every winding of the way
The echo shall prolong;
So shall no part of day or night
From SACREDNESS be free,
But all my life, in every step,
Be fellowship with Thee.





(from the hymns "How Firm a Foundation" and "Fill Thou My Life" for a dear one going through deep waters right now - may they be made holy to you - and may you be blessed.)

Status

My apologies to all family and friends to whom I may seem to have fallen off the planet. I've got the perfect storm going on over here, and we are in survival mode. We're in good spirits, and all is well, but we are only managing the necessities of life. I haven't even had time to follow up "A Mother's Therapy (Part 1)" with a Part 2!

It's so crazy it's almost funny.

Last week we got Anthony all set to go, and, as we should have expected, unexpected extra errands came up. We began processing the emotion of sending a child off to college for the first time. My new semester of work began (with all the requisite inservices and meetings) - so I had to put my emotional processing on hold. David is in Michigan for college orientation with Anthony, so I'm "single-parenting." And, hey, why not, we threw in some extra social activities over the weekend. Oh, and I had a birthday in there somewhere too.

And then I got sick!!!! (which made my 9:35am to 9:05pm teaching day yesterday a bit of a challenge)

It's kind of a fun challenge though - to have all that in the works - and to make it work - just as long as I don't have to do it too long!

Did you hear that David? COME HOME SOON!!

I got a message from Anthony this morning that has had me smiling all day in the midst of our "storm" over here. It looks like he's got some great people in his room and suite and floor. At least two of them play Magic! YEA! And he not only got classes he needs but the ones he was most hoping for - Honors Calculus III, Fundamental Questions in Philosophy, Introductory Physics: Mechanics and Gravity, and Biblical Literature and Theology. His brain is going to be so happy! And that makes his momma happy too! I've had a goofy grin of happiness on my face all day!

And, by the way, David, COME HOME SOON! :-)

"Twins" :-)

Happy Birthday to my "twins" out there:
Nethe, Keith and Lawerence!!
Have a good one!

A Mother's Therapy (Part 1)

I am up late even though I have to get up super early . . . but sending one's first-born 2000 miles away to his freshman year in college can cause one to be unable to sleep, and that is the situation in which I find myself. So, in an attempt to reconcile myself to how the years have passed I pulled out picture albums -- and found about a hundred thousand pictures I want to scan and post -- if for no one other than myself! I am tired, though and ran out of steam once I hit "First Day of Kindergarten!" So I'm putting up what I've got so far with more to come. I can't believe I'll be saying "good-bye" to this guy at 4:15 tomorrow morning. Where DID the years go?!

Daddy loved it when Anthony "melted" on him.
Look at those baby blues!!

An early outing to one of our favorite places, Knight's Ferry.

We taught our kids many things early on. Here Anthony is learning to skip stones.

David and Anthony at another of our favorite places, Capitola.

Getting acquainted with the ocean.

A first trip to Yosemite -- seems happy about it!

The classic one year picture.


Back at Knight's Ferry -- a pensive moment.

Always good to have Dad to lean on!


Anthony in his "suit-coat" -- his favorite church attire back then.

-- helping Dad mow the lawn.


In the backyard by Mom's daffodills.


Back at Knight's Ferry and finding an interesting sight.


Like I said, we teach 'em young, and what's more important than card games?


Ah yes, the long ago Duplo days -- always building -- later it was K'nex.


BROTHERS!


First day of kindergarten . . .

. . . and now off to bed for this mom or she won't be able to get up at 4 to see him off!