Friday, May 30, 2008

Of Tin Foil and Home Remedies

I'm always amazed at how easily young people seem to understand computers. I don't know what I will do when my teenagers grow up and leave me~~I call on them often for help in figuring out computer related problems. Most of the time they are successful.

Joy solved a problem we were having with our WiFi signal. If you have a large house or a two-storey house and use a router, you have perhaps experienced the same difficulty we were having. The signal is strong in certain parts of the house, but fades as you get farther away.

Fifteen minutes, a little tin foil, and a glue stick solved the problem. The signal can be boosted significantly by making a little parabola shaped "sail" to insert onto the router antenna. There is a short instructive video here, and a template suitable for printing here.

Amazing results! I love home remedies of this sort, don't you?

More on Ideas Have Consequences: Egotism in Work and Art

I've had a great deal of difficulty summarizing this chapter on egotism and the arts. Though I've read it several times, mused over it, and taken notes, every time I put pen to paper something was missing.

When I wrote about mathematical patterns in my recent post, I suddenly realized a connection and the ideas that Weaver had expressed in this chapter began to congeal. It was one of those "Eureka!" moments for me, though it will probably not sound nearly so dramatic here!

Because he was created in the image of God, man has an inborn drive to create. History records a succession of artistic endeavors in which man sought to emulate the patterns of life, the orderly ways of the Creator. As time marched on, man's creative fruits became increasingly realistic as his understanding of truth unfolded. Up through the eighteenth century, art and music mirrored the strength of an ordered, hierarchical society: traditional, balanced, and rendering a faithful portrayal of nature.

As an example, think of DaVinci ~ a man who understood fully the correlation between mathematical patterns and art. His notebooks are full of his studies of proportion, symmetry, and pattern. He was even known to study cadavers in his pursuit to accurately portray the human body. His work ( and the works of other masters of his ilk) are universally apprehended because nature is the enduring reality. Great art will accurately embody great themes understood by people of all times.

Music and Literature also reflected themes with transcendent appeal. Think Mozart: highly structured, ordered, and complex. Or Milton, poetically painting universal themes such as sin and redemption.

As I mentioned in my article on mathematics, humans seem to be programmed to perceive beauty within concrete parameters. As long as the artist created works that adhered to the elegant structure and rhythms within those boundaries, he was working in harmony with the Creator and to the benefit of society.

I was interested to come across a quote by a current songwriter who seems to embrace this very truth:

"Music it true. An octave is a mathematical reality. So is a 5th. So is a major 7th chord. And I have the feeling that these have emotional meanings to us, not only because we're taught that a major 7th is warm and fuzzy and a diminished is rather threatening and dark, but also because they actually do have these meanings. It's almost like it's a language that is not a matter of our choosing. It's a truth. The laws of physics apply to music, and music follows that. So it really lifts us out of this subjective, opinionated human position and draws us into the cosmic picture just like that."
~recording artist James Taylor, in the May 2002 Performing Songwriter

So there are men of every generation who grasp the elegant structure of beauty, but in the general flow of history, man seems bent on being independent; not satisfied with God's truth he seeks to create his own truth outside the natural and established patterns. "Let us tear their fetters apart, and cast away their cords from us!" Having reached an apex artistically, he began to unravel all that he had achieved. According to Weaver, this started happening at about the time of the French Revolution, when romanticism began to flourish. Instead of looking upward for virtue and truth, man began to explore the "inner landscape." The old foundational themes such as original sin became passe, and art became much more subjective. Weaver boldly names this"egotism" as the culprit in the ravaging of aesthetic expression.

Weaver speaks of the "sanctioning of impulse" and the "uncovering of the senses". Foundational templates were replaced by splashes of pizazz or gimmicks. Exploration turned away from universal themes and turned inward, to the individual consciousness. Artists began to tap into an inner well of "appalling ....melancholy and unhappiness," leading to aesthetic bankruptcy.

Jazz is an example that Weaver spends considerable time evaluating. Here is his pronouncement:

"Jazz, by formally repudiating restraint by intellect, and by expressing contempt and hostility toward our traditional society and mores, has destroyed this equilibrium. That destruction is a triumph of grotesque, even hysterical, emotion over propriety and reasonableness. Jazz often sounds as if in a rage to divest itself of anything that suggests structure or confinement."

Note that Weaver is NOT saying that art "outside the box," cannot have interest or that those who produce it lack skill. He is not criticizing the workmanship so much as he is pointing out how modern art reflects the ideas of the times.

This makes me think of a recent news article about the arts. In it, the author suggested that by providing melancholy people with anti-depressants we may be hindering their ability to produce great art. Apparently, this news writer felt that great art could not be produced by "happy" people; that people with a dark pathos were the ones who capitalize on their sadness to produce great art.

If we are talking about this degraded sort of art of which Weaver speaks, the author of that article has a point. But if we are talking about structured, realistic, truthful art that depicts the great themes of humanity~~it's nonsense.

This chapter in Ideas Have Consequences closes with some very profound thoughts:

"When masses of men reach a point at which egotism reigns so blandly, can their political damnation be far distant: They have rejected their only guaranty against external control, which is self-discipline, taught and practiced. If they no longer respect community and direct their efforts according to a common understanding, they fall out......An ancient axiom of politics teaches that a spoiled people invite despotic control."

What to you think? Do you detect egotism in modern art? Are we a "spoiled people" ?

Monday, May 26, 2008


My husband and I have felt it important to establish family traditions for Memorial Day, as we have for the more major holidays. For us that means taking just 5 minutes to walk to the local cemetery, where there will be a military speaker, a gun salute, and a bugler who plays taps. Today the guest chaplain spoke with wisdom and brevity. I loved the words of the hymn he quoted, and wish I could have written them down~~it was not something I had heard before. We walked home in silence, contemplating the words and with the haunting melody of "taps" lingering in our hearts.

Another small element of tradition that we return to every year is the reading of the poem "In Flanders Fields." I remember buying those little plastic poppies from the veterans when I was a kid, but never really understood their significance until I was an adult and learned this poem. It's meaningful to follow up the reading with three other poems that were written as a reply to "In Flanders Fields":

*America's Answer
*Reply to In Flanders Fields
*Another Reply to In Flanders Fields

The last one, by J.A. Armstrong also mentions poppies: eagles, fly
The fierce destroyers of the sky;
With stains the earth wherein you lie
Is redder than the poppy bloom,
In Flanders Fields.

We put on the patriotic music as we readied the house for the 30+ guests with whom we enjoyed a barbecue and the first day of swimming. My old, faithful Great American Favorites CD never fails to touch me and set me to whistling. I think the "Fanfare for the Common Man" would have to be my #1 favorite on that album, with the variations on "America" running a close second.

Do you play patriotic music in your home?

I took a walk alone this evening to unwind after all the busyness of the day, and I was thinking to myself how sad it is that all of the lovely lilacs that have greeted me the past week are spent. But then I turned the corner, and spied the most vivid red poppies waving at me. What an appropriate moment to see them. What an appropriate day for them to be showing forth their glory.

Tuesday, May 13, 2008

Beauty and Mathematics

"One thing have I desired of the Lord, that will I seek after; that I may
dwell in the house of the Lord all the days of my life, to behold the beauty of
the Lord and to inquire in His temple." Psalm 27:4

One way to behold the beauty of the Lord is to examine His creation mathematically, for the natural world speaks loudly of the Creator's remarkable orderliness. Take for example, the sequence of numbers known as the "Fibonacci Numbers":

1, 1, 2, 3, 5, 8, 13, 21, 34, 55..........

In this sequence, each number in line is the sum of the preceding two numbers. We can trace these numbers in nearly everything that we would call "beautiful" in the world of nature: the spirals on a pineapple, the whorls at the center of a sunflower, the pattern of a pine cone. As you see the predictable pattern in growing things, you begin to surmise that nothing is truly random. That is a comforting thought to me! Foundational structure provides much safety.

Comprehending patterns visually can lead to the next step, which is to apply knowledge of the seen to the unseen. The patterns we can see become a hook onto which we can hang our understanding of things invisible. The workings of the cell, DNA strands, atoms, the concept of aerodynamics-- all of these things we can understand to some extent because we are acquainted with similar, concrete models of the same sort.

"For by Him all things were created....visible and invisible...." Colossians 1:16

The ability to think abstractly is a strictly human attribute and mathematical patterns such as the Fibonacci Numbers give us a starting point onto which we can connect deeper understanding. And it is here that I have only recently made the startling discovery that mathematics is really NOT just about numbers. It is more accurately the science of patterns. How I wish I would have known this years ago!! To have been able to trace the foundational patterns of the universe to the God who made it would have perhaps given me a fresh outlook on all of the math assignments I so dutifully endured but failed to enjoy.

*Music has a definite, mathematical pattern.

*Linguistics involves the study of grammatical pattern.

*Genetics link DNA patterns with physical attributes.

*Chemists understand the orderly pattern of the periodic table of elements.

*Astronomy incorporates the study of orbital patterns of moving objects in space.

*This list could go on endlessly and become a mathematical object lesson for the word "infinity"!

I think that perhaps the most fascinating thing about all of this is that humans recognize beauty within the boundaries of orderly pattern. We perceive only some patterns as beautiful, and those are usually linked to the Fibonacci numbers. Look again at that sequence: take two adjacent numbers and make a ratio; for example 3:5. Now, do the math:
5 divided by 3 = 1.6

The 1.6 quotient has become the famous "golden ratio." Our bodies were designed according to this ratio. The Greeks built the Parthenon in keeping with this pattern. Even the 3x5 inch index card you use for a bookmark is cut to pleasing proportion according to this principle. Whether it is a building a painting, a face, or a song--humans seem innately attracted to anything designed in the 3:5 ratio. Conversely, the things we would dub grotesque or deformed fall outside of the Golden ratio. Beauty has a design, a predetermined orderliness and life becomes endlessly fascinating as we uncover layer after layer of these divinely-conceived patterns.

Here are some beautiful words by a mathematician:

"The mathematician's patterns, like the painter's or the poet's, must be
beautiful, the ideas, like the colors or the words, must fit together in a
harmonious way. Beauty is the first test; there is no permanent place in
the world for ugly mathematics....It may be very hard to define mathematical
beauty, but that is just as true of beauty of any kind--we may not know quite
what we mean by a beautiful poem, but that does not prevent us from recognizing
one when we read it. " --quote by G.H. Hardy from his book, A Mathematician's Apology.

Thursday, May 08, 2008

Stretching the Food Budget Painlessly

Like many people, we are feeling the crunch from higher food prices. Frugal food articles abound on the web right now, and I can hardly offer anything that is truly innovative. Still, I have my little cache of tricks.....

*Nonfat Dry Milk- keep it on hand for cooking and for stretching the last of the milk in the gallon jug. Don't let the kids see you doing this!

*Add complexity to recipes without buying expensive fresh herbs by using already seasoned items such as herbed croutons in a breakfast casserole or V8 juice (instead of tomato juice) in gazpacho or in any recipe requiring a red sauce.

*Roast your own canned tomatoes. This can be done by drizzling them with olive oil, placing them on a cookie sheet, sprinkling with dried basil and baking for 30 minutes at 375 degrees or just until they begin to brown around the edges. Great in soup, pasta sauce, or stew.

*Don't waste anything. My biggest area of waste is with produce, so I have purchased the highly advertised Green Bags and store my fruits and veggies in them. I cannot rave about them, but I have noticed a marked improvement with lettuce and strawberry longevity. The secret seems to be to place items in the bag DRY. They don't seem to work well with bananas but.....

*Slice limp bananas and freeze them. Whir in the blender with yogurt, berries and juice for a great smoothie. If you like your smoothie to have a velvety texture, frozen bananas are the answer.

*Instead of buying expensive vegetable-wash spray, make your own in a spray bottle using a little vinegar and water.

*Buy head lettuce instead of pre-chopped. I wash mine when I get home from the grocery store, put it in a lingerie bag that I keep only for this purpose, and place it in the clothes washer on the "spin" cycle. I know this sounds crazy, but it works great! Just don't walk away from the washer. I repeat, DO NOT WALK AWAY FROM THE WASHER ! You can guess why ;)

*Speaking of lettuce, a great salad makes even a cheap spaghetti dinner satisfying. One of my favorites is dark greens, slivered beets, roasted asparagus, a sprinkle of feta cheese, and balsamic dressing.

*Keep a package of real bacon bits on hand. For some reason, the moist bits sold in those little pouches seem to have a really concentrated bacon flavor, and a little goes a long way. They are good sprinkled on green beans or a salad, but also on a melted cheese sandwich. This is one convenience food that is worth the money for me.

*Include a pancake dinner into the menu for one really cheap meal.

Where I refuse to cut corners......

*I will not buy cheap margarine in place of butter.

*Nor will I buy fake cheese

*Meat. Adults need no more than 4 oz. at a meal, and children even less. We can continue to buy good cuts of meat because we don't eat 6 or 8 oz. portion sizes. Instead of huge hunks of meat, provide 2 vegetables at the dinner table.

What are your tricks?


My lilac trees are old and tall;
I cannot reach their bloom at all.
They send their perfume over trees
And roof and streets,
to find the bees.
- Lousie Driscoll, 1875 - 1957
My Garden Is a Pleasant Place

Sophie Anderson
The Time of the Lilacs

On the Teaching of Math

The world appears to be split into two types of people: symbolic thinkers who seem to be born with the "math gene" and concrete thinkers who more appreciate words. The language and word lovers are often left scratching their heads when a symbolic thinker makes a mathematical explanation, whether orally or in writing. Listen to what Jacques Barzun says about this:

"....from the very first grade one child "loves" math and another hates it. This is the beginning of the school's difficulty. (SNIP) What is seldom noticed is that the trait in students who favor math is also the cause of much poor teaching. For the mind that feels at home with math is likely to lack the qualities that make a good teacher. (gasp!!) SNIP

....the math or science teacher may fail, although well prepared and of course well intentioned. He or she, moving easily among abstractions and their symbols, has no idea how the "other mind" works---does not perceive how strange the square root of minus one seems to the concrete-minded (SNIP) It is a case of two minds out of tune with each other. And a proof that the disparity is not accidental or occasional is that the same fault is found again and again in math and science textbooks. The author assumes a kind of scientific common sense which will make things clear at once. Accurate with symbols, as writer or teacher he often uses words carelessly, failing to see that to the concrete-minded words have distinct connotations."

Barzun follows this with an example from a textbook, and shows methodically how the poor wording would befuddle any word lover.

Being myself a word lover and a recovering math-o-phobic, I've given serious consideration to this dilemma. As a student who was befuddled by murky explanations, I now sit in the seat of a teacher who wants to make math come alive for my students. My solution: DO NOT RELY SOLELY ON A TEXTBOOK.

Most people who know me know that I am allergic to textbooks :) I use them more in math than in any other subject, but try not to over- rely on them. Steve Demme has taught me that "teachers teach~textbooks drill." I think there is a lot of wisdom in those words.

So how do you wean yourself from dependence on a textbook? The first thing is to set apart one day a week to do math in a different way; no textbook allowed. Friday is that day at our house.

Here are some ways to use that time:

*Play games. Lots of games: dice games, strategy games, board games, card games. Remember that math is not just about numbers; it is the study of patterns. Games are invaluable in imparting the art of logical thinking. It's fun, too!

*Choose math stories to read together. Look at Julie's list of literature books that qualify as "math" here. Some of our favorites have included The Number Devil, Math Smart Junior, books by Greg Tang , and Sir Cumference series books.

*Keep a math journal. Write where and how you saw math being used in your everyday life.

*Narrate. Some people are surprised that you can use narration in a math lesson, but it is very effective. To have a child explain HOW he works a math problem brings it out of the realm of symbols and into the world of words. This can be done as either an oral or written narration. For very small children, you can switch roles. Pretend you are the student and ask them to be the teacher and explain their current math concept to you. They won't even know they are doing school! Today, one of my highschoolers explained very lucidly how to approach an algebra problem using the correct order of operations. Narration works for young or old.

*Play with math. My husband is a true symbolic thinker and it is second nature for him to pose math problems at the table as though he were thinking out loud. This week, he mentioned to us that he had determined that his car gets 2 more miles per gallon if he uses regular unleaded gasoline rather than ethanol. "Yes, Daddy, but doesn't it cost 10 cents per gallon more?" And then ensued a real brain teaser. What is the difference in price between a tank of ethanol vs. a tank of unleaded? How many miles can you drive on each tank? Which is the better value? Keeping alert to these kind of applications brings math down to earth.

*Build things. Buy bridge building kits. Make geodesic domes out of rolled newspapers (that is what you see in today's picture). Construct architectural models using marshmallows and toothpicks.

*Buy a few age appropriate math computer games. My kids enjoyed Cluefinders when they were younger. There are probably better ones now.

Next time....stimulating your own passion for the subject of math.

Tuesday, May 06, 2008

Vacation Souveneirs

Finding Seashells

Author Unknown

Come walk with me
Along the sea
Where dusk sits on the land
And search with me
For shells are free,
And treasures hide in sand.

Monday, May 05, 2008

Spring Recital and Musical Thoughts

Here is a picture of my three girls with their piano teacher, taken yesterday after their spring recital. I am amazed at the progress they have made under Mrs. T's wise tutelage. Melody, my oldest, started her musical education early with a Suzuki teacher. She played amazingly well at a very young age, but as she progressed it became evident that she was not reading music. She did a good job of convincing us otherwise, but she had learned to rely solely on her ear.

Her second teacher tried to straighten her out by requiring mind-numbing drills and repetitions, sometimes 50 times at a practice session. It was like boot camp, and Melody would dissolve into tears after her piano lesson; all the joy of music was squeezed out of her.

My desperate prayer was answered and we found our way to Mrs. T. She knew exactly what to do and taught Melody how to practice smart. Her method requires the mind to be 100% focused on the pieces you are practicing. This is accomplished by saying the names of the notes as you play them, and after getting familiar with the music using the metronome and counting aloud. This forces the brain to be engaged and strengthens the reading skills. Mrs. T. explained that the brain loves to be lazy by relying on the ear, and speaking aloud the rhythm or notes remedies that problem. You can accomplish more with less repetitions using this method.

The one residual plus from her Suzuki experience is that she learned to play her pieces in any or every key. Once a piece was memorized and perfected, it would be re-assigned in a different key and used as a practice exercise. I am slightly jealous of the ability Melody has of switching keys so effortlessly. For some reason, I always found key signatures with sharps more difficult than key signatures with flats. I do not know why this is, but I have talked to other pianists who seem to share this weakness.

Suzuki recitals were, I must admit, BORING. Because all children had the same repertoire, you heard the same songs over and over and over. Mrs. T. has an innate gift for guiding her students to choose music that perfectly fits their personalities. She has mentioned to me the need for the girls to be playing not only pieces that hone their technical skills, but songs that feed their souls. Her recitals are anything but boring! You may hear ragtime, pop, contemporary Christian, patriotic, classical, and original compositions. To be allowed to play in the recital is a privilege that must be earned. There are deadlines for preparing the music, and if those deadlines are not met the student has to sit out. I love the gentle discipline in this rule; it teaches young pianists to pace themselves.

This recital the girls played the following musical works:
* Melody- Nocturne in C Sharp Minor (posthumous) ~Chopin. Beautiful, ethereal runs
Nightfall- her own composition
A fun duet entitled Big River Barn Dance

* Joy- Morning Snowfall by Matz
Reflections--her own composition (She wouldn't let me hear this one until the recital! What a wonderful surprise!)

* Artiste- this was Artiste's 2nd recital, and she played a cute little beginner piece called The Magic Pony. She was nervous, but came out all smiles in the end.

Part of the wonder of the day was all the support our girls received from Grandparents and members of our church family. I was touched to see an older man from the church with his hands on the girls' shoulders after the recital praying for them; asking the Lord to continue to give them fresh music and to use their gifts and talents for His honor and glory always. This kind of support makes parenting so much easier. I am a blessed woman.

Thursday, May 01, 2008

A Short History of Lemonade

This Anchor-Hocking Hobnail set belonged to my late Mother-in-law, and has now found a new home in my cupboard. I'm guessing the set to be about 50 years old; it appears to have never been out of the box. I'm crazy about dishes, so I've had fun this spring pairing the tumblers with my new polka-dot dishes. The set is perfect for serving lemonade.

I don't often make homemade lemonade, because with 4 thirsty kids it is just more work than I care to invest. Store brand frozen lemonade works for us; I sometimes doctor it up with strawberry syrup, whole berries, or float lemon slices in the pitcher. Schwanns makes a great frozen lemonade, but that is a rare treat because it has to be delivered at your door and is not available in stores.

Laura Ingalls Wilder writes about her first introduction to lemonade in her book, On the Banks of Plum Creek:

" 'Is your lemonade sweet enough?' Mrs. Oleson asked. So Laura knew that it was lemonade in the glasses. She had never tasted anything like it."
Naturally, lemons would have been few and far between on the prairie where Laura lived, although the drink became increasingly popular in the 1800's as a result of the fact that sea captains were recommending lemon juice as a scurvy preventative on long sea journeys.

The history of pink lemonade is less medicinal and more humorous. I had to chuckle at this explanation, which I found on Wikipedia:

"An article from a New Jersey newspaper cites William "Billie" Henry Griffith of Three Bridges, NJ as the discoverer of pink lemonade. The article reads as follows: ' A stiff breeze lifted those tights from the line and deposited them into the container. Dyes in those days were not color-fast and to Billie's dismay he saw his lemonade take on a pinkish hue! It was too late to make more for the crowds were already milling around. Always a trooper at heart, living by the creed that 'the show must go on' Billie used the occasion and shouted in his familiar way "Step right up and get some pink lemonade! Absolutely new! Better than any lemonade ever made!" The customers crowded in, they drank and came back for more and Billie had made a name for himself.'"
For the record, pink lemonade was more often colored with beet juice. Whatever your opinion of beets, you have to admit it is an improvement over Billie's pink lemonade!

My Math Makeover

If you would have told me 10 years ago that I would be teaching a math class at a cooperative school, I would have laughed at you. I have been, for most of my life, a math-a-phobic. It's true I managed to get decent grades in my math classes at school, but that was the result of hard work, drudgery, a lot of prayer, and a little luck.

When I began to homeschool my children, I started to think about my attitude toward math. I did not want to pass along a math aversion to the next generation. My hope was that my own kids would not dread or fear this subject and that they would connect its orderliness to the God who designed an orderly universe. I was not so ambitious, however, to set myself a goal of creating math LOVERS.

I began my "math makeover" with a book by Marilyn Burns, entitled Math: Facing an American Phobia. It was a fantastic start, written by a math educator who finds delight in real-world applications rather than in rows of "right" answers on a worksheet. For me, she put to death the myth that there is only ONE way to come up with the answer to a math problem. If you had to quickly tabulate the sum of 37 plus 50 would you first add 40 to 50 and then subtract 3? Or would you make an addition problem in your mind, lining up the 37 above the 50 as you would have written it on the blackboard at school? Different strokes for different folks. There is nothing wrong with either way of doing it. I think Marilyn gave me a warm little boost as if to say, "You can do this, and although it may never become your passion, you
can learn to enjoy math."

At about this time I had to select math curriculum for my oldest child. I remember being so overwhelmed with all the choices-- interviewing veteran teachers, poring over reviews, looking at a myriad of samples. I ended up making what would be a good choice for our family of 4 children: Math-U-See. There are many things to like about Math-U-See, but what contributed to my "math makeover" were the video segments in which Steve Demme teaches the teacher HOW to present the concepts. This man has a bag of slick math tricks, jokes, and quirky explanations that hold your interest and make learning painless, if not fun. This curriculum was a perfect fit for all but one of my children (and that is another story), but what happened as I used it was that I gained confidence in my ability to explain math concepts.

People who write math books have what is playfully called the "math gene", and because they do, their explanations appeal mostly to other kindred spirits who share the "math gene", while language and word-lovers are left scratching their heads. Steve Demme's jokes and stories and games added the language dimension that helped me immensely.

What I didn't know at the time is that
the curriculum really did not matter very much. It was my attitude that mattered. A good teacher uses curriculum only as a tool; her enthusiasm and confidence can make cake out of dry bread crumbs.

I have more to say about my previous mention of symbolic thinkers (math geeks) versus language lovers (word geeks), which I will address separately in another post. It took me a few years to realize that there is a complementary, even synergistic relationship between the two. I'll save that until next time.