And I heard a sound from heaven like the roar of rushing waters and like a loud peal of thunder. The sound I heard was like that of harpists playing their harps. And they sang a new song before the throne and before the four living creatures and the elders. No one could learn the song except the 144,000 who had been redeemed from the earth (Revelation 14:2-3 NIV).
I recently attended a lecture about the interface between science and faith. One of my fellow audience members, a woodworker named Ed Bond, mentioned The Golden Ratio. Specifically, he focused on the Golden Rectangle, which influences the dimensions of the tables he creates.
I am going to oversimplify this, because I just don’t know how to explain it clearly without using a lot of words. (My mathematician daughter would do a much better job. She gets this. She also has a Fibonacci spiral tattooed on her shoulder—more about that later.)
The Golden Ratio is a phenomenon that occurs in nature and mathematics, and has been used by engineers and artists for millennia. Plato knew about it, and referred to it in his Timeas when describing three-dimensional geometric solids. It refers to the relationship between measurements a and b where a is to b as a + b is to a.
The Golden Ratio is known by the Greek letter phi, and like another mathematical concept, pi, has an infinite, unrepeating sequence of numbers following its decimal point. Phi’s approximate value is 1.618. In the equation (a + b) / a = a / b, if a = 1, then (a + b) = 1.618…
Ed Bond says he likes to build tables whose sides are multiples of 1.5 x 2.5—for example, a 3-foot by 5-foot coffee table. The dimensions look good; they feel “right.” That ratio is 1:1.666…, approximating that magic number, phi. He says it’s no accident that the humble index card is 3 inches by 5 inches.
Le Corbusier, a Swiss-French architect (1887-1965), claimed that the human form, subdivided at the navel, yields the Golden Ratio; and if you subdivide those sections further, at the knees and throat, they also fall into the same ratio. Leonardo da Vinci’s famous drawing Vitruvian Man is often used to illustrate this idea (though, actually, the math in the artwork doesn’t match).
This drawing by Heinrich Agrippa (1486-1535) is a better representation:
Phi turns up frequently in geometry. In Salvador Dali’s The Sacrament of the Last Supper, the edges of the dodecahedron framework conform to the Golden Ratio.
The Golden Ratio manifests again in the Fibonacci sequence, which is a sequence of numbers starting with 1 (or sometimes 0) and then you add the preceding two numbers to get the next number: (0,) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. Starting with 5, if you divide any number in the sequence by its preceding number, the result is close to phi. The sequence can be used to generate a spiral shape (don’t ask me how). This is the shape tattooed on my daughter’s shoulder. It suggests the inner pattern of the multi-chambered nautilus shell and the Snail Trail quilt block.
Getting back to woodworking, Ed Bond wondered how long the Golden Ratio has been used in making furniture. One day, while reading the Bible, he found God’s directions to Moses for building some of the furnishings for the Tent of Meeting. For the Ark of the Covenant, God said, “Have them make a chest of acacia wood—two and a half cubits long, a cubit and a half wide, and a cubit and a half high” (Ex. 25:10 NIV). “Make an atonement cover of pure gold—two and a half cubits long and a cubit and a half wide” (Ex. 25:17). There it is, God’s own design, executed before 1400 B.C., incorporating the Golden Ratio.
It was His idea. God determined the laws of mathematics and physics. God created all of nature. We discover the mysteries of the universe through science and math; we celebrate them through art.
If you would like a more thorough explanation of the Golden Ratio, read this article.
In your own creative work, does mathematics or science come into play? Share in the comments below.
Actual bumper stickers found on actual cars:
Horn broken. Watch for finger.
Your kid may be an honor student, but you’re still an idiot.
All generalizations are false.
Cover me. I’m changing lanes.
I brake for no apparent reason.
I’m not as think as you drunk I am.
Forget about world peace. Visualize using your turn signal.
We have enough youth. How about a fountain of smart?
He who laughs last thinks slowest.
Lottery: a tax on people who are bad at math.
It IS as bad as you think, and they ARE out to get you.
Auntie Em, Hate you, hate Kansas, taking the dog. Dorothy
Change is inevitable, except from a vending machine.
Time is what keeps everything from happening at once.
Out of my mind. Back in five minutes.
Forget the Joneses. I keep us with the Simpsons.
Born free, taxed to death.
The more people I meet, the more I like my dog.
Laugh alone and the world thinks you’re an idiot.
Rehab is for quitters.
I get enough exercise just pushing my luck.
Sometimes I wake up grumpy; other time I let him sleep.
Work is for people who don’t know how to fish.
I didn’t fight my way to the top of the food chain to be a vegetarian.
Women who seek to be equal to men lack ambition.
If you don’t like the news, go out and make some.
Sorry, I don’t date outside my species.
No radio–already stolen.
Real women don’t have hot flashes, they just have power surges.
I took an IQ test and the results were negative.
Where there’s a will, I want to be in it.
OK, who stopped payment on my reality checks?
Few women admit their age; fewer men act it.
I don’t suffer from insanity; I enjoy every minute of it.
Hard work has a future payoff. Laziness pays off NOW.
Tell me to “stuff it”–I’m a taxidermist.
IRS: we’ve got what it takes to take what you’ve got.
Some people are only alive because it is illegal to kill.
How can I miss you if you won’t go away?
Warning: dates in calendar are closer than they appear.
Give me ambiguity or give me something else.
We are born naked, wet, and hungry. Then things get worse.
Make it idiot-proof and someone will make a better idiot.
Always remember you’re unique, just like everyone else.
Very funny, Scotty. Now beam down my clothes.
Consciousness: that annoying time between naps.
i souport publik edekashun
Be nice to your kids. They’ll choose your nursing home.
Beauty is in the eye of the beer holder.
There are three kinds of people: those who can count and those who can’t.
Why is abbreviation such a long word?
Ever stop to think and forget to start again?
Keep honking–I’m reloading.
Caution: I drive like you do.
Many of us take reading for granted.
But if you’ve ever watched a child discover the connection between words written on a page and names and stories and ideas, you’ve seen the sparking of magic, the bestowal of power.
I read the story long ago (sorry, I can’t find the source; if you recognize it, please credit it in the comments below) of missionaries in a culture that had no written language. The chief was very unimpressed with the Bible; he had no concept of book.
To illustrate how a book conveys a message, a missionary asked the chief to tell him what was going on in his life. The chief described how his “woman” had recently become ill and died. The missionary wrote down the chief’s words, then took the chief to see his (the missionary’s) partner. The partner read the missionary’s note, and said to the chief, “I’m so sorry your woman died.” The startled chief began to comprehend the power of the written word.
At a pre-concert chat I attended recently at the Phoenix Symphony, pianist Shai Wosner shared how his parents insisted on sending him to piano lessons at age five (Wosner started playing piano on his own when he was three) because they wanted him to learn how to read music notation. He really didn’t appreciate the value of that skill until, a few years later, they gave him the orchestral score of Mozart’s Requiem. There, laid out in front of him, was a visual representation of a complex work of genius. He could see the entrances of the instruments and the voices; the patterns of melody, harmony, rhythms, and dynamics; the techniques the composer utilized to develop his themes. The power of that moment affected him deeply, and I experienced it vicariously through his relating it.
Here is what the music above (an excerpt from a section of the Mozart Requiem) sounds like (up to the 0:49 mark):
Can you follow along? Do you have the power to connect the symbols to the sounds?
Friends, it is of vital importance that our children tap into that power. They partake of it when they learn to read, when they learn another language, when they grasp mathematic principles, when they discover the laws of physics by building a structure, when they create art, when they look through a magnifying glass.
Music literacy is as important as English literacy. Acquiring the skill of reading music notation exercises the brain in a way that makes the decoding of other symbols easier. Music literacy is not a frill; it’s a strategic component of a comprehensive education. Our kids deserve a rich, experiential education. Anything less limits them.
I’ll get off my soapbox now.
Back to beautiful music. Here is an example of the artistry of Shai Wosner:
Can you read music? Can you speak more than one language? Can you write computer code? Do you agree that there are many kinds of literacy? Can you think of any reason that would justify eliminating music literacy instruction from public education? Share your thoughts in the comments below.