DEVOTIONAL
The Divine Proportion
(Reflection - June 2005)
Who marked off earth’s dimensions? Surely you know!
Who stretched a measuring line across it? (Job 38:5)
Please
look around you at this meeting room here in Kingston,
Jamaica. It is 21.2 meters by 13.1 meters. The proportion is 1.618 to
1. I had nothing to do with the design of this meeting room: but I can
tell you that its dimensions are exactly the “divine proportion.”
The
Creator’s idea
Johannes Kepler (1571-1630) a mathematician, commented, “I believe
that this divine proportion (1 to 1.618…continuing indefinitely)
served as an idea to the Creator when He introduced the creation of likeness
out of likeness…The pentagon is constructed by means of this divine
proportion which I assume to be the prototype for the Creation.”
It is easy to prove that pentagons are constructed from 1/1.618. Euclid
proved it twenty-six centuries ago. But it is by faith we deduce that
it is the Creator’s idea (Heb. 11:3). Scientists who have a problem
with anything “divine” in their lives call 1.618
to 1 the “golden ratio.” Actually, it doesn’t
make a lot of difference what you call it. It’s still real, and
hard wired into the universe, including our brains.
An astute twelfth-century Italian named Leonardo Fibonacci was investigating the breeding of rabbits and discovered a series of numbers which has ever since been called the Fibonacci sequence. Each new term equals the sum of the preceding two, like this: 21, 34, 55, 89 and so on ad infinitum. The ratio between adjacent numbers is the divine proportion: 1.618. The bigger the numbers, the more exact the proportion. Mathematically, the divine proportion is expressed simply but most precisely by the equation half of (1 + the square root of 5). The five coming in there is why Kepler wrote about polygons, five sided figures. And lots of living things, like starfish, have five-fold symmetry. Kepler said “I see the number five in almost all flowers.” Today we would say that the “divine proportion” is hard wired into their genes.
A diatom is a microscopic marine creature averaging only 0.0466mm by 0.0288mm. That is a proportion of 1.618. Phyllotaxis, the study of how leaves are arranged on plants, informs us that the same angle separates successive leaves as they spiral around a twig: 222.5 degrees. A complete circle, 360 degrees, divided by 222.5, yields the divine proportion, 1.618. A sheet of legal size copy paper measures (if cut properly!) 360mm by 222mm, a ratio of 1.618. That particular size of paper was chosen long ago by lawyers who must have known something about the divine proportion. I have a human vertebra in my drawer which measures exactly 100mm by 168mm; we are “fearfully and wonderfully made” (Psa. 139:14).
Expressions
of perfection
Why are ancient Greek sculptures priceless on the world market? Michelangelo’s
David and Moses? Because when the divine proportion is applied to art
and culture, it is recognized instantly as expressing perfection. In thirty-eight
years, from 1220 to 1258, Richard Poore designed and built Salisbury Cathedral
in England as “a worthy expression of the greatness and glory
of God.” Eight centuries later, as the visitors’ book
reveals, it is admired by millions as “ravishing,” “instinct
with grace,” “one of the wonders of the world”,
“the most beautiful structure in the world.” The
nave to the west and the quire to the east of the tower have a ratio of
exactly 1.618. Above the 75 meter tower rises the marvellous 47 meter
spire, almost exactly the divine proportion. So many brothers and sisters
and visitors have come into our Kingston meeting hall for the first time
and said almost instinctively, yes, instinctively: You sure have a beautiful
meeting hall. We have. Its proportions are divine.
Look
in awe
Look in awe at the giant statue of Christ the Redeemer on its mountain
top in Rio de Janeiro and marvel at its perfect proportions. That is because
the ratio of its height to the outstretched arms is 1.618. The façade
of the United Nations Building in New York has a proportion almost exactly
1.618. That is why it has such stability and appears so well proportioned.
It will withstand earthquake or disaster better than many other buildings
in the city.
The logarithmic spiral is defined by the divine proportion of 1.618. You will find it, and can measure it, in the tiny turritella seashell on the beach, in a fossil ammonite from the stone quarry, in the pearly nautilus floating in the ocean, in the wild spiral arms of hurricane Gilbert and all its lesser brother and sister storms, to the unimaginably vast spiral arms of the galaxies in the farthest heavens. In nature the divine proportion is all around us, from the microscopic to the astronomical. It is hard wired into the universe, and into our brains. When things are in proportion, our minds find satisfaction and rest.
The height and width of Solomon’s porch in the Jerusalem temple measured 50.5 meters by 31.2 meters, a ratio of 1.618. Herod’s massive platform on which the Temple rested averages 457 meters from north to south and 282 meters from east to west: proportion 1.620. In the back of my Bible is a map showing Israel divided among the twelve tribes: north from Jerusalem is 181km, south from Jerusalem is 112km, ratio 1.616; west from Jerusalem to the coast is 56km, to the ill-defined eastern border of Reuben is 90km, a ratio of 1.607. In ancient times, Jerusalem was called the “navel of the land” indicating its precise location to the rest of the land.
Who has marked off the heavens with the breadth of his hand? Whom did the Lord consult to enlighten him, and who taught him the right way? Lift up your eyes and look to the heavens: who created all these? You have made the heavens and the earth, by your great power and outstretched arm. Nothing is too hard for you (Isaiah 40:12,14,26. Jeremiah 32:17).
Maintaining
a right proportion
There’s an old Greek word used both in science and in the Bible:
analog. It means a right proportion, a proper relationship. Paul uses
it in Romans 12:6, when he is discussing the ‘gifts’ with
which God blesses us: If a man’s gift is prophesying, let him use
it in proportion to his faith. We live in a world – indeed, a universe
– where things are “very good” and work well
when they are kept in proportion, when they are in a right relationship
(Gen. 1:31).
The writer of Ecclesiastes (5:18) realized that it is good and proper for a man to eat and drink, and to find satisfaction in his toilsome labor under the sun. This is telling us that food faddists, ascetics, and workaholics have got things out of proportion.
Brethren who will not rest until they have torn ecclesias apart over one single issue – whether it be divorce or the divine name or a hymn book or whatever – have lost all sense of the divine proportion. Some of Jesus’ own closest disciples wanted to incinerate a whole village because they couldn’t find anyone willing to accept them. They just couldn’t see things in proportion.
Here’s a proportion to think about. In the Bible we are instructed to love, help, care, bless, welcome, invite and comfort a total of 1691 times. Hate, curse, hinder, ignore, rebuke, reject and contend appear 490 times. The Bible is much more, three and a half times more, about loving our God and our neighbour, and comforting the distressed, than about rejecting the wayward or hating the garment spotted by the flesh. It’s all a matter of keeping things in proportion.
Brian Greene, author of the best-seller The Elegant Universe, wrote this with great insight: the collective effort of numerous scientists has revealed some of nature’s best kept secrets. And once revealed, these explanatory gems have opened vistas on a world we thought we knew, but whose splendor we had not even come close to imagining.
The love of Christ is divinely proportioned. The apostle Paul knelt in prayer that his beloved brethren and sisters in Ephesus might be able to comprehend with all saints its breadth, and length, and depth, and height. Like the divine proportion in nature, the love of Christ surpasses knowledge. When we have grasped the divine proportions of the love of Christ, and appreciated the riches of his glory, then we poor humans will be filled to the measure of all the fullness of God (Eph. 3:17-19).
Submitted from Kingston Jamaica from an exhortation by Glen Isaacs