Snowdrops and daffodils
Butterflies and bees
21st March 1970. The Eurovision Song Contest is taking place in Amsterdam, the Netherlands. United Kingdom’s Mary Hopkin with her song Knock, Knock, Whose There? is expected to win. With one last contestant to perform, she is leading with 24 points.
Then an 18-year old Irish schoolgirl walks to the stage. Long brown hair, short white dress. She sits down on a high stool, smiles and begins to sing. No disco lights, no dancing girls (or boys), just Dana, a simple ballad and her fabulous voice:
Snowdrops and daffodils
Butterflies and bees
Sailboats and fishermen
Things of the sea
Wishing-wells
Wedding bells
Early morning dew All kinds of everything remind me of you.
Many of the things the song mentions are created, but a few are man-made:
Seagulls and aeroplanes
Things of the sky Winds that go howlin' Breezes that sigh (…)
While All Kinds of Everything speaks of the enduring love between a girl and her sweetheart, we can also understand the song as a paean to the wonders of our created world.
The girl, whose real name was Rosemary Brown and who would later be known as Dana Rosemary Scallon and would defend the unborn as a member of the European Parliament, got 32 points and won the contest.
Budding trees
Autumn leaves A snowflake or two
All kinds of everything remind me of you.
It would probably not be too far-fetched to say that everything in creation ultimately reminds us of the greatest artist and architect of all times.
The Fingerprints of God
We can discern the fingerprints of God in the fine-tuning of the universe, in our DNA that is without doubt the most effective code ever invented, and in our cells that are full of self-replicating factories, nanomachines and quality control systems. And, above all, we can see it in the beauty that surrounds us.
The Golden Ratio Even after 2,500 years of wars, pillage, vandalism, a 17th century explosion and modern pollution, the Parthenon in Athens still looks impressive. Obviously, the Greeks who designed it and built it from 447 to 438 BC also thought that this Dorian temple was an object of great beauty. In the early years of the 19th century the Earl of Elgin shipped some of its sculptures to London, where they are still housed in the British Museum. He left the columns supporting the building in Athens, though.
Although some mathematics have tried to dispute it, the remains of the Parthenon display the proportions of the golden ratio, at least in certain respects.
Luca Bartolomeo de Pacioli (1447–1517), a mathematician and Franciscan monk, wrote a book entitled De divina proportione (On the Divine Proportion), associating the ratio with God’s handiwork. This should not surprise us, as the golden ratio is a hallmark of great beauty. We will get it if we divide a straight line into two parts so that the longer part divided by the shorter part is as long as the entire line divided by the longer part. It is often symbolized by the Greek letter Φ (phi).
We see this ratio in the proportions of some of the columns of the Parthenon. We also see it in a number of other great buildings erected in many cultures and at various epochs in history, including the modern ones that imitate classical Greek architecture.
Likewise, the ratio is displayed in some of the finest paintings of all time, including several drawings by Leonardo da Vinci as well as in Michelangelo’s sculptures.
Beauty might not only be in the eye of the beholder. It seems that there are universal criteria for comeliness.
The beauty we see in architecture is merely a reflection of what we see in nature. “He has made everything beautiful in its time,” the writer of Ecclesiastes reminds us (3:11, NIV), and that is no understatement.
It is becoming increasingly obvious that great architecture, paintings and sculptures merely imitate that what we see everywhere in nature – in things big and small, animate and inanimate.
It seems that beauty is woven into the very fabric of the universe, at all levels, from the micro to the macro.
What is interesting is that we can also see the golden ratio in us. The distance from our navel to our heels and from our navel to the top of the head follows the ratio, as does the distance between our forearm and our hand. It is also seen in the proportions in the different parts of our fingers. As the psalmist says, “I will praise You, for I am fearfully and wonderfully made; Marvelous are Your works” (Psalm 139: 14, NKJV).
The Fibonacci Series in Nature
Information, mathematics and great beauty also come together in the Fibonacci series. The journal Science describes it as “a hidden mathematical rule shaping the patterns of life.” Named after a 13th century Italian mathematician, it was probably initially discovered by the ancient Indians and then forgotten for aeons. Fibonacci re-discovered it and discussed it in his book Liber Abaci (1202).
The series involves adding together two integers to produce a new number. Each new number is the sum of the previous two numbers, for instance
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, or
Fn = F n-1 + F n-2.
When we divide any number in a Fibonacci sequence (except the few first ones) by the number preceding it, for instance 233 by 144, we get approximately 1.618.
Numerically stated, the golden ratio also roughly equals 1.618.
This almost magic number is seen in all kinds of everything – from the arms of huge spiral galaxies to tiny seeds, the shells of both extinct and modern sea creatures, in humans, the compound eyes of dragonflies and in many other insects, as well the petals of various kinds of flowers.
In the ammonite shell, the Fibonacci sequence results in intricate beauty and harmony.
In many plants the way the leaves are arranged around the stem is a Fibonacci number. The same applies to the number of petals in flowers. The beauty in sunflowers, for instance, is much more complex than we would have thought. Their seeds can form very elegant Fibonacci arrangements.
The pineapple is a fascinating illustration of a complex Fibonacci arrangement. An article published by the University of Georgia states: “In the case of tapered pinecones or pineapples, we see a double set of spirals – one going in a clockwise direction and one in the opposite direction. When these spirals are counted, the two sets are found to be adjacent Fibonacci numbers.”
Recent expeditions by NOAA’s ship Okeanos explorer and video footage filmed by its remotely operated vehicle (ROV) have shown that this incredible beauty is also seen deep below the ocean surface. Both the ghost octopus and the cosmic jellyfish, as they are called, are astoundingly beautiful.
Most starfish have five arms, which as such is a Fibonacci number. Technically, this phenomenon is known as five-point radial symmetry. In like manner, an octopus has eight arms (another Fibonacci number), and is symmetric in other ways as well.
Fractals
The golden ratio and the Fibonacci series are not the only types of mathematical beauty we see in all kinds of everything. Patterns called fractals occur everywhere in nature, from fern leaves to the branches of a tree, snowflakes, ocean waves, animal colouration patterns and even Saturn’s rings.
Writing in The Conversation, University of Oregon physics professor Richard Taylor describes this phenomenon:
“My scientific curiosity was stirred when I learned that many of nature's objects are fractal, featuring patterns that repeat at increasingly fine magnifications. For example, think of a tree. First you see the big branches growing out of the trunk. Then you see smaller versions growing out of each big branch. As you keep zooming in, finer and finer branches appear, all the way down to the smallest twigs. Other examples of nature's fractals include clouds, rivers, coastlines and mountains.”
In some cases, the various forms of mathematical beauty can be combined: The Romanesco broccoli has a fractal form, a logarithmic spiral, and the arrangement of its spirals on its head conform to a Fibonacci sequence.
In spite of the bad things happening around us (executions, shipwrecks, bombings and earthquakes, to name a few) that are evidence of the Fall, there is no shortage of beauty in our world.
And the best explanation for it is that the Lord God made it all. As the Apostle Paul writes in Romans 1:20:
“For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse.” (NIV)
Sources:
Bohannon, John. 2016. Sunflowers show complex Fibonacci sequences. Science.
Hom, Elaine J. 2013. What is the Golden Ratio? Live Science
Lindsay, Derry and Jackie Smith. 1970. All Kinds of Everything (lyrics).
Parveen, Nikhat. Fibonacci in Nature.
Reich, Lee. 2013. Nature follows a number pattern called Fibonacci. Phys.org.
Taylor, Richard. 2017. Fractal patterns in nature and art are aesthetically pleasing and stressreducing. The Conversation.
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