Nature

The Passion of Grandparenting … and of Writing

Like for most things, you can only understand the strong emotions grandparents feel towards their grandchildren once you’ve experienced it.

Some live only for their children and grandchildren. I cannot imagine this. I feel so lucky and priviliged to have my twin passions, my family AND my writing.

I’ve reconnected recently with people from my past, one who told me that he is bored with his life. What about the joys of learning new things, of travel, exploring different places, cultures and scenery? How can anyone be bored when there is so much to do and to see, even in one’s own country, not to mention other places on planet earth?

September 9, 2016 6 comments

Nature

The Golden Ratio in Nature

I was never interested in mathematics at school, because of the way it was taught; it was seen as a subject for boys in the 50s. Perhaps today, things have changed a bit. In any case, from early on, I was on the creative spectrum, rather than the logical/rational one. Was this a result of nature or nurture? Perhaps a little of both. plant-geometry Today, however, I’m fascinated by the idea of The Golden Ratio, and its links with mathematics, nature and art. In fact, it also has links with science, architecture, music, and many other areas besides. The golden ratio essentially states that a + b is to a, as a is to b.

$golden-ratio-math$

The Golden ratio is a special number (1.618), found by dividing a line into two parts, so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part. It is often symbolized using phi, after the 21st letter of the Greek alphabet. In an equation form, it looks like this: a/b = (a+b)/a = 1.6180339887498948420

Around 1200, mathematician Leonardo Fibonacci discovered the unique properties of the Fibonacci Sequence. This sequence ties directly into the Golden ratio: if you take any two successive Fibonacci numbers, their ratio is very close to the Golden ratio. As the numbers get higher, the ratio becomes even closer to 1.618. For example, the ratio of 3 to 5 is 1.666. But the ratio of 13 to 21 is 1.625. Getting even higher, the ratio of 144 to 233 is 1.618. These numbers are all successive numbers in the Fibonacci sequence.

Here is a visual representation of a Fibonacci spiral which approximates the golden spiral, using Fibonacci sequence square sizes up to 34. Notice how the lengths get smaller in a spiral pattern.

This spiral pattern is used throughout nature. Many shells, including snail shells and nautilus shells, are perfect examples of the Golden spiral. shell-nautilus

fibonacci-sunflower-centre The seeds of a sunflower, which start in the centre and radiate outwards to fill the space, repeated endlessly, are a perfect example of the Golden Ratio in nature. There are no gaps from beginning to end. Some spiders form their webs in spirals that suggest the repetitive pattern of the golden spiral. And the beautiful designs on the wings of moths and butterflies approximate the golden mean. Similarly, hurricanes often portray the golden spiral. Other examples are roses, spiral galaxies, such as The Milky Way, dolphins, starfish, sea urchins, ants, cauliflowers and honeybees, which all exhibit the fibonacci proportion.

The symbol that has come to represent this ratio is the 21st letter of the Greek alphabet phi.

butterfly-beauty

Leonardo of Pisa, also known as Leonardo Pisano or Fibonacci, was an Italian mathematician, born in Pisa about 1175 AD.

Fibonacci popularized the Hindu-Arabic numeral system in the Western World through his Book of Calculation in 1202. In the same publication, he introduced the sequence of Fibonacci numbers to Europe.

Scientists today, have moved away from thinking about such considerations, as they are deemed to belong to an ancient time. Darwinian evolutionary theories, and findings from archaeological diggings are more likely to be of interest to the modern mind, because they are evidence-based.

It still amazes me to see how much order, beauty and patterning exist in the natural world around us. I wonder at the time it took, and the processes at work, to create all of this amazing diversity surrounding us, and of which we are a part. red-rose-spiral-pattern

Photographs on this post have been renewed and resized to fit the new format and theme of my blog. The content remains the same.

August 24, 2016 7 comments

Art Nature

More About The Golden Ratio

The Vitruvian Man is a drawing created by Leonardo da Vinci circa 1490. It is accompanied by notes based on the work of the architect Vitruvius. The drawing, which is in pen and ink on paper, depicts a male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square. The drawing and text are sometimes called the Canon of Proportions or, less often, Proportions of Man (Wikipedia).

vitruvian-man

Golden Ratio and Art This drawing is based on the correlations of ideal human proportions with geometry described by the ancient Roman architect Vitruvius in Book III of his treatise De Architectura. Vitruvius described the human figure as being the principal source of proportion among the Classical orders of architecture. Vitruvius determined that the ideal body should be eight heads high. Leonardo’s drawing is traditionally named in honor of the architect. (https://en.wikipedia.org/wiki/Vitruvian_Man (Wikipedia)

The human body: The measurement of the human navel to the floor and the top of the head to the navel represents the Golden ratio.

In a previous post, “The Golden Ratio In Nature“ I pointed out how this ratio appears in many forms of nature and of science.

August 23, 2016 5 comments

Nature Poetry

The Parable of the Twins

I came across this parable at the time my daughter was about to give birth to her first son and was enchanted by it. I had studied “The Republic” by Plato at Armidale Teachers’ College, and had learnt about a similar metaphor, that of The Cave, included in The Republic. Plato describes slaves imprisoned in a cave who are ignorant of the real world outside their prison. “The Parable of the Twins” expresses a similar idea of dislocation and ignorance linked to being expelled from the womb at the time of birth. My daughter has become avidly interested in the Cave Metaphor, even though she has never read “The Republic” by Plato, nor was ever willing to hear me talk about such things.

two-babies-womb

It goes something like this …

Once upon a time, twin boys were conceived in the womb. Seconds, minutes, hours passed as the two embryonic lives developed. The spark of life grew and each tiny brain began to take shape and form. With the development of their brain came feeling, and with feeling, perception—a perception of surroundings, of each other, and their own lives. They discovered that life was good and they laughed and rejoiced in their hearts.

One said to the other, “We are so lucky to have been conceived and to have this wonderful world.”

The other chimed in, “Yes, blessed be our mother who gave us life and each other.”

Each of the twins continued to grow and soon their arms and fingers, legs and toes began to take shape. They stretched their bodies and churned and turned in their little world. They explored it and found the life cord which gave them life from their mother’s blood. They were grateful for this new discovery and sang, “How great is the love of our mother – that she shares all she has with us!”

Weeks passed into months and with the advent of each new month, they noticed a change in each other and in themselves.

“We are changing,” one said. “What can it mean?”

“It means”, said the other, “that we are drawing near to birth.”

January 22, 2016 2 comments

Guest Post Nature Writing

“Snakey” by Roger Britton

I soon learnt Death Adders were dangerous in more ways than one. The common belief among us school boys was that, once you were bitten by a death adder, you only had three minutes before your tongue went black, the whites of your eyes turned pink and you fell over and died in a writhing spasm. This belief sounded reasonable, so no one questioned its accuracy.

In a large preserving bottle was a big ugly brute. It had a wide triangular head, huge fangs and a thick bulbous body with a tapering tail. The grey, black and brown bands would help camouflage it as it lay in wait for its prey. The adder’s eyes seemed to follow us as we dawdled into our Year Six classroom. I knew it was dead and covered with formaldehyde, but I always gave it a wide berth. It had to be the meanest, thickest and wickedest snake that I had ever seen. Bertie Butterfly reckoned its real name was a ‘deaf adder’ as these snakes were stone deaf, but death or deaf, we all knew you didn’t muck around with them.

My first real encounter with one was the day I discovered that I had left my lunch at home. Rather than starve to death, I decided to break school rules and risk a quick bike trip home to retrieve it. I grabbed my trusty push bike and headed off.

The road was so hot that summer that the tar was melting and sticking to my bicycle tyres. When I reached the bottom of our hill, I rode up as far as I could go, before dismounting and pushing my bike at a run.

I was on top of the death adder before I realized it. I gave a shriek of terror and tried to put my right foot over my left shoulder. The bike crashed down on the road and I fled up the embankment.

The snake stayed still. From my vantage point of two metres up, I observed the scene. The death adder seemed stuck to the tar and was, apparently, dead. Gingerly, I crept down the bank and collected my bike. Once more, I resumed my run, though I kept a wary eye out for any other scaly reptile that might have been parboiled.

“Mum! Mum! There’s a death adder stuck on the road!”

The house was empty. She wasn’t home.

I gulped down my lunch and headed back to school, with a biscuit stuffed in my lunch bag.

The snake was still there, and that was the beginning of my downfall. How could I resist acquiring a new specimen for our science table? A handy stick was found, and the dead death adder was poked and prodded into my lunch bag, minus the biscuit.

I arrived at the school corner just as the line-up bell rang. All the students were gathered on the parade ground and, knowing that I’d be late, I parked my bike and snuck in the back door. I was peeved that I didn’t have time to show off my prize to my mates.

Upstairs, I stole a glimpse out the window and saw our class about to ascend the stairs, while the headmaster kept time with a marching drum.

Now, I thought, how should I introduce the snake to the class? Hmmm, why not share the fright that I had had? Without thinking too much, I lifted the lid of Frances’ desk and slipped the death adder on top of her books.

Kenny Curll bounded into the classroom, racing Ferret to be first. The others staggered in, aware that they had a few minutes to gossip before the headmaster could pack away the drum and stride to the classroom. Ferret took up his usual role of cockatoo, ready to call a warning when Old Thumper was in sight.

“Hey Britt, where yuh been?” Curlly enquired.

“Ah, mate, you won’t believe what I found! Come here.”

Curlly sauntered over to my desk. Before I could explain, Ferret sounded the alert.

“Ssshh, Old Thumper’s comin’!”

Students dived for their desks to avoid a confrontation with the headmaster.

“Tell you later, Curlly.”

Frances and I tripped over each other to get to our shared double-desk.

“Quick, Fran, get a book out.”

The expectation was that we had to read quietly whilst awaiting the headmaster.

Frances gave me a smug look, lifted her desk lid, and put her hand in. Her hand touched something warm and clammy.

“Aaaaaaaaahhh!”

Her screech made my hair stand on end. Terrified kids ducked in all directions, screaming in fright and unison with Frances. Something terrible had happened somewhere.

Frances’ eyes widened. She paused for breath, then her shriek grew louder. Suddenly her bladder cascaded down her chair like Niagara Falls. She sprang to her feet and knocked over her desk. The death adder spilled into the jostling crowd.

Instantly the class realized why they were screaming. Additional yelps rent the air. Bodies pressed against the walls and a few pupils collided as they shot out the door.

“What the hell is going on?” bellowed the headmaster.

He was running down the corridor now.

“Stop it you idiots! Keep still the lot of you!”

Classroom conditioning kicked in. Instantly all was hushed. Students remained backed against the wall, warily eyeing the adder of death.

Frances, her chest racked with dry sobs, stood amidst a pool of piddle, her feet frozen to the floor. The death adder’s menacing gaze held everyone in fear, including the headmaster. I edged to the centre of the classroom.

“Its dead, Sir.” I whispered.

All eyes swivelled towards me. Somehow, everyone knew I was the instigator of the chaos. I wanted to ooze down through the floorboards like the slowly receding pee.

“Britton, get that bloody snake out of here!” yelled Headmaster Nebone, forgetting about teacher decorum.

I picked it up on my ruler and once more pushed it in my lunch bag and left the room. Outside in the corridor, I could hear classroom order being restored. Desks were picked up and chairs straightened. Two girls led Frances out and down to the sick bay to change into something from the clothing pool. The three of them gave me reproachful glares. Frances was still softly sobbing.

Curlly came to fetch me, but the snake was to remain outside.

“Oh, man, that was marvellous,” beamed a delighted Curlly, “but boy, are you going to get it now!”

That afternoon I could hardly hold the handlebars of my bike. Three strokes of the cane on each hand had left them stinging and throbbing. Through my watery eyes, I couldn’t help giggling, despite the pain. As Curlly had said, it was an absolutely marvellous event.

It was sad, but Frances never ever saw the funny side of it.

Editor’s Note: I fondly believe that Roger, when he became a teacher of a small school in the 60s, must have experienced a huge wollop of karma from the behaviour of schoolboys in his classes.

January 20, 2016 7 comments