Nature’s Golden Calculations

Amit looked at his completed painting with satisfaction. He wondered if he could get the prize at the National Painting Competition by making the very same painting. He quickly ran to the kitchen, where his mother was making Kachoris. “Mumma, look at what I’ve drawn”, he urged and proudly handed over the sheet. His cousins, who had visiting, crowded around her and peered into it. 

It was definitely a beautifully coloured drawing. The colours of the sky were a lovely mix of grey, orange and pink, the colours of dusk. The sea was an equal reflection of these hues, and there was no doubt that the boy was a genius with his brush. 

But there was something very, very wrong with the picture! Amit’s mother saw it as soon as she took the painting from him. She told him, “The painting is quite fine, but why do these people here on the beach have such long legs and arms?” 

Amit peered into the painting. Was it really a mistake? How could that happen? Ten –year- old Amit had always been appreciated for his talent. At a very young age, he was gifted with a taste for the right colour combinations and the uncanny ability to get various hues right, almost as exactly as they appeared in nature. And now his mother was pointing out a mistake! But the truth was that, this was what Amit had been doing in most of his drawings!

“Well, I had to draw them tall”, he said, a little obstinately. He still couldn’t see what was wrong with the figures he had drawn. 

The people he had drawn had abnormally long hands and legs. They were so disproportionate; in fact, they didn’t look like people at all! They instead looked like four-legged spiders, and his mother burst into laughter at the thought. Even the trees looked strange, with their branches sprouting at odd angles at odd intervals. His cousins also squealed with laughter. 

Amit pouted in anger. “Don’t laugh at my drawing”, he said in an annoyed voice. “You’re simply finding fault, Mumma.”

“I’m not”, said his mother, “If I don’t correct you, you’ll repeat the same mistake at the Competition. And then you’ll feel worse if you don’t win.” 

“I will definitely win”, said Amit, stubborn and arrogant. “Hey Amit, imagine yourself with those terribly long arms and legs”, said one of his cousins. “Then we can call him Daddy-Long-Legs”, said another older cousin who had read that classic novel, and the children burst into laughter again.  Amit closed his ears and went up to bed, and refused to come down for tea and snacks. Tears flowed down his cheeks. How perfectly horrid of everyone to make fun of his painting!

He was just lying there, thinking of his painting, when a voice whispered into his ear “Daddy- Long-Legs! Get up!” Amit was enraged. Thinking it was one of his cousins who had come to annoy him again, he threw a pillow behind him, hoping it would hit the offender. “Go away!” he said, “I don’t want any tea. Just go!”

But there was no one behind him. The voice came again in his ear. “Daddy- Long- legs! Just look at yourself in the mirror!” Now Amit was really mad. He jumped up, and made for the door. But that was when he realized that he could no longer walk properly! His arms and legs were so spindly and long! He rushed as fast as he could to the mirror. He was horrified at what he saw- he had been transformed like one of those figures he had drawn in his painting! 

Amit almost cried out loudly. Then he remembered his cousins who would laugh at him if they saw him this way! He quickly shut his mouth, but the tears kept rolling down his cheeks. But the voice in his ear whispered again. “Do you want to get back to being normal again?” “Oh yes, oh yes!” cried Amit. “All right then”, said the tiny voice, “Pick me up and place me in your palm and walk out of the house.”

Amit put his hand where the voice was coming from. He found a tiny black ant, and he placed it carefully on his palm, while he tried to figure out if the ant had really spoken to him. The ant seemed least perturbed and quietly settled into Amit’s hand. Now for the second order, thought Amit. How would he manage to slip out unnoticed? But luckily for him, he managed it without any of his cousins or grownups noticing him. 

As soon as he was outside, he started questioning the ant, scolding it and worrying it, hoping that no one, including his neighbours would see how he looked. The ant cut him short and asked, “Have you seen snails?”

Amit was bewildered and taken aback. “Umm.. no”, he said. “Then go to the pond in your courtyard”, said the ant confidently. When Amit reached there, he saw a number of snails crawling all around. “Well, what’s so special about them?” he asked hotly.

“Do you see their shells, Amit?” said the ant. “Do you see how they are different from the ones you draw?”
Amit peered closely. They more or less looked the same! But then he saw that the real shell was a beautiful shaped circular shell, whose spiral became larger and larger with each coil. “Remember how you drew us?” The snails were all talking! Amit got the shock of his life. “You drew us with shapeless, large shells”, they complained. Amit hung his head. 

The ant spoke to him again. “Now go to the flower fields”, it said, and Amit obeyed. Amit looked at all the pretty flowers there. But they started complaining as well! “Do you remember how you drew us Amit?” The sunflowers complained the most. “You just scattered some dots to show our florets and seeds! Don’t you know that we have a set pattern in our florets? That’s how we look so pretty!”

The trees all around were darkly looming in on Amit. “We have our complaint too”, and then they started telling him how he had drawn their branches all wrong! 

“What am I even supposed to do?” cried Amit to the ant. “I want to get back to normal!”

“Do you know what ‘Normal’ means, Amit?” said the ant. “Nature has its own way of ensuring the best symmetry in its living creatures. It sets everything according to a calculation called the Golden Ratio. If Nature goes by this value, then there will be no ugly gaps, and no ugly forms. Your limbs are an example of this golden ratio, which is the number phi or (φ), with a value of 1.618. That means, if you measure your entire arm, and then divides it by the distance from your elbow to the tip of your fingers, you will get this value. The same applies to your legs. 

Similarly, the spiral shell of the snail, the growth of branches on the trees and the pattern of florets on the sunflower head, are all similar examples, where they go a pattern that follows the Fibonacci Sequence- a sequence of numbers defined by the Golden ratio. Divide each number in the sequence by its previous number, and you get the Golden Ratio!” 

Amit was beginning to understand where he had made the mistakes in his drawing. “Whenever you draw us, you forget this Golden Ratio!” the ant said. “You have drawn me too, shapeless and non- symmetrical! Now that you know of the Golden Ratio, will you draw us well? Will you?”

The atmosphere had suddenly turned threatening. The ant, the flowers, the trees and the snails seemed to be advancing towards him. Amit was tired and scared. What was happening? If only he could escape! He tried to push the ant away, as it was closest to him. It gave a sharp bite!

“Aaaahh!” Amit was suddenly awake. He looked at his hand. An ant had really bitten him, but thankfully his arms and legs were now back to their normal size! Had it been a dream? Amit quietly tried practising drawing according to the Golden Ratio rule. He now understood why everyone had laughed at him. He was now more confident of winning the Trophy. But most of all, he didn’t want a crazy, unhappy ant worrying him anymore!