Thursday, March 30, 2017

Newton's Apple Tree

Newton’s Apple Tree ~ A short story inspired by the limit, the number zero, Newton, and a favorite Calculus lesson.

Isaac wandered distractedly through the town, paying no attention to the people he jostled. His mind was walking around a problem, scrabbling for purchase on its slippery slope. He made his way to the farm and found his favorite apple tree. He sat down and leaned against the tree.

“What can I do?” he asked the branches overhead. “I know that the slope of the tangent exists in theory–I’ve drawn it on paper–but does it exist organically? Does it have a representation in the natural world?”
In response, the tree dropped an apple on Isaac’s head. BONK!
“Ouch!” yelled Isaac. “Why did you do that?”
“Pick up that apple, you dolt,” said the tree. “Notice its curved surface? Now rest that stick in your hand against it.”
Isaac did as the tree commanded.
“At how many points does the stick touch the surface of the apple?” asked the tree.
Isaac looked more closely.
“At only one!” he cried. “This is stupendous! I wonder why I did not see this before? Many thanks, tree! I have to leave now!”
Isaac hastened to his study where he spent the next fortnight making calculations. He worked in a fever, like one possessed, checking and rechecking his figures. His family grew worried about him and wondered at the agonizing moans emanating from his room.
 Isaac’s father was on the verge of breaking down his door when Isaac emerged from his study. His parents gasped. Was this pale, disheveled ghost of a man their son?
Isaac stared blankly at his family and his surroundings a few minutes before stumbling blindly out the door. He headed back to the apple tree.

“It’s no use,” Isaac groaned. “I shall never find the fluxion that proves the tangent line slope, even though I know it exists. It was almost mine; I had the function, the fluent, and the difference quotient all set up. I was all ready to merge the two secant points into one. So close…so close…”
BONK! Another apple landed on Isaac’s head.
“OUCH! I say; that was uncalled for! Here I am in the depths of misery, pouring out my soul, and all you can do is toss apples at me!”
“QUIET!” barked the tree, “Or I will unload an entire bushel on your head! That’s better. Now, you have your function, your fluent, and your difference quotient.”
“Well, then, go ahead and find the limit as delta-s approaches zero.”
“But I can’t!” Isaac wailed. “That would mean division by zero. I can’t do that!”
“Why not?”
“Are you wanting in the upper story?” said Isaac. “In the first place, zero is a dangerous number. It does not behave respectably like the other numbers. No reputable mathematician would ever attempt to divide by zero–it’s just not done in polite society. If I tried that, I would be worst than a laughing stock; I would be shunned.”
“What do you care what other people think?” asked the tree. “You have always considered yourself a mathematical rogue, haven’t you?”
“It’s not merely that,” said Isaac. “If I were to actually divide by zero successfully, the rational world would collapse. There would be riots in the streets, dogs with cats, incompetent rulers on the throne–er, never mind that last one, it’s true anyway. The point is, if I prove division by zero, then I could prove anything, whether or not it is real. You see my problem?”
“What I see is a person not willing to take a little risk,” said the tree. “How do you know the limit does not exist unless you actually prove or disprove it? I say, throw off your shackles of caution and bonds of convention! Have faith in your difference quotient and believe in the limit. So you destroy the world–so what? Are you going to let a little thing like that stop you?”
Isaac slowly rose and faced the tree.
“You are right,” he said. “I am a mathematician. They think I’m mad anyway, whether or not it’s true. I will do it. I will find that limit if it is the last thing I do.”
Isaac gently touched the tree.
“Good bye, old friend. We may never see each other again.”

A week passed with the tree wondering what became of Isaac. Did he or did he not find the slope of the tangent line? Suddenly Isaac came bounding down the lane. The exultant look on his face said it all.
“I did it!” he said, trying to catch his breath. “I successfully found the limit!”
“Congratulations!” said the tree. “I see the world did not end.”
“No, it did not end–it exploded! Oh, tree, the vision I had of new vistas to be explored. This has opened the door to another world of mathematics! Why, I foresee engines flying in the air, wagons moving along without animal power, strange and unusual food of the gods that heals boils, the pox, and the plague, buildings towering over the city, and…” BONK!
“OUCH! This is really too much! What is the reason for this apple?
“I thought you might be hungry.”
Isaac picked up the apple. Now that he thought of it, he was hungry.

“Thanks,” he said.

Tuesday, March 28, 2017

Official Grammarian

According to a recent article in the Washington Post, the rules of grammar have changed recently.  “Their” can be used as a singular possessive pronoun instead of “his or hers.”  “They” can be used as a gender-neutral singular pronoun.

In addition, you (note I’m replacing “one”) may now single-space as the end of a sentence. Who decides these things?  Apparently a select group of linguists do.  I happened to stumble across this information while I was racing down a sidetrack.  Otherwise, I might never have known and would have continued to foist “his/hers” on the reading public. 
I think those who change the rules of grammar should make public service announcements at regular intervals for fourteen months.  And I have just the way to do that.  Recruit someone who likes to tweet–a lot!

Suppose we find someone who tweets all the time to everybody about everything.  A person like that could make himself really useful to the American people by making public service announcements.  Perhaps we should give the job of Tweeter-in-Chief to someone well-known, someone in the spotlight. He would not have to necessarily be popular, just someone who draws press coverage. That way, not only would his followers read them, they would be broadcast in every home by the media.

And as for the content, the Tweeter-in-Chief could tweet out all sorts of useful information such as weather conditions, road closures, schools’ foggy day schedules, airline flight delays and cancellations and, of course, changes in the rules of grammar.

Saturday, March 25, 2017

C. S. Lewis ~ "Lucy's Story"

Clive Staples Lewis (1898–1963) was born in Belfast, Ireland, the son of a solicitor and a clergyman’s daughter.  He taught medieval literature at Oxford University and at Cambridge University and was a prolific writer.  C. S. Lewis’ better known works include The Chronicles of Narnia, The Screwtape Letters, Mere Christianity, and Out of the Silent Planet, the first book in his space trilogy.

The following is an excerpt from Voyage of the Dawn Treader

It was a large room with three big windows and it was lined from floor to ceiling with books; more books than Lucy had ever seen before, tiny little books, fat and dumpy books, and books bigger than any church Bible you have ever seen, all bound in leather and smelling old and learned and magical. But she knew from her instructions that she need not bother about any of these. For the Book, the Magic Book, was lying on a reading-desk in the very middle of the room.
She came to a spell “for the refreshment of the spirit.” The pictures were fewer here but very beautiful. And what Lucy found herself reading was more like a story than a spell. It went on for three pages and before she had read to the bottom of the page she had forgotten that she was reading at all.
She was living in the story as if it were real, and all the pictures were real too. When she had got to the third page and come to the end, she said, “That is the loveliest story I’ve every read or ever shall read in my whole life. Oh, I wish I could have gone on reading it for ten year. At least I’ll read it over again.
But here part of the magic of the Book came into play. You couldn’t turn back. The right-had pages, the ones ahead, could be turned; the left hand pages could not.
“Oh, what a shame!” said Lucy. “I did so want to read it again. Well, at least, I must remember it. Let’s see…it was about…about…oh dear, it’s all fading away again. And even this last page is going blank. This is a very queer book. How can I have forgotten? It was about a cup and a sword and a tree and a green hill, I know that much. But I can’t remember and what shall I do?”
And she never could remember; and ever since that day what Lucy means by a good story is the story which reminds her of the forgotten story in the Magician’s Book.

The Book of Rhino is one of Lucy’s stories for the refreshment of the spirit.

Thursday, March 23, 2017

Eternal Spring

Flash Fiction Challenge fro Terrible Minds: Write a story about gods or goddesses.

            “Hurry, Caril, it isn’t much farther.” 
            Ceridwen tugged at her companion’s arm, a boy ten years of age, red-faced and sweating.  In spite of her pulling, Caril stopped and shaded his eyes from the sun.
            “This had better be worth it,” he groused.
            “Just wait; you’ll see.”
            Ceridwen resumed her hike up the gentle slope with Caril trudging behind her.  After twenty minutes, Ceridwen halted and pointed triumphantly to a rock by the path.  In front of the rock was a small lawn; Caril could hear the sound of water.  On one side of the rock was a tiny spring that trickled into a small basin.  The basin was obviously man made.  Curious, Caril edged closer to the rock as Ceridwen pushed back an overhanging growth of fern.  There was a niche carved into the rock above the basin and resting in the niche was a figure about a hand span in height.
            “Don’t touch it!” Ceridwen said, as Caril stretched his hand toward the figure.  “The goddess does not wish to be disturbed.”
            “How do you know what the goddess wants?” Caril asked.
            “Well, if you were a goddess would you want to be handled by a grubby boy?”
            Caril started to protest but Ceridwen grabbed him by the shoulders and looked into his face with eyes glowing.
            “Isn’t this an exciting discovery?  Just think of how long she has resided in this rock, year after year, holding court by her spring!”
            “How do you know it’s a goddess?”
            Ceridwen looked at Caril primly.
            “It’s because she has breasts,” she said.  “See?” 
            Ceridwen pointed at the figure.
            “Now we must give her an offering for trespassing in her sacred place.”  Ceridwen reached for something on the other side of the spring and pulled out a wooden cup.  She filled the cup with water from the basin, poured out a small amount, and then offered it to Caril.  When he had drunk from the cup, she refilled it and drank of it herself, and then shook the remaining drops on the ground.  Then they both lay down on the lawn hand in hand and watched the leaves flutter overhead.  Presently Ceridwen broke the silence.
            “It’s a wonder that Father Paul didn’t find this altar and tear it down,” she said.  “You know how he feels about idol worship.”
            “What if Mother discovered it!” replied Caril.  He and Ceridwen looked at each other aghast.  Caril’s mother, Lady Irmtraud, was a battle-scarred warrior in the fight against all things non-Christian.
            “Well, then, we will have to cover our tracks especially well and hide the altar so that the goddess may rest in peace,” said Ceridwen.  “We must protect her from those who know just enough of God to be dangerous but not enough to be kind.”


            Amalia strolled leisurely among the trees.  Her two companions romped on either side of her; all three of them rejoiced in the mild warmth of the weather.  Amalia lifted to head to watch the passing clouds.
            “AMALIA!” Mole shouted. “Watch out!”
            “Too late!” Skunk groaned.
            Amalia plowed into a figure kneeling in front of her. She tumbled head over heels and landed on the ground.
            “OOMPH!” she gasped.  “What happened?”
            “I’m afraid that would be me,” said a young woman sitting next to her.  “I happened to you–or rather my hindquarters did while I was poking about in this bush.  Are you hurt?  I did not hear you coming else I would have moved out of your way.”
            “I’m quite well,” said Amalia.  “It’s my fault for not watching where I was walking.  Although I must confess I did not expect to find…Oh!”
            While Amalia was talking, the woman rose to her feet. She was tall and beautiful.  Though dressed in a simple tunic, she radiated the aura of a queen.
            Amalia scrambled to her feet.
            “I beg your pardon,” she said, with a curtsy. “My name is Amalia and these are my friends, Skunk and Mole.”
            “Well met,” said the young woman.  “I am the goddess of the spring–or at least I was.  At the moment I am rather springless.  I have lost my spring.”
            “What!” Skunk exclaimed. “How could you lose your spring? (Don’t shush me, Mole.) I mean, being a goddess and all, isn’t that rather unusual?”
            The goddess smiled.
            “Not at all. Life escapes, you know.”
            “Well, we will be happy to help you look for it,” said Mole. “Especially Skunk.”
            “Thank you. That is most kind of you.”
            “So, what does your spring look like?” asked Amalia.
            “Wait, let me guess–it’s wet,” said Skunk.
            Mole rolled her eyes and shook her head.  But the goddess nodded.
            “Skunk is quite right,” she said.  “My spring is wet; it’s about eight feet tall and two feet across at its widest point. It was around here somewhere.”
            The goddess got back down on her knees and began feeling along the ground; Amalia, Mole, and Skunk joined her.
            For the better part of an hour, the four carefully searched the area for some sign of a spring. Skunk, who had wandered away from the others, spied something in the bushes and pounced on it.  Suddenly the goddess sat upright and sniffed the air.
            “My spring is close by–I can smell it!”
            She rose to her feet.
            “And I can hear it!” She looked around and spotted Skunk.
            “Skunk, dear, what do you have in your hand?” she asked, running over to him.
            Skunk held up a small object. It appeared to be made of wood.  He handed it to the goddess.
            “Oh, thank you!” she said. “You’ve found it!”
             Then she walked over to a rock over hung with ferns. She parted the ferns to expose a small niche and basin carved into the rock. She gently placed the object into the niche; immediately a stream of water burst forth from the top of the rock and trickled into the basin before cascading down the side of the path. The others crowded around.
            “What is that?” asked Amalia. “It looks some sort of figure.”
            “I am the goddess of the spring, and this is my image.”
            Amalia looked more closely at the image and then at the goddess.
            “I beg your pardon, Goddess, but this doesn’t look anything like you.  I mean, you are beautiful while this image is… well… it’s rather… ‘unfinished,’ to put it nicely.”
            The goddess caressed the figure. 
            “You see me as beautiful; that is because one’s character is revealed by the gods they create. My creator was a person of boundless joy and great integrity.”
            She turned to the others, her eyes shining.
            “I wish you could have know him, the young man that made this image and carved this resting place for it. But that was centuries ago.  He was still a youth then, newly arrived to this country. He was no artist, but his hands did what they could to express his love and gratitude. He knew this figure was merely a symbol. Like all creators, he fashioned his imaginary world out of his inner self, but he did not make the error of mistaking his imaginary world for the real one.”
            “You’ve been here for centuries?” asked Mole.
            “Over seven hundred years.”
            “And in all that time, you’ve never lost your spring?”
            The goddess shook her head.
            “Unfortunately, it has happened a few times. There are those who see the image as a symbol for something else, something that offends them. When they discover my resting place, they tear down the image and destroy the spring.”
            “Then we must keep you safe,” said Amalia.  We must find a way to hide you better so that you and your spring are protected.”
            “No, my dear, that will not do.  I am not meant to be safe.”
            “But someone else might destroy your image, and then you would lose your spring.”
            The goddess embraced Amalia and smiled.
            “Wherever there are thoughts of joy and thanksgiving, I will always find the Eternal spring.”