Thursday, April 20, 2017

Carl and the Golden Ball

Upon a great adventure he was bond.
That greatest Gloriana to him gave,
That greatest Glorious Queene of Faerie Lond,
To winne him worship, and her grace to have.
Edmund Spenser ~ The Faerie Queene, Book 1, Canto 1

The Gentle Knight rode through the wood, following the sound of someone in distress.  His companion Carl walked at his side.  Presently they came to a clearing and beheld a Lady weeping by the side of a small stream.  So intent was she on her mournful state, she did not hear the Knight’s approach.
            “My Lady,” said the Knight. “Why do you weep?”

            Startled, the Lady looked up in wide-eyed wonder at the Knight.  Then she buried her face in her hands and began weeping anew.  The Knight immediately dismounted and knelt as a supplicant.
            “If you would but tell me the cause of your tears,” he said, “I will banish it ere this day is done.”
            The Lady raised her fair head and placed a trembling hand on the Knight’s arm.

            “Good and Gentle Knight,” she said, “you have truly shown yourself to be most noble to stay your journey for a poor maiden’s trouble.  I would not delay your high purpose…yet my heart is so grieved that I will forego the usual courtesies and pour forth my tale of woe.”

At her words, Carl rolled his eyes and went chasing after a moth.  The Lady continued.

            “See yon stream?  Early this morning I was playing with my golden ball, tossing and catching it in all manner of merriment.  But misfortune stayed my hand on my final toss, and my golden ball landed in the stream.  From there, the water swiftly carried down, down, down to a tunnel through with the stream flows.  And now my golden ball is stuck like a pig in the mud.”
            “The worst of it is the clouds have gathered together in preparation for a mighty thunderstorm.   The rain will eventually cause the tunnel to overflow, and my golden ball will be lost forever.”

            Having told her tale, the Lady recommenced her weeping.  The Knight said not a word but followed the stream until he espied the tunnel.  Casting himself on the ground, he reached into the tunnel in an attempt to snatch the runaway ball.  When that failed, he grabbed his lance and poked it into the tunnel, trying to push the ball to freedom.  But however skillfully the Knight wielded his lance, the ball remained beyond his reach.  At length the Knight withdrew from the tunnel and returned to the Lady, defeated and dishonored.

           “I am defeated and dishonored,” he cried.  “I am no longer worthy to bear the title Gentle Knight!”  With a wail of anguish, the Knight began removing his armor.  Seeing that her golden ball was still stuck in the tunnel, the Lady joined in the general lament.

            In the meantime, Carl, who had overheard the Lady’s tale, started taking measurements and gathering data.  He determined that the rate at which the rainwater would flow into the tunnel was modeled by the function R(t)  cubic feet per hour.  The rate at which water drained from the tunnel was modeled by the function D(t) cubic feet per hour.  It was his intent to use these two functions to determine the time at which the amount of water in the tunnel would be at a minimum and what the amount would be.  His biggest problem would be getting the Knight and the Lady to stop their wailing long enough to listen to him.

            “Gentle Knight!  Lady!” he shouted.  “I have a plan for retrieving the golden ball!”
            With these and other words, Carl finally persuaded the Knight and the Lady to stop crying.
            “Listen,” he said, “I can figure out the minimum amount of water in the tunnel; if it is not too deep, I can go into the tunnel and get the golden ball.  Will that work for you?”

            The Knight and the Lady were awed by his words and could only nod dumbly.  Carl set to work with his calculations.  As the minutes passed, and the sky grew dark, the Lady began to fret.

            “Oh, Sir Knight, what if your brave companion cannot find an answer?  Can there really be a solution to such a problem?”

            The Knight groaned in response and began removing his outer garments.
            “Whatever the outcome, I have proved myself a knave and a beast.”

             Carl ignored the two of them and continued to calculate.  After about quarter of an hour, he threw down his notes.

            “Done!  The amount of water in the tunnel will be at a minimum of 27.9945 cubic feet in approximately 3.2719 hours.  Now all we have to do it wait; then I will retrieve the golden ball.”
So the Knight, the Lady, and Carl sat down and waited.  At the end of 3.2719 hours, Carl went into the tunnel and found the Lady’s ball.  He carried it over to her with a warning to be careful of where she tossed it.  The Lady was so thankful that she asked Carl to name his reward–she would give him anything, even her own hand in marriage.  This, however, Carl refused.

            “Lady, I appreciate the offer,” he said, “but I am a cat.”

Then he told the Knight (who by this time was naked) to put on his clothes and his armor.  Carl was thoroughly wet from his excursion into the tunnel and wanted to get indoors to the nearest fire as soon as possible.  Because the Knight was a gentleman and Carl was a cat, they took the Lady with them, along with her golden ball.

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