Friday, February 27, 2015

Probability

Probability Overview
By Madison Nef

What is probability?
Probability deals in the realm of the unknown, and of all things we are uncertain of. Probability gives a meaningful numerical description to things that we admit to not knowing; so it gives us a sense of what to expect and an answer to our question that we can act on. A great example of this is the weather- If we hear a report saying there is an 80% chance of rain tomorrow, if you leave the house you are likely to take an umbrella. If the report was right, and it rains, then you are glad you brought an umbrella. If it doesn’t, there WAS after all a 20% chance of no rain, but better safe than sorry.

Examples of probability and more experiments using it came around in the early 1700’s. From 1730-1770, there was a smallpox epidemic in the US that killed fast. A vaccine was developed to cure it, but there was a one in two hundred chance of death in getting the vaccine. In today’s standards, that’s an incredibly high risk to take and a risk like that could be brought to the court of law. On the flip side of things, smallpox was said to kill one in every seven people who were not vaccinated; so in the long run it was a better choice to get the vaccine.

The earliest known example of probability, however, is when Antoine Gombaud asked two skilled mathematicians for gambling odds. The two mathematicians were Fermat and Pascal. Not much was told about them besides that they were the first people to really experiment with probability in the lecture, but it did bring up the sport of gambling. Gambling is one of the best examples of random events and possibilities simply due to the fact that many gambling games are built around probability and “luck”.  One of the worst forms of gambling that goes unnoticed is lottery tickets- to win the Powerball; there is a 1 in 75,000,000 chance. With such low odds, you’d think it a wonder that ANYONE ever wins- but the key factor is that SO MANY PEOPLE buy tickets with random numbers over and over again that it happens on a weekly basis. A theory in probability that I don’t necessarily agree with is that if you do something over and over again trying to get a rare result, it will EVENTUALLY happen. My problem with this is that just because it IS certain to happen does not mean you SHOULD do it… because God only knows how long it WOULD take.

In a game of poker, people are always looking for a good hand of cards. For example, everyone loses their mind if they get a royal flush- but no one cares if you get an average set of cards, such as a 2, 9, 5, 6, and Jack. In reality, you have the same chance of getting either set of cards because they are all coming out of the same deck, with the SAME chance of being in any particular order. It’s estimated that there are 2,750,000 different combinations of five cards you could be dealt in a game of poker- meaning if you play non-rigged games for the rest of your life, you probably will never get that same hand ever again.
Probability really is strange, but useful- and we use it everyday with knowing it to make decisions, whether big or small. We use it when determining to go out, what to wear, what to eat, and what to do… and most of us barely know how to use it properly. I’m glad I actually listened to these lectures because I actually DID pick up a few little bits and pieces from it that I will store in my memory and that may come in handy… so thank you.

Maddie

Square Roots: How to

Square Roots: How to
By Madison Nef

What is a square root?
The square root of a number is the number that, when multiplied by itself, produces the number you are trying to find the square root of. For example, the square root of 100 would be 10, since 10*10=100. Finding perfect square roots is easy- the square root of 16 is 4 and so on, because there are no decimal places involved. However, without a calculator, it is much harder to find the square root of a number like 10- and to get to an accurate answer, simplification is needed. Otherwise, you could be doing math for hours just to get to your conclusion!

So: how DO you find the square root of a number with an imperfect square?
Start off by finding two perfect squares that your number is in between. For example, the square root of the number 5 would be somewhere between the square root of 4 (2) and the square root of 9 (3). Since 5 is a number closer to 4, we can figure that the square root of 5 is going to be closer to 2 than it is to 3. This gets rid of all the numbers above 2.5, and cuts down the size of the work we need to do.

Next, you want to take the number you are trying to find the square root of and divide it by the number closest to it (in this case, we would divide 5 by 2). If needed, round off your answer. The next step is to get the average of the answer you’ve come up with: so for the problem we are using, (2.5+2)/2… which would equal 2.25. Repeat the second step of the process, and divide 5 by 2.25. This leaves us with 2.2222222… which can be rounded off to 2.22. Finally, average out 2.22 and 2.25. Take the number you get and square it. If the number you come up with is accurate enough for you, then you have your answer: but to get the EXACT square root would be a more complicated process of repeating the same step over and over again; and sometimes the decimals go on for 15-20 places before coming to the EXACT number.

In conclusion, here is the written out problem that we solved:
1) Find two numbers with perfect square roots that 5 is between. In this case, the numbers are 4 and 9.
2) Since 5 is closer to 4 than to 9, we can assume that the square root of 5 is closer to the square root of 4 (2). 
3) Divide 5 by 2. Simplify your answer if necessary.
4) Average the answer you got from the previous step with 5. 
5) Repeat step 5 with the number you got.
6) Round, and you have your answer.

5/2 = 2.25
2.25 + 2 = 4.25 / 2 = 2.22 (simplified)
2.22 + 2.25 = 4.47 / 2 = 2.235
2.235^2 = 4.995225 (round to 5)

* This technique can be used to find the square root of any number.

Wednesday, February 4, 2015

Emily Dickinson Poetry Analysis

Emily Dickinson Poem Analysis
By Madison Nef












Success is counted sweetest
By those who ne’er succeed
To comprehend a nectar
Requires sorest need
Who took the flag today
Can tell the definition
So clear of victory
As he, defeated, dying,
The distant strains of triumph
Break, agonized and clear.

I think that in the first two lines, Dickinson is simply saying that for someone who fails regularly, winning can seem far greater to them than it would seem to someone who is used to winning. If you live without something, and then get to see what it’s like to live with it, albeit for a short time, the time still seems a lot nicer. However, if you are used to living comfortably, it becomes a part of your life and you take it for granted. Too many things are taken for granted- food, water, clean clothing- there are some parts of Africa that have no electricity, barely enough food and water and not enough clothing and/or ways to wash what they do have.
In lines 3-4, I think Dickinson is saying that to see the value of something truly, you have to absolutely need it… not just want it. If you just want something for the sake of wanting it, you don’t ever see its true worth or value at all. Medicine is just medicine, until you are sick and dying and need it to live. Once again, it winds down to taking things for granted. Lines 5-7 befuddled me a bit, but upon thinking over it, I believe Dickinson was trying to say that to those who see victory every day (in war, in politics etc.) it is far more apparent than to the average person who only sees victory every once in a short while.
I believe that lines 8-10 show that as you die, and think about your life (if you are given the chance; Emily’s death was prolonged over the course of a few days), you see that it doesn’t matter how many personal victories you had or how many things you won- because in the end, you’re dying and all you have is your own memories and happiness. No small victory can stop death, nor can a memory of victory. It is better to live your life happily and treat each day as your last, because we all have an undefined timer on us that could run out at any minute. When I die, or when I begin to, I want to be able to look back on my life and feel accomplished, and feel like it was well spent- not wasted worrying about nonsense.
That’s how I interpreted the poem- what do you think? Do you think I was accurate? If not, why? Leave me a comment below, and leave me suggestions for poems to decipher.
Maddie

I Am David

I am David – Book Report
By Madison Nef
Protagonist
The main protagonist of the story is a 12 year old boy name David. He is somber, serious and very mature for his age due to the fact that he was raised in a concentration camp from age 3. However, he is also very oblivious to life outside the concentration camp, and knows little about the world in general. He is well learned in many different languages due to the many men he shared the camp with, which he often uses to his advantage. David is described as a skinny boy with shaggy brown hair and grey-green eyes, often dressed in shabby clothing. He trusts few because of his past and is hesitant to let people care for him.
Antagonist
The antagonist in the book is made out to be “them” or the people who run the concentration camp… but the true antagonist of the story plays an over-looked role in the book. The antagonist is David’s conscience in and of itself. David’s lack of knowledge about the world outside the concentration camp leads him to be withdrawn, untrusting and almost bitter to the world from a very young age. He also witnesses a lot of death and suffering in his time at the camp which warps his image of the world and sets him aside from most children his age- and makes him stand out as different to most well-knowing adults.
Setting
“I am David” takes place in a multitude of settings due to the switching plotline. The first place mentioned is the concentration camp David grows up in- described as colorless, dreary and lifeless. After escaping the concentration camp, David goes to Italy- Italy is described as lush, colorful and extremely beautiful. Italy has many small towns that are well populated and welcoming. Keep in mind that this setting is being described through the eyes of a boy who has only known the black and whites of a concentration camp- so seeing so much color and life is almost shocking to him. Italy is also a free country, with no concentration camps or war, so it is a lot more cheerful.
From Italy, David travels to Sweden. Sweden is described as even more beautiful than Italy, with brighter colors and more to see and do. It is here that David meets Sophie, a lady who enjoys painting and asks him to sit still so she can paint him. The only reason I would mention this in the setting is because I think it shows that as the story progresses and as David gains more trust and understanding of the world around him, more and more color comes into his life. Think about it: the concentration camp, where David starts, represents lack of understanding, captivity and sadness.
It’s even said in the book when David first arrives in Italy that his first thought is that he no longer wants to die after seeing how beautiful the world is. Italy represents him beginning to come around to reality and realizing there is more to life than just black and white and misery- and his first steps in learning to trust others.  Sweden is the final block of “color” for David- being painted, seeing the many different cultures of the world in objects when staying at Sophie’s house, and coming to understand that his mother is still alive.
Plot
The story begins in a concentration camp, after World War II. David has been a captive there since he was 3 years old and all he has known in death and suffering. He believes that his parents are dead, and the one friend he did have in the camp, a man by the name of Johannes who taught him much of what he knows, is killed before the book even begins. The book opens on David being given a chance to escape- one of the commandants tells him that he will put out the lights for exactly 30 seconds, and in those 30 seconds David will have to climb over the camp’s walls and escape.
The commandant tells David to head south to Salonika, catch a ship to Italy, and then go north until he reached Denmark. He also tells David that in a clearing to the side of the road he will take to Salonika, he has left a bundle with a water bottle, a compass, and some bread. David sits, waiting for his signal and debating whether to take his chance of not. He decides to try and escape, but fears being shot upon making it over the wall.
David gets over the wall safely and begins to run from the camp- but his brain stops him and tells him that they probably want a running target, to deceive him and make him think he can run before they shoot him. David slows to a walk, deciding not to give the men the glory of a good fight. If they were going to shoot him, David didn’t want them to have any joy in doing so. But as he walked towards the road, no shots came… so he went to the clearing to see if there was a bundle. There was, but David automatically suspected a bomb or foul play of some sort. He carefully undid the bundle… but it was just as the commandant promised: a water bottle, bread, and a compass.
David runs out of food and water quickly, but fortunately enough finds a shepherd’s camp and is able to steal some soup while the shepherds are asleep. He then makes his way to Salonika, where he quickly finds a ship heading to Italy. He hides in the storeroom of the ship, assuming that no one will look in the storeroom until the ship reaches Italy. He finds a large bottle of wine behind 3 large sacks, and decides to hide there since he will have something to drink. He drinks a bit of the wine, and then falls asleep. David is discovered by an Italian sailor whose wine he has been drinking, and upon seeing him, the sailor is angry. David apologizes to the sailor, saying that he didn’t know it was his wine, and then thanks him for letting him have some.
The sailor is surprised by David’s behavior, and proceeds to ask him why he is stowing away on the ship. David only says that he is trying to reach Italy, and the sailor says that when they near Italy, he will toss David overboard in a lifebelt so that he can float to shore. He brings him food and water, and when they reach Italy he gives David a lifebelt and teaches him how to use it properly.
David is then tossed overboard and floats for 5 hours before reaching land… and when he does reach land, he automatically checks his compass to make sure it isn’t damaged from the water. He follows in north, up and over a hill- and gets his first glimpse of a small Italian village… beautiful green grass, clear blue skies with fluffy white clouds and fresh, clean water flowing in a river below the hill. The first thing David does is run to the river, undresses and pins his clothing into the water under a rock. He then takes his cake of soap and begins to clean himself, scrubbing all the dirt out of his hair, off his face and out from under his nails. He then washes his clothing, determined to get all dirt and any sign of the concentration camp off of him.
David walks toward the town, noticing it has a church. He goes to the church, standing outside it and gaping at it in wonder. However, he is too nervous to go inside it, and so he walks away from it to explore the town more. He sees a man baking loaves of bread and pauses to look, even though he knows he has no money. The man sees David, and gives him a loaf of bread for free. David accepts it, says “thank you” and then goes back along the road. He had found a small cave along the side of the road, and it gave him enough shelter from the elements where he felt safe.
David goes back to the town a few more times, but on one of his visits overhears the man talking to the priest from the church about him. He remarks on how different David is from the other children, and how withdrawn yet polite he acts. When David hears this, he thinks they are going to send him back to the concentration camp; so he goes back to his cave, packs up his bundle, and starts heading north.
As he walks, he finds a strange fruit with a tough skin. He hacks it open to find that it is sweet on the inside, and realizes it is an orange. It is then that he discovers he barely knows anything about food… all he knows is porridge, bread, soup, and now, oranges. He finds another and stores it in his bundle for when he might need it later, and then continues on. He settles down under a rock for the night as it grows dark.
Upon waking up, David is shocked to see that there is seashore down below him, and he checks his compass to make sure it is still working correctly. He sees that it is, and figures out that he must be on a part of the land where the sea wraps around. As he walks, he trips over a rock and the compass falls from his hand, over a ledge and far down into the sea. David is distraught and has no idea what to do without his compass- it was his one way of knowing how to get to Denmark, and without it he felt lost.
He decided then and there that he needed a God to pray to- but not the Jewish or Catholic Gods because they demanded sacrifices and David had nothing to give them. He tried to remember what the men in the camp had spoke of when they prayed, but besides those two, all he could remember was Johannes speaking of David, the god of the green pastures and the still waters. David was a protector who did not demand much of anyone, but watched over those who prayed to him. David decided that he would pray to this God, and he told him who he was and asked that God watch over him on his way to Denmark.
David walked on for a bit, but then paused to sit and think at the side of the road. As he sat there, a man in a car came along and pulled over further down the road, stopping and yelling something about losing his eyeglasses. David quickly got up and went to help the man, and found his glasses not too far off. The man tried to pay David for his help, but David wouldn’t accept the money. Eventually, the man convinced David to come home with him and his wife and have dinner with them, and David readily accepted, having not eaten in a day. After dinner, the man asked David if he wanted to stay with them, explaining that they were from England.
David inquired whether there was a king in England, and the man’s wife told him that there was only a queen- but she was very pretty, and had a golden crown. David discerned the difference and thought to himself “Who cares what she has; are the people there free?” He declined their offer and asked to leave, and they let him. He moved on to the next town, finding a broken bit of mirror there and picking it up for himself. A woman had discarded it, but David took it and found that he could still see himself in it, even though it was small. For the first time, he saw how he looked and the first thing he saw was his eyes; and he couldn’t figure out why people made such a fuss over them. They were normal grey-green eyes, nothing too spectacular.
David gets to Naples and starts to do odd jobs for money. He starts by getting coffee for people at a small café in exchange for a loaf of bread. He then begins asking tourists if they need help with anything- watching luggage, giving directions, and other small jobs. Often times David only had enough for a loaf of bread to live off of, even though his cake of soap had run thin and he was in desperate need of a new one. David was finding it easier to do work for tourists than for people who lived in Naples, because usually the travelers paid better money for smaller jobs.
One day, David finds an American couple whose car is broken down on the side of the road. They are in need of petrol, and the nearest service station is a good long walk down the road with 2 heavy cans to carry the gas back in. David asks them if he could go with the money and get the people to walk down and get the cans in exchange, but the woman thinks David will steal their money and declines his offer rudely. David is offended, but still offers to go with just the cans. Without waiting for a reply, he asks them to watch his bundle while he is gone, grabs the cans, and starts off down the road with the cans.
Upon his return, the couple offers to pay him, but by now David felt that he didn’t want them to pay him if they hadn’t trusted him. He knew they felt he would steal, but thought the best way to show them the error of their ways was to leave them something of his own to guard. That showed them that he thought better of them than they did of him, and he felt that that was enough to make his point. So when they offered to pay him, he simply told them that he only worked for money sometimes, and that he didn’t need any more today. He then took his bundle and continued on his way down the road.
Soon enough, David stopped to eat some of the bread that he had been keeping in his bundle. To his surprise, there was a cigarette box at the bottom of his bundle that hadn’t been there before. He opened it, and what he saw struck him speechless. There was a LOT of money in the box- 2000 lire! One lira couldn’t by you anything… but 2000!? David had enough money to buy bread for days, and also a new cake of soap. Even after that, he would have a lot of money left over; maybe even enough to buy a comb!
In the end, David bought bread, a new cake of soap, and a comb. He still had a lot of money left, but he wanted to save it for things he REALLY needed. The first thing he wanted to do was combing his hair, and getting it straightened out. This proved difficult, as no one in the camp had had a comb. David’s hair was very messy, but he was able to comb out all the mats after a bit of tugging. He discovered that his hair was wavy, which he liked, since the people of Italy had wavy hair- but his hair was also longer than any man’s he had seen. David decided to buy scissors, so he could cut his hair and look more in place.
After purchasing scissors, David also bought pens and paper for himself, so he could learn to write. Johannes had been teaching him before he died, and David hoped that with practice he could learn to write properly. He then took out his mirror, leaned it up against a tree, and set to work cutting his hair. Like combing his hair, it took a long time, but in the end David was happy with the results. He now looked more like those around him, which gave him a small sense of security in the place he didn’t know.
David knew he had to keep moving, trying to get to Denmark. He decided that he would try to flag down a food or produce truck, since “they” never drove those types of trucks. However, each time a truck passed by, David felt too shy to flag it down, and so he sat down at the roadside. Finally, he asked his god for protection, and got up the courage to flag down a truck. The truck he flagged down was driven by a man named Angelo, and much like the sailor; he was confused by David’s story. However, he was a nice man, and he shared his food and drinks with David and was happy to have a talking companion for the time being.
Angelo let David off at the side of the road in Perugia. The road was surrounded by thick forest, and David, having never seen a forest, decides to take a few hours to walk through one and see what it’s like. He hears music as he walks through the trees, and upon trying to find its source accidentally trespasses onto mansion grounds. A boy of about his age is playing a radio, and when he sees David, he misunderstands his intentions and chases him off, threatening to beat him up. David flees and hides in the woods for a little.
He finds a stream in the woods, and decides to wash himself. He strips and starts washing his clothes and himself when he hears the voices of children in the woods. David grabs his wet clothing from the stream and hides behind a tree, trying to observe the children. The larger boy that chased him before was there, along with 2 other boys and a young girl.  David took careful notice of the boys, but couldn’t take his eyes off the girl. She had long black hair tied in red ribbon, a gorgeous red dress on, and she had a pretty smile. Her movements were fluent, and she was all around beautiful to David.
He listened, and discovered that they were going to play a game in the shed that was nearby. They would tie up the girl (Maria), and put her in the shed. Then, they would go in and rescue her. That was the jist of the game, as far as David could tell. They carefully tied up Maria with shoelaces and then put her in the shed. David decided that there was no more to see, and was about to close his eyes and take a nap when a strange smell of burning met his nose. He heard the boys cry out, and when he turned, he saw the shed was on fire!
Two of the smaller boys were crying, and the other boy looked petrified. David knew that the shed would burn, and the girl, who was tied up, would surely die. David didn’t want her to die- and he suddenly knew what he had to do. He said a quick prayer to his god, saying that this was his sacrifice. Then, David grabbed his clothing and ran across the stream and into the shed. There was fire everywhere, and the girl was crying and tied up. David made his way over to her, and quickly broke her ties. Unfortunately, the smoke was getting thick and the girl looked ready to pass out. David took his wet shirt and wrapped it loosely around her head, making sure that she could breathe inside it. However, because she was so weak, David knew he would have to carry her out of the shed. He picked her up and made his way out of the shed… he had some bad burns, but all that mattered to him was getting Maria out safely.
When he made it out of the shed, a man and woman were outside. The children’s parents looked extremely worried, and the man scooped the girl out of David’s arms. The woman saw David’s burns, and insisted that he come with them so they could have his burns treated. Even though he resisted their attempts at consolation, they made him come with them, telling them that once he healed up he could leave if he wanted. They bathed him and gave him more comfortable clothing, and also fed him a good meal.
After all this pampering, David saw that this was a life of things he could never have. While the family was nice to him for the time he was there, he felt that the parents were uneasy around him and felt him strange. David knew that the life of this family was not for him, that he didn’t fit in with them at all and never would be able to. The only reason he stayed was because of Maria… but one night, he stayed up and heard the parents talking about him in a way that made him uneasy and he packed and left. Before he left, he wrote a letter to the family explaining why he was leaving, and thanking them for their kindness. He then packed his bundle and ran away into the woods, not looking back.
David knew he had to get to Florence, because he was out of food. He walked on for a long time, but finally reached the city. No one questioned him; they just sold him the bread and were silent. In Florence, David found a large Catholic church. He finally got up the nerve to enter it, pushing open its doors and entering. It was dimly lit inside, but David found the church beautiful. It had an altar, and many statues and paintings. A man in a long robe was sitting in front of one of the paintings, mumbling strange words. David walked over to him, asking what he was doing. The priest told him he was praying, and talked for awhile with David, about how God worked and who God was.
David learned that there was only one God, but he told the priest that he was going to continue to pray to his God anyway. He then left the church and continued his journey. From Florence, he knew he had to get to Lugana, the town that lay on the other side of the mountains. However, he never reached Lugana. On his way, he saw a hill and climbed it to search for fallen oranges, hoping there might be some. He found none, but he saw beautiful scenery below him. He could look down into the valley, and from the top of the hill it was gorgeous. He was about to leave when a voice said “Stop! Do you have time enough for me to paint you?” David turned, surprised. An older woman stood behind him, carrying an easel and watercolors.
David agreed to let the woman paint him, and he sat remarkably still. The woman was surprised, but when she was done painting she thanked him and invited him back to her house. He went with her, and while she made food she asked David to set the table for her. David remembered that Maria’s family had always had a nicely set table- with fine china, silverware, glasses, flowers and a tablecloth. David found that the woman (whose name was Sophie) did not have a lot to set with- she had no fine china, but she did have plates. David set out the plates and glasses on a piece of red cloth that he found and also put some flowers on the table.
When Sophie walked in, she was shocked by how well the table was set. She and David got to talking over lunch, mainly about the items she had in her home. She had many different pictures from other countries, but one struck David in particular. It was a picture of a young woman with her husband, and a smiling baby boy. David asked Sophie about the picture, and a strange smile came to her face. She shook her head and told him that the woman’s husband and child had been killed, and that she had been taken away to a concentration camp. One of the guards had fallen in love with her and had allowed her to escape, and she had fled to Denmark. She then told David that the woman’s son had also been named David- and David realized in looking at the picture that the woman he was looking at was his mother.
The next day, David told Sophie that he must leave at once and catch up with the circus. He packed his bundle, and, filled with new hopes, set out for Denmark again. He walked for a long time, catching a ride from a man in Lugana and getting let off in Faido. The man said that the weather was bad, so the pass would be closed. It was snowing heavily, and David could barely see the road in front of him. He was determined to get to Denmark- to find his mother, to belong! He slept on the outskirts of the town and struggled on the next day.
As David walked, he turned it over in his mind. The guard… the guard who had fallen in love with his mother had gotten the papers for her to cross the border. He had killed his father, because he hated him for being married to his mother… but he had kept David alive because he was her son. Why hadn’t he sent David with her, then? David initially thought that maybe the man had only been able to get the paperwork for one person… but no, that wasn’t it. “They” always looked for revenge… and since David’s mother had not loved him back, the guard had kept David from her. However, he had seen to it that David was well cared for. He gave him his vitamins regularly, taught him, made sure that Johannes looked out for him… and eventually, set him free too.
David stumbled along, and bashed his head into something. He fell unconscious, and the last thing he remembered hearing was a snarling voice saying “What little thief is this, come staggering in the snow?” David knew he had been found. He was found by a farmer and his family, knocked out in the snow after bumping into a stable door. The farmer and his family were cruel- they abused their animals and their children and were harsh to David. They threatened to turn him in to the police if he did not work for them, and he heard them talk of turning him over in the spring. David decided that while the farmer was cruel, forcing him to work, barely feeding him and making him sleep in the barn, that it was better than nothing and freezing to death as he surely would have outside.
Soon, spring was coming near. David befriended the farmer’s sheepdog, sleeping with it every night and caring for it to the point that the dog turned on the farmer and protected David. David knew he would have to leave soon, and so he began digging his way out of the barn. Soon, he had a tunnel ready and he packed his bundle. As he started to leave, the dog tried following him. David told him to stop and stay, because he would not be able to provide for the dog AND himself. Then, he left, taking the road down the mountain. As he trekked on, he came to notice that the dog had followed him!
David was happy that the dog followed him… it was nice, to not be alone and to feel loved. The dog followed him faithfully, not minding that the food supply was low and that its semi-lavish life was gone. Soon enough, David reached a city called Basle. Here, he caught a ride from a kindly truck driver, who took him over the border of Germany and into Frankfurt. David and the dog were very lucky- everything was going well. David was happy, happy to be alive… Denmark was so close, as was his mother! But, as usual… nothing ever comes as planned. It was at night, and cold and frigid when David and his dog ran into trouble: “them”.
“They” had a camp near the border of Denmark, and David knew he would have to pass in front of the guards. He said his prayers, and was about to run in front of them when the unthinkable happened. His dog, his faithful companion and his guard, sacrificed his life so David could run. The choice was all its own- it CHOSE to give its life. David was upset at first, but realized the dog’s sacrifice was so that he could run.
He didn’t waste the dog’s life- he ran and ran, and he was soon in Denmark. He wasted no time in finding the woman’s address through the phone directory, and was soon at her house. He knocked on the door, and when his mother opened it, he simply said “I am David.” And she let him in, hugging him and crying… The end.