Month: July 2014

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Literature Spotlight: Dystopian Novel vs. Dystopian Setting

ALERT: This week’s Literature Spotlight contains spoilers for The Hunger Games trilogy. Read at your own risk!

This week my Bring Your Own Book club met for tea, and our topic for the month was Dystopias. I had offered to host this month, because dystopia is one of my absolute favorite genres. As I sat listening to the others recount various dystopian tales, I was struck by a thought that had been niggling at me for weeks – there’s a significant difference between a dystopian setting and a true dystopian novel. With the increasing popularity of brilliant YA novels such as The Hunger Games and Divergent, it’s becoming more and more common to see stories set in corrupt dystopian societies – but are these stories true dystopias, in the classic sense of the word? There’s more to a dystopian novel than a corrupt society setting – classic dystopias also share certain plot and character elements. When viewed in this way works such as The Hunger Games seem to fit more as other genres of stories, such as adventure, mystery or thriller, that are set in dystopian-inspired worlds.

In a classic dystopia, the protagonist is an anomaly within the Society. He either starts out as the lone dissatisfied person in a world of good little worker bees – like Winston Smith in 1984 – or he is one of the good little worker bees himself. He may even be a somewhat celebrated member of the society; Guy Montag in Fahrenheit 451 has a respected job as a fireman, while D-503 in We is the builder of the spaceship Integral. Highlighting the protagonist in this way makes it easier for the reader to see why we will be following this person as opposed to anyone else; the majority of citizens are unaware of the flaws in the system, either because of relentless propaganda or status quo bias. Compare Winston’s colleagues in 1984 or the ciphers in We to the citizens of Panem in The Hunger Games; while the Party and the ciphers are sheep who follow the teachings of their government unfailingly, it seems that everyone in the outer districts of Panem is aware of the awful reality of the Games and refuses to swallow the Capitol’s propaganda. In a classic dystopia the protagonist’s journey is one of awareness, as he becomes more and more aware of the flaws and shortcomings of the Society, and simultaneously becomes less and less able to fit into the compartment the Society has given him. But in the Hunger Games, Katniss is already aware of the flaws in the Capitol’s rhetoric, and so is everyone she knows.

Most classic dystopias also contain a character of the archetype known as “The Manic Pixie Dream Girl.” In a dystopia, this character exists to show the protagonist the faults in the Society. She generally has her opinions already formulated, so that she can effortlessly denounce the Party or foretell the coming rebellion. In contrast to the protagonist, whose mental state tends to break down as he becomes more aware of the corruption, the Manic Pixie Dream Girl has everything figured out already. She may end up as a love interest for the protagonist, and if so he will probably betray her at the climax. He is weak and indecisive compared to her strength and rhetoric. From Julia in 1984 to Clarice in Fahrenheit 451 to I-330 in We, the Manic Pixie Dream Girl enters the protagonist’s life to give him freedom within the structure of the Society. In The Hunger Games, however, this character doesn’t seem to be present, probably because there is no real need for her when the citizens are already aware and fighting back.

In a classic dystopia, the Society never loses. The protagonist may think he’s figured out a way to escape or to bring down the Party, but the Party is always three steps ahead. If the protagonist refuses to bend, the Society will break him, conforming him by force. Whether it’s the last scene in the Chestnut Tree Cafe in 1984 or the final Record in We, the Society always wins and the protagonist is once again a happy little worker bee. A classic dystopia ends on a note of hopelessness – the Society is too strong. The Hunger Games shows a brilliant subversion of this arc with the ending of Mockingjay. President Coin suggesting one final Hunger Games with Capitol children is a punch in the gut to the victors who have been through the arena – the reader can almost see the cycle of the Games beginning again. First one final Games, then another – and then it’s back to square one, but with roles reversed. Coin has become Snow, and the power will wield her just as it did him. Katniss sees this, and manages to break the cycle by assassinating Coin instead of Snow, realizing that the real enemy is the power of the office, not the broken, dying man presented to her. By breaking the cycle, Katniss allows a hopeful – and very un-dystopian – ending for her society.

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WWTK: Real-World Writing

I received this WyzAnt Wants To Know prompt this morning:

“Students often want to know how they’ll use a subject “in the real world.” Pick one of your subjects and tell us why it’s important outside of the classroom.”

As it happens I wrote an article on this very topic as it relates to Algebra a few months back. You can check out that article here. So since I’ve already answered this in relation to math, I’ll discuss another of my topics: writing.

It’s true that once you finish college you’ll probably never need to write another term paper. Unless your career path tends towards academics (or blog posting), regular paper-writing is probably not going to show up very much. But what will show up quite frequently is the need to clearly and concisely articulate your thoughts and opinions in writing. In today’s text-based world, first impressions are often written rather than spoken – whether that be a cover letter for a resume, a request for information about a position, or a proposal for a new project. If you plan on being self-employed, starting your own business or going into certain fields such as arts administration, you can expect to run into larger writing projects as well. Business plans, grant applications, and press releases all require skill in clear and concise writing. But even something as simple as an email introduction still deserves a careful and articulate hand.

I experienced this myself when I first started tutoring; each time I wanted to respond to a job posting on WyzAnt I found myself sitting on the response screen deleting and rewriting for several minutes to get the phrasing just right. Realizing this, and also realizing that I generally ended up using the same specific phrasing for certain situations (such as finishing all introductions or requests for information with the sentence “Thank you for your time, and I look forward to hearing from you”), I finally decided one day to sit down and write up a template response, one that incorporated all of the best phrasings I’d come up with over the months of writing and rewriting. This way I can now save time on each response by simply tweaking any specific details, and still be sure that I’m putting my best foot forward and including all relevant information.

Writing papers and essays in high school and college provides you a valuable chance to develop and hone your written voice. As you complete assignments, you’ll begin to learn what a good sentence looks and sounds like. You’ll practice thinking ahead, going through each next point as you type the one before, and you’ll become more skilled at translating that inner monologue into a smoothly-flowing paragraph. Writing papers also teaches you to edit, whether that means drafting, proofreading and rewriting or simply stopping in the middle of a sentence to think through a few different ways of finishing it before continuing. You’ll learn to be straightforward and confident, whether that means stating your opinions as facts in persuasive pieces or citing just the right piece of research in history papers.

Speaking of research, the act of researching for a paper is an invaluable lesson for when you need to figure something out in the real world. Taking notes, highlighting and marking pages with post-its are valuable organizational skills, and they are usually learned first in the context of researching a history paper. In the real world you eventually realize that not everything can be found with a wikipedia search, and that sometimes you need to go old-school and hoof it to the library to find the book you need.

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Mathematical Journeys: Carl Gauss and the Sum of an Arithmetic Series

There’s a famous (and probably apocryphal) story about the mathematician Carl Friedrich Gauss that goes something like this:

Gauss was 9 years old, and sitting in his math class. He was a genius even at this young age, and as such was incredibly bored in his class and would always goof off and get into trouble. One day his teacher wanted to punish him for goofing off, and told him that if he was so smart, why didn’t he go sit in the corner and add up all the integers from 1 to 100? Gauss went and sat in the corner, but didn’t pick up his pencil. The teacher confronted him, saying “Carl! Why aren’t you working? I suppose you’ve figured it out already, have you?” Gauss responded with “Yes – it’s 5,050.” The teacher didn’t believe him and spent the next ten minutes or so adding everything up by hand, only to find that Gauss was right!

So how did Gauss find the answer so fast? What did he see that his teacher didn’t? The answer is simple, really – it’s all about pattern recognition. Let’s look at the problem more closely.

1 + 2 + 3 + 4 + 5 +…+ 95 + 96 + 97 + 98 + 99 + 100 = ?

Now it’s true that adding all that up by hand would take forever, but we don’t really need to add it all up by hand. Look at this series from each end simultaneously instead of just left to right. You’ll see that we can think of this series as a set of pairs of numbers, each of which adds up to 101:

1 + 2 + 3 + 4 + 5 +…+ 95 + 96 + 97 + 98 + 99 + 100 = ?

1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
4 + 97 = 101
5 + 96 = 101

and so on right through to the middle, where:

48 + 53 = 101
49 + 52 = 101
50 + 51 = 101

So we’ve got a total of 50 pairs, each of which adds up to 101. Since all our chunks are the same size, we can take a shortcut and simply multiply the size of the pair (101) by the number of pairs (50). Which is really easy to do in your head, since it’s just (100 x 50) plus (1 x 50), or 5000 + 50 = 5,050.

This reasoning can actually be extrapolated to work with any arithmetic series, and in fact is how we get the formula for the sum of an arithmetic series. Check it out:

Each pair added up to the same number, so we could actually use the mathematical expression for any one of those pairs in our formula. Since the first and last term are the ones most often known, let’s use those. Remember, the last term in the series is written as an, where n is the number of terms in the series. So that 101 will be represented by:

The first term (a1) + the last term (an), or (a1 + an)

Check out the first term in each of our pairs above. They range from 1 to 50, so there are 50 terms – exactly half the number of terms in the series. Which makes sense, since we’re pairing up the terms and that by definition gives us half as many pairs as terms.

So 50 in our example is represented by one-half of n, or n/2.

And what are we doing with these two bits of information? Multiplying them together. So our final formula would be:

Σ = (n/2)(a1 + an)

Now, sometimes you see this formula written as n[(a1 + an)/2],

or the number of terms times the average of the first and last terms. Practically that is exactly the same thing as the way we wrote it first, it’s just written a little differently. But they both have the same value, so if it’s easier for you to remember it as the average times the number of terms, do so.

This formula works for any arithmetic series, so the next time you come up against one, remember Gauss and his pairs of terms!