Month: March 2016

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Ellen’s Choice: When The Story Affects The Book

I’m a huge fan of the novel structure known as epistolary, where the story is told through primary sources such as diaries, newspaper articles, or letters back and forth between characters. Bram Stoker’s Dracula is one of my favorite examples of epistolary, as the mystery is heightened by Stoker’s clever choices of whose diary to show at which point in the story. Epistolary form allows the author to strengthen the reader’s immersion in the story by allowing the story itself to influence the final form the novel takes. Leave off a character’s diary in a tense situation where he’s about to go do something dangerous and stupid, with the cry “Goodbye all!” and then cut to someone else’s diary for the next hundred pages, and you leave the reader begging to know what happened back there – did he make it out? Why are we not reading more of his diary? Is he okay? Tell me please!

I recently finished another epistolary novel that has quickly made it onto my list of great examples of the craft of writing – one I think everyone should read. It also takes the prize for longest title of any book I’ve read. The Astonishing Life of Octavian Nothing, Traitor to the Nation, Volume I: The Pox Party is a young adult novel written by M.T. Anderson. The Pox Party tells the story of a young boy growing up in a scientist-philosopher’s commune in revolutionary-war-era Boston. The first half of the novel is all from the boy’s perspective, and feels like a relatively standard first-person narrative with the exception of the fact that it begins with the statement “Drawn Primarily from the Manuscript Testimony of the Boy Octavian”. Already the epistolary format is working its magic, albeit subtly. Manuscript Testimony, eh? Why is Octavian writing this testimony – what happened that he needs to testify about? Is he testifying for the defense or the prosecution? He alludes several times to some kind of looming tragedy that he didn’t expect at the time, reinforcing the reminder that he’s producing this story as a testimony. The wheels are turning in the reader’s head, trying to piece the puzzle together ahead of the narrative and worrying over the possible outcomes they’ve imagined.

And then, in the middle – everything changes. I don’t want to go too much into it, because it blindsided me completely and was extremely effective that way and I don’t want to spoil it, but something happens that renders Octavian unable to continue to write. This plot point causes real changes to not just the story, but the book itself. The story so far has been told through Octavian’s manuscript, after all, so what happens now that he cannot continue his writing? The resolution of that question makes the second half of the novel a completely different reading experience and drastically heightens the dramatic tension. I’m sorry to be so vague here, but the surprise was part of the effect for me and I don’t want to spoil it. Suffice it to say that the story affected the book in a very real way, and I’m still thinking about it a week later. I highly recommend it.

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Mathematical Journeys: The Three Types of Symbols

We’re going back to basics today with a Math Journey covering the three broad categories of symbols. I’ve found this concept very handy when introducing Algebra to middle school students. So let’s go!

Math is a language, and I find it often helps to think of it as such right from the beginning. Just as there are different parts of speech in a language, so there are different ‘parts of speech’ in math. Where a spoken language includes parts of speech such as nouns, verbs, and adjectives, math has three major types of symbols: constants, operators, and variables. Let’s go over each one in detail.

Constants
These would be the equivalent of your nouns. A Constant is a number – it has a single, discrete place on the number line. Even if the number itself is ugly – a non-terminating decimal, for example – it still does exist in a specific spot somewhere on the number line. In addition to the obvious constants, math frequently uses what I refer to as ‘special constants’ or ‘named constants’ – ugly numbers that are important enough for some reason or other that mathematicians have given them special names and symbols. Pi is a good example of this; mathematicians figured out that performing a specific calculation on a circle always yields the same number, regardless of which circle is used, and figured that that number was special enough to warrant a name. In much the same way, other constants such as e and i have been given names and special symbols to represent them due to their importance for certain calculations. But the important thing to remember here is that all of these named constants do have specific spots on the number line – they don’t change value depending on the situation. Pi will always be approximately 3.14159, no matter what you do to the rest of the problem.

But that’s not always the case.

Variables
Variables also represent constants, however in this case the actual value of the constant is unknown. The variable does have a specific spot on the number line, but we don’t know where it is. Its location on the number line can vary from problem to problem, but within a single problem it is always consistent. We generally refer to variables using lowercase letters, traditionally starting with x, y, and z, and then moving to others if necessary. In practice, a variable behaves just like a constant, since it does actually represent a constant. It can be manipulated the same way you would a constant, except of course you don’t know the value so you’ll have to leave some calculations unfinished until you get to a point where you can identify the mystery number. Funnily enough, many elementary math programs use the concept of variables, but they don’t define them as such. If you’ve ever seen a basic math worksheet with a question mark in a problem, you’ve seen a variable. All algebra does is change over from using a question mark to a series of lowercase letters.

3 + ? = 7
3 + x = 7

Operators
All the constants and variables in the world won’t help us without an operator. Remember how your grammar teacher was always going on about how every sentence needs a verb? Well, every mathematical sentence or phrase needs an operator. An operator is a symbol that performs an action on a constant or set of constants. Plus signs, minus signs, multiplication and division symbols are all operators, but so are square root bars and fraction bars. In fact, as you may have read in one of my earlier Math Journeys, a fraction is just an indication of the top constant being divided by the bottom constant. The equals sign is also an operator of sorts, though it doesn’t perform an action on the constants so much as declare a relationship between them. The greek letter Sigma is an operator as well, used to represent taking the sum of a series.

And then there’s the special operator known as ‘a function.’ We’ve talked about functions multiple times before in my blog, and I usually introduce it as a machine that turns one number into another by applying a set rule. That sounds like an operator to me! The key here is that a function is kind of a general operator, one that you can define within a given problem any way you want or need it to be. Want to indicate a specific sequence of operations performed on a number repeatedly over the course of a single problem? Use a function and define it appropriately!

Breaking down the world of math symbols in this way helps to clear up some of the confusion that often results from the particulars of traditional naming conventions. Consider, for instance, the following six symbols:

e ∏
x Ѳ
f() ∑

All three in the first column are lowercase letters, and all three in the second column are greek symbols. However, their usage in math is better represented by the horizontal rows. The first row are constants, the second variables, and the third operators. And the way they behave differs accordingly. So the next time you’re confused, take a look at which type of symbol you’re working with!

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Writing Rundown: Word Cloud Brainstorming for A Clockwork Orange

Last week in my Literature Spotlight, I explored the connections between humanity, free will and morality in Anthony Burgess’s A Clockwork Orange. For this week’s Writing Rundown, I thought I’d share with you my brainstorming process.

As I mentioned in this blog post, there are many different ways to brainstorm for a project. For this one, I chose to use a Word Cloud. I chose the Word Cloud because it’s a much more flexible and organic method than going straight for an outline, and I was anticipating this particular topic being tricky to organize. All of the ideas bouncing around in my head were interconnected, and I felt a Word Cloud would help me sort them out and figure out the best way to structure my essay.

Take a look at my finished Word Cloud:

In the center of the page, I began with the phrase “Loss of Free Will.” I knew that was the central key to my current thought process – that the loss of free will was what actually affected the main character’s humanity, far more than any other event in the book.

From there, I began to work outward with a second set of large ideas. My second ring contained four phrases: “Title: Clockwork Orange,” “Loss of Humanity,” “Link between humanity, free will, and morality,” and “Becomes tool of the state.” I knew these were all things I wanted to touch on in my essay, but couldn’t quite figure out yet how to distribute them. All four of these phrases were connected to the main point in the center.

Next came the outlying phrases, where I began looking for supporting evidence for my various big thoughts and jotting down anything that seemed important. Spiraling outward from those four big ideas were a sequence of phrases indicating both concepts I wanted to explore and specific quotations I knew I wanted to use, along with their page numbers for easy reference later. Each of these spirals connected back to its main idea, but for the most part there wasn’t any cross-connection between them at this stage. I went back through and began adding extra connections between some of the ideas to show which things belonged in the same train of thought, and which things shared a causal relationship that I wanted to make sure I touched on. I was beginning to see my paragraphs forming.

But something wasn’t quite right.

I inspected my word cloud further. The title connected to the loss of humanity, which connected to the link between the three ideas. I found I had a little triangle surrounding the idea of that link between humanity, morality, and free will. Even though that phrase was not the original center of my cloud, it had emerged as the glue that held all these thoughts together. If I removed that piece, large parts of the rest of my cloud wouldn’t connect up anymore. That told me that the concept of that link was actually my thesis, more than simply the loss of free will. That phrase became the new center of my cloud, and I re-adjusted my visual conception of the rest of the cloud to surround that point.

I then added in some dividing lines to visually separate the cloud into the points that would become each of my three paragraphs. One involved the title and its connection to the idea of a loss of humanity, a second dealt with Alex becoming a tool of the state after the loss of his free will, and the third involved a discussion of the final chapter and the commentary on morality presented within it.

I now had a pretty clear idea of how to structure my essay. I translated this cloud into a more traditional five-paragraph outline and wrote from there. Of course, all pre-writing should stay flexible throughout the writing process. As I went into my drafting phase, I found myself organizing and re-organizing multiple times, and I referenced my word cloud several times to keep myself on track as the shifts happened. Word Clouds are really handy for topics that are intricately interconnected, or that you think might run the risk of getting tangled up in themselves as you write. I don’t always use one, but this essay really needed it.