Math

When I was eight, I and my classmates made journals out of construction paper stapled together. We were then encouraged–not quite assigned–to write entries in them periodically, entries about our lives. My life at the time included learning about pie charts in math class, so I drew a pie chart in my journal and proudly showed it to my teacher. She gently chided me for putting math in what was supposed to be a language-arts project. I never made another entry.

Now, to be clear, I wouldn’t categorize the event as traumatic, merely frustrating and annoying. I abandoned the journal, not out of any deep-seated pain, but simply because I understood that using the project to please the teacher was impossible, and I had no other motivation to work on the thing. In general I would not call her a bad teacher–she was actually a very good one–but she pretty clearly did not understand me at all.

Also, she was wrong about the relevance of math to creative writing.

For example, how big is Oz?

The question matters, if you’re working on Oz fan fiction, as I am. The characters travel largely by walking, and while the original canon makes no mention of seasonal changes and very little mention of the fact that three out of the five main characters (counting Toto) must eat, I do pay attention to that sort of thing. So depending on how big Oz is, these trips could last days, weeks, months, or years–you can see how that would have an impact on the story. And there are other, related, questions, too.

So let’s look specifically at the first leg of the journey, from Munchkinland to the Emerald City.

I’ve decided, more or less arbitrarily, that Oz is a circle about 2,000 miles in diameter. That puts it at the same scale as the United States, though not exactly the same size. The Emerald City is at the center of the circle, as per canon, so it’s 1000 miles from the eastern edge of Munchkinland to the City. The Yellow Brick Road has a more or less a straight route, but not a perfectly straight route–no road is perfectly straight over that kind of distance. So the journey is perhaps 1,200 miles long.

With this information, we can figure out a few basic facts about the journey, such as how long it takes (does the season change during the trip?) and how often they need to resupply.

How long the journey takes depends on how fast they can walk.

Neither Scarecrow nor the Tin Woodsman get tired (that’s canon), and Toto can easily be carried, so until the lion joins the group, Dorothy is the limiting factor for the group’s speed. On mostly flat ground with even footing, an adult could average 20 miles a day without too much trouble (that means walking 25 miles most days–the average is always five miles less than the typical), but Dorothy is a child. Since she is both physically fit and highly motivated, let’s say she can can average 15.

But then the lion joins them, and HE becomes the hold-up. I realize that sounds odd, because of how big and strong lions are, but they are not distance animals. Wild lions cover little more than five miles a day. We’ll say this lion, being unusually motivated, can keep up a five-mile-a-day average (meaning his typical day is close to ten).

1,200 at 15 miles per day is 80 days. At five miles per day, the same distance is 240 days.

Clearly, we need to know when the lion joins the party!

Canon makes it clear he joins the group in a very wild forest where the road is not regularly maintained. In my elaboration on Oz geography, that translates to beyond the western boarder of Munchkinland, at least halfway to the Emerald City. The sooner the lion joins them, the sooner the partly slows way down, and the longer the trip takes. As the author, I don’t want the trip to take too long.

If the lion joins on Day 40, the trip will take 160 days total.

If the lion joins on Day 50, the trip will take 140 days total.

If the lion joins on Day 60, the trip will take 90 days total.

So how long do I want the trip to take? Well, there are two critical things to consider. First, if they take longer than four months (120 days), the summer rainy season will catch them on the road. Because neither the tin woodsman nor Scarecrow can afford to get very wet (straw will rot if it stays wet too long), hiking in the rainy season presents serious logistical problems I don’t want to get into. But if the trip lasts over 100 days, that presents a different logistical problem I do want.

See, between the edge of Munchkinland and the Emerald City, there is no practical way to resupply, except to hunt–and, as per canon, the question of whether the lion should hunt for Dorothy and Toto, rather than for himself alone, causes a really interesting crisis for the tin woodsman. That question doesn’t come up unless there is a serious danger of Dorothy and Toto running out of food.

Ordinary backpackers can carry only about a week’s worth of food without the weight becoming too problematic. Some carry more, some less, depending on various factors. But this is not an ordinary group of hikers.

Scarecrow and the Tin Woodsman don’t eat, sleep, or change their clothes, nor do they drink water. They do carry some gear (an oil can, an ax, a sewing kit, etc.), but their personal burdens are very slight. That means they can carry food for Dorothy and Toto. Dorothy doesn’t carry a full pack because she’s a child, and Toto carries nothing because he’s a very little dog, but their limitations are more than balanced by the fact that Scarecrow and the tin woodsman don’t get tired–and their bodies behave otherwise like those of fit, young men. Although they are both Munchkins, and therefore very short (about four and a half feet tall), they are very strong. They can carry about 60 pounds of food each, in addition to their own gear and perhaps some of Dorothy’s.

So they leave Munchkinland on Day 40 with a total of around 140 pounds of food total, all lightweight travel food.

Dorothy and Toto together eat at least two pounds a day, so to avoid running out of food, they need to get from the boarder of Munchkinland to the Emerald City, a distance of six hundred miles, in less than 70 days. Call it 60 days, to account for a daily consumption of just over two pounds.

So to make the trip long enough to cause the interesting crisis for the tin woodsman, we need a total trip length of at least 100 days, meaning the lion must join the party somewhere between Day 50 and Day 60.

That time line implies certain things about the relationships among the characters–how long have Scarecrow and Dorothy known the tin woodsman before the lion joins the party, for example? Is he a new acquaintance or an old friend? The time line also suggests details about where they are, geographically, when, and what the physical setting of certain scenes is.

See why this matters?

Is it complicated mathematics? No. It’s basic arithmetic. But it IS math, and it’s part of my writing process.

Edit: yes, I did just edit this piece–I decided I wanted to change the scenario slightly, and also that lions are a little slower than I’d said at first.