Over at her blog, Mary wrote an interesting post (which I’m quoting with permission):

Typing innocently along and abruptly realizing: there will be math.

Given that our heroine is a member of a class of five students — admittedly, the girls’ class, and a specialized course of study, and I can make make it a small one, but not astoundingly so — how large is the town they are in?

If this much of the population does the work that this course trains them for, and they are half of one year, the percentage should be feasible to work out. Though I might consider having more than one school in the town. And I still have to work out how many do it. (Not enough to make it easy!)

And then I have to break it down because the town also is divided in several populations, which I have already shown as rather large. Or perhaps they were supplemented by visitors? Still, a non-trivial number must live in the town. . . .

I’ve run into similar things, especially in writing mysteries. What may seem like a simple choice has all sorts of implications to it which you need to think out in order to avoid plot holes. I also hit this sort of thing all the time when I was designing the space ship for A Stitch in Space.

Part of what caught my eye about Mary’s post is that typically when people say “there will not be math” they mean “this won’t be hard” which is partly about math being exacting and partly about math generally being taught badly. I have a background in Math—I got a master’s degree in mathematics for fun—so I tend to think of “there will be math” differently than most do, but in this case I think that the symbolism is actually quite helpful.

The case that Mary is considering involves math because the relationships involved are well defined. A child has two parents. That simple fact imposes a great many restrictions on a storyteller. The moment you have a character you have two parents and (unless they’re very inbred) four grandparents and eight great-grandparents. The novel writer can kill or otherwise get rid of as many of these off as he pleases, of course, but on some level the mere presence of a single character obliges him to do something with this much larger cast. Even in Young Adult fiction where the parents are nowhere to be seen, achieving that limits the possible settings. You can’t set a ten year old and an eleven year old as neighbors in London each owning his own house. You can’t have two eight-year-olds with adjoining estates in the country. You can do either, of course, if you permit the parents to be present, even if you get them out of the way by being very busy. Within society, somebody must be in loco parentis. (You can, of course, come up with nearly anything you want if the children are the last survivors of a doomed ship on a desert island. But then, you are stuck with the ship and the island.)

Mary’s example shows these restrictions on the author even further. If there are parents and this isn’t Little House on the Prairie, there will probably be a butcher and a baker and possibly even a candlestick maker. Somebody will do the carpentry and somebody will have to sell the carpenter the lumber to do it with. People will have to have some way to earn money in order to pay for whatever they can’t pick up locally, too.

Of course, to do this properly one would have to be God. The best a human author can do is some believable approximations. That said, I find it very helpful to figure this stuff out ahead of time. Having thought it through, at least once, tends to make one’s later decisions much easier to reconcile with one’s earlier decisions, which cuts down quite considerably on plot holes.

The other thing—which I’ve learned the hard way—is that after you do this sort of planning, write it down. I can say from experience it’s really annoying to have to reread your earlier books to find out how tall a character is, or in what year he joined your order of consulting detectives, or such-like. Because Mary is quite right. If you’re not writing stand-alone short stories, there will be math ahead. The only open question is whether you’re going to take the trouble to do the math (as Mary is), or whether you’re going to get it wrong by making up the answers as you go.

A lot of people go the make-it-up-as-you-go route, but this isn’t being fair to your readers, since it amounts to asking them to forget what you wrote in previous books. Forgetting a book is the opposite of deriving benefit from it. If you’re going to do that, why ask them to read it in the first place?

We’ll all make mistakes, of course. One of the unfortunate things about being a fallen creature is that we will all hurt those we love—I assume all writers love their readers, otherwise, why write at all?—and must act anyway because curling up into a ball and softly weeping for four score and ten years won’t do anyone any good at all. My point in all this is merely that it’s good to be aware of the crosses that you’re going to have to take up before you get to them. When they’re not a surprise, you can settle them on your shoulder better to distribute the weight. They’re still crosses, of course, but this way you have a better chance of carrying them the distance.