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Writing about a subject on which you have no expertise?

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So I signed up for a novel workshop, and within a month the first chapter will be due. Problem is I that want to use characters who are well-versed in mathematics, especially group theory or model theory, yet I have no expertise whatsoever in those fields.

I know a smattering of those subjects, but how do I give the illusion of realism to the intellect of a mathematician with a PhD?

Although my focus is mathematics in this question, it can of course apply to any field such as botany or physics.

I could take some courses or do studying on my own, but time is of the essence, as always.

Thank you. [Ideally I wanted to ask this in a math.SE]

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Most fiction that includes technical details get them wrong. Fiction does not sell based on the accuracy of its technical details, but on the strength of its story. Indeed, many stories absolutely depend on getting the technical details wrong, or, at very least, ignoring obvious technical solutions, in order to manufacture the turning points of a plot. Fiction is fundamentally moral, not technical, and if it is convincing in the moral sphere, its technical shortcomings are mostly overlooked or easily forgiven.

Where some point of plot turn on technical detail, the writer's art is more often in creating convincing bafflegab than in actually getting the details right. (This is akin to one of the other great truths of fiction, which is that dialogue is not speech.)

Of course, there will always be a few overly literal people who simply cannot see past these sorts of technical errors and will plaster the intewebs with their scorn. But you know what, your work is amusing them to, and as long as they keep buying your books to feed their habit, it is all money in the bank to you. Plus, their carping is free publicity.

There do seem to be one or two genre's where it genuinely does matter, where there is a higher than normal percentage of geeks in the audience that can genuinely sink your chances. Novels of the age of sail seem to be one such category. If you want to write about that stuff, you had better know a bowsprit from a yardarm. But even then, only for those books in which much of the action depends on the mechanics of sailing.

But this does not mean you can be cavalier about it either. Story tech may not be much like real tech, but it has its own conventions. It may be bafflegab, but it needs to be good enough bafflegab to satisfy the reader that you are painting a complete picture and not leaving parts of the canvas curiously blank.

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It is not unusual for writers to consult outside sources (both books and people) to describe details and dialogue about little known things.

One thing Stephen King describes in his book On Writing is to do a lot of research, but avoid including too much of the information you learned. Purely out of insecurity, newbie writers tend to include too much specialized information in their stories. But doing that is unnatural and distracting for the reader. It is far better to resist the temptation to include too much information -- and try to include as little info as possible. Not merely because you are a nonexpert, but because an expert probably wouldn't explain things in such a dense fashion.

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I'm a mathematician and physicist who's routinely annoyed when fiction gets mathematical and/or physical details wrong, even in works that are meant to be about geniuses in the field, such as Good Will Hunting or A Beautiful Mind. You can easily Google examples of people pointing out where either the facts were wrong or their difficulty for people at a given level of expertise was exaggerated. In The Big Bang Theory (among others), I even object to the implications of specific details to characterization. (For example, in S8E2 a character who refers to a technique by a name only a physicist would use later admits struggling with something every physicist understands well.)

But I'm also a writer, and I know the most important thing is doing what's right for most of your audience. And whether the specific problems Will solved on the blackboard are as hard as claimed in-universe, or whether John Nash's "if we all go for the blonde" thought experiment properly exemplifies Nash equilibria, isn't the point. The point is, do the work's consumers develop the inferences about and attitudes toward the work and its characters that you intended, and are they glad they did?

If you want to try harder than those successful scriptwriters and don't gave much time in which to do so, try searching for people discussing the topics' use (well or badly) in fiction. Futurama uses group theory occasionally; one episode was even written by a PhD in the subject, with the mathematics being integral to the plot. You'll learn more about how to use group theory in fiction from The Prisoner of Benda than from a group theory textbook.

Good luck!

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Writing a story in which math plays a pivotal role when you know little about mathematics would probably be a mistake. There is, unfortunately, no way to fake knowing something. You either have to do the research, or write the story anyway, hoping your guesses are right. Guessing wrong will make you look foolish.

Of course, the question of how much research you need to do is one without a good answer. But a story about math will probably attract readers who are interested in math. And those readers may well know a lot of math themselves.

If you do choose to write this story anyway, run it past some beta readers who are mathematicians or math teachers. They may be able to tell you where you've made mistakes.

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For a first draft, you can use placeholders. XXX, TK (publication shorthand for "to come"), TECH, literally the word [placeholder] in square brackets — anything to indicate that you'll fill in the mathguffin details later. Also, feel free to gloss or summarize. The point of the scene is not going to be the math anyway, right?

The professor pointed to the blackboard.

"You see? If you [TK math thing], you get this result. But if you do this — " He changed some variables and added a new line to the equation. " — then you get [different result]!"

Ben gasped. "Of course! It makes perfect sense! How could I never have seen this before?"

"Because I'm a genius," said the professor smugly.

"And because you had me helping you," came the tart voice of the professor's wife from behind them. Ben winced. "I was the one who pointed out XXX to you," she continued. "You never would have gotten to TKTK if I hadn't pushed you halfway there."

If the point of the scene is the math, then you're going to have to do a lot of research very fast.

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