multijimbo

I am currently working on both a mathematical paper (and to be fair, I’ve been working on it for longer than I want to admit) and a story (built around the same basic idea of my second published story). Both are still in progress, and I thought it would be interesting to (very occasionally) compare and contrast my thoughts as I go through the process of finishing both.

The math paper keeps growing. The original paper was relatively short and focused on one theorem, which is a question that had been kicking around my head for twenty years. It’s a question that I gave to a PhD student, who decided to focus their attention in a different direction and never focused their attention on this question. And so I have an idea, and I went back to it, and I was able to push the idea through.

There is still some work to be done in the details of the proof of that theorem, but I’m confident that I’ll be able to make them work. One of the interesting things about a math theorem, a math paper, at least for me, is that until I actually work through all of the details, in their full detail, there is always the ghost of a nagging doubt that I’ve missed something that will come back and haunt me.

There is an aspect of this ghost in crafting a story, in that there are the continuity errors. If I want something to happen later in the story, the early part of the story can’t then set up something that precludes that which needs to come later. In the math paper, though, the ghost can be something we can’t get around. If only I can do this thing that unfortunately isn’t true, is something that I suspect most mathematicians have said to themselves, and the art and craft then comes in finding the true steps to the true end result.

For me, and for these two projects, the interesting thing is that I can see the ending to the math paper much more clearly than I can see the ending to the story. For the math paper, I know all of the results that I want to be part of the final work, whether I can push them through and make them part of this paper or whether they will require more thought and be part of a future paper. I have a very clear picture in my head of what I believe should be true.

For the story, I have no idea how it ends. Reflecting on the stories I’ve half-written but haven’t yet brought to a final version, I have a problem with the endings. And I can see what I’m doing. I have an idea, I craft a story around that idea, and I lose my energy and end up with something that I don’t find satisfying at the end.

I read a lot of short stories, science fiction and fantasy and neither, and there are some spectacular stories out there. I don’t like to think about how some of those authors would handle my ideas, because they’re (for the time being at least) my ideas, and I want to see what I can do with them. (And it can also be remarkably intimidating.) The same thought also lurks in the back of my mind with the math paper, but both have the common feature that once we send those ideas out into the world, others will be able to read them and start doing their jazz with the ideas.

With both, there is the temptation to keep going. I’ve accepted that fiction needs editing, and editing, and a bit more editing, constantly refining, and removing everything that doesn’t advance the story. With the math paper, there is more of a temptation to include all of the associated and related results, not being as concerned about removing everything that doesn’t advance the story of the paper, and perhaps this is something to reconsider.

I can see that I’ve always adopted the Columbo protocol with math papers – just one more thing, and so an exercise I’ll add to my list of exercises is to read math papers with the same eye I use when reading and critiquing the stories I read. I’m curious to see what happens.

~ by Jim Anderson on 18 April 2021.

Posted in bizarre and random things, mathematics, writing ephemera