a sequence of decreasingly stupid conjectures
As we close on the start of our academic year (we start typically at the end of September or beginning of October), I’m working through the materials for my teaching. I’m teaching a class I’ve taught a number of times already, and there is the familiar deja vu.
One thing I’m always reminded of is the iceberg-ness of this preparation, and of teaching in general. Each topic in the classroom, each exercise, each paragraph and section of the Notes, all of these are just the tips of much larger icebergs.
The class I teach is graph theory, a subject that’s approaching its formal 300th birthday, though an interesting topic that I haven’t explored enough is what pre-echoes exist, in terms of graph theoretic topics before 1736 when Euler showed we cannot walk the bridges of Koenigsberg.
And so, the icebergs are large. Each small topic we take, one of my favorites being graph coloring questions, leads to an expanding cloud of related questions, variations on the basic theme. I subscribe to the daily arxiv update for graph theory preprints and each day, there are many.
I’m also in the final stages of writing a paper, one that’s been partially written for far too long. In thinking about this paper, and other papers written and not yet written, and here the iceberg is different but still large.
Here, I have a much better idea of the size of the iceberg, because I’m aware of all of the false starts, all the paragraphs that were written only to be rewritten, or deleted, and so I have a clear idea of all of the work that’s gone into my working through of the ideas, even when that work didn’t make it onto the page.
Sometimes this other work might be the starting point for a different strand of work, hopefully leading to another paper (or papers). Sometimes, it might be that what’s left out is better left out, since it wouldn’t lead to something more, or at least it wouldn’t lead to something interesting.
And where the title comes from is that sometimes, the path to a paper is working through this sequence of decreasing stupid conjectures, from the first idea, often incomplete, through to the final version.
Fiction writing is much more like writing a paper. There are the false starts, the paragraphs (or plot lines or characters or other scenes) that are taken out, perhaps put back in, rewritten over and again, until we get to a complete version.
But there is one significant difference between math paper and story. Perhaps this is just me, but I find it much easier to bring a math paper to an end than a story. There is a theorem and the path to that theorem, perhaps a few related conjectures.
On the other hand, I find it very difficult to bring a story to a clean end. It’s as though the characters don’t want to be constrained, imprisoned almost in a story declared DONE, and they fight. And I need to get better at winning that fight.
multijimbo 