Starting with meta.

First posted on January 7, 2018

Writing on non-trivial subjects in a way which is of any use to realistic prospective readers is difficult. There is a tricky interplay between motivating the text with forward-looking glimpses of the goal, and supporting the text with backward-looking logical progression. There are difficult decisions of when to provide background, and when to credit the reader’s existing knowledge.

Here I am going to collect my thoughts on how best to write for an audience. Historically (term papers excluded) my writing has primarily consisted of point form notes: sufficient information for me to recreate my own thoughts and arguments at a later date, but not enough for a reader to follow.

The ordering of the presentation of information and of the rendering of arguments is particularly tricky. This is a common pattern I find when I come to a new belief:

  • I’m considering a problem, something in need of explanation
  • I note down features of the problem and set to work exploring possible explanations
  • I discover an explanation for more general phenomena which includes the original phenomenon

When I go to relay a new argument to someone else I have to choose between motivating the general phenomena, regurgitating the often messy actual route I took to the argument, and building the argument from the ground up, blind, with no motivation given.

It is common in mathematics to take this blind leading approach. You are walked through various basic definitions and simple properties with a lengthy build-up before being shown how to put those definitions to use, and are then pleasantly surprised by the power of the simple tools you were given. This has problems even in mathematics. It is an extremely effective means to teach a mathematical theory. It is probably necessary in order to speed the student through generations of discoveries. Yet it doesn’t teach much of anything about how to approach new problems in math.

I’m tempted to suggest that what’s needed is a small overview, something like a table of contents for an argument, so that the reader can see at a glance both where we’re going and the general route we’ll take to get there. This suggests something like the structuring of Wittgenstein’s Tractatus, but that’s famously unapproachable so maybe I’m completely off track here.

I’ll cut myself off here as my goal is very much not to blog about blogging, and even less so to blog about this blog (a sin far too common). To that end, any further thoughts on the subject will be spliced in above without notice, and will not become new independent posts.