Sometimes it is hard to know what the point in some particular discourse (or experience) is. Sometimes many arrows seem to be pointing at something – but you don't know what it is, do you, Mr. Jones?
Well, the calculus of self-referentiality can help you make sense of these complex and confusing situations, and, indeed can help you use them to your advantage. You'll learn how to either come to the point quickly or avoid it gracefully (and still get somewhere).
Briefly, here is how this calculus works in a simple case. You think, you write, you read what you have written, and you react in writing. Then you think again, making some new or formalized connection between your previous reaction and previous thoughts. You then write down what you thought, and continue. In this continuing process, you are allowed to use earlier thoughts and reactions as well as the current ones. But think knitting with syllogisms and you won't be far of the mark.
I've described here a "2-dimensional" version of the calculus, which is a form of 2-column bookkeeping for ideas. The artifacts produced by this algorithm are basic examples of "scholium-based documents".
But there are higher-dimensional versions of this sort of thing. For example, the processes that one goes through when updating a long paper resemble this model locally (original plus side-comments, call and response), but these local instances are strung together temporally, sometimes with loops, producing a complicated action-reaction set. I don't have a full grasp of the details, but I would argue that following this sort of calculus is how people get things done, in general. Big claim, I know. While I'm not going to go into details right now, I might mention that I'm haven't come up with any counterexamples.
Well, OK, I lied. Here is a weak sort of counterexample: outside references. In other words, sometimes self-reference isn't enough and you need to ask questions of someone else or do some other experiment to figure something out. True, the results do get incorporated into your model somehow, first as gaps, and then maybe just as pointers (but also sometimes as de-referenced pointers). This is strictly "second semester" stuff.
When thinking about how to build a "mental map", the basic calculus is all you need. You're less concerned with leaving things out (via outside references to points in terra oublietta [cf. "forgetful functors"]) and more concerned with building up some kind of coherent presentation.
--jcorneli