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Jon Bannon
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Halmos has already been mentioned, but I'd like to record the following: It may be helpful to employ spiral-writing (a-la Halmos) but at the paragraph level, rather than the chapter or section level as he suggests. So, write a paragraph, then the next one, looking back to see if the previous can be clarified in light of the one written. I suggest this because the paragraph is supposed to be the natural unit of composition, and if C.S. Peirce was right, clarity is utility. Spiral writing at this level may help not only exposit mathematics but also do mathematics. Each subsequent thought we attempt requires a better utility from what has been previously written...and the only way to guarantee such increased utility is to have attempted this subsequent thought and then carefully had a look at exactly what was needed in prior paragraphs to develop that thought.

I guess that in summary I have only two new things to add here. 1. Halmos's spiral writing is philosophically sound from the standpoint of early pragmatism, and 2. Maybe it can be effectively employed at the paragraph level instead of the section/chapter level.

Of course, Halmos suggests writing a chapter at a sitting as a way to fight inertia...so my second suggestion in the previous paragraph may not be actually better, only personal.

Anyhow, I was going to record this thought in my own personal notes, but thought maybe someone else may have a use for it as well.