How?


What’s been happening? Among other things, I have been so busy putting math out here that I’ve completely forgotten to talk about the doing of it.
Of course, doing mathematics is fundamentally different from putting mathematical posts out here. Last Monday I was all set to prepare a set of posts for the coming week, only I got distracted by doing mathematics.
Can you imagine that? Well, math is my fundamental goal after all. Even the blog is secondary.
But the blog is very good for me, and I want to get stuff out here. Unfortunately, it’s a nontrivial task. I need to stop doing mathematics for a while in order to publish stuff. And because it’s a different activity, I need to develop different habits.
For the longest time, I’ve really done two or three different things when I “do math”. The easiest is to curl up in a reading chair with a book and a recorder, and browse and take notes. I do this with new books as they arrive, or with any book I’m about to do some work in. In fact, I try to have the recorder handy whenever I read anything. The point is to record whatever thoughts I have or whatever I see of interest. It’s a comfortable thing to do. (Yes, I usually read first and compute later, though I’ve been known to run to the computer to verify something that just couldn’t wait.)
This doesn’t commit me to doing any real work in a book; I can always come back to the notes later.

The most straightforward thing to do is to sit at my computer doing computations or whatever in Mathematica. (That’s a program from Wolfram Research, and it does symbolic, numeric, and graphical stuff, all in one. Oh, and its files are called “notebooks”)
For those things best done by hand – proofs and some kinds of algebraic manipulation – I use spiral-bound 3- or 5-subject notebooks. (So, yes, I have both paper and electronic notebooks.) Mathematica does algebra very accurately, but sometimes it just doesn’t do what I want it to. And rather than fight with it, I go do algebra by hand. 
And there’s another way I do math, but I can’t force this one: sometimes I dream about it, sometimes I just wake up in the morning knowing how to solve a problem that was open when I fell asleep.
Thinking about it, I’d list two distinct activities: taking notes without obligation, and actually doing math. I could call those stages 1 and 2.
What would it mean to take notes with obligation? That’s when I’m tying to get an accurate summary of some material. That’s a form of doing math.)
The blog has added a few different activities to those two. 
First off, my working Mathematica notebooks are not well written.
Not even for me. Oh, yes, I can open a file three years later and see what I was doing. But I often wonder why I was doing it.
(I usually think of that as “What the hell was I doing?”, but in fact, the “what” is pretty clear in my own mathematics – I can see exactly what I was computing: the correct question is: “Why the hell was I computing that?”, and I’m still learning to write that down.)
To put some math out on the blog, I start with something I’ve already worked out in Mathematica. Then I try to add all the what and why. This isn’t particularly difficult, and it’s often rewarding. But it is time-consuming.
Rather often, too, I think of and add things I was too focused to wonder about as I was heading toward an answer.
I’ve spent a few years now fighting my way through different forests, so to speak, and periodically I get back to an old forest; I walk the trails I had cut, and then I hack my way out creating another trail. But I’ve not spent much time looking over a trail right after I’ve made it.
The blog is forcing me to assess the trail I’ve cut. As I said, not difficult; but it doesn’t have the same thrill as breaking new ground. (It’s new ground for me, even if it is old hat to the cognoscenti.)
That’s three kinds of things, then: adding commentary for readability; thinking of side issues I missed along the way; and summarizing material.
Having done all that, however, I face a less enjoyable challenge: producing source for the blog. Mathematica will write TeX output; the wordpress editor can handle something like TeX, but it’s touchy.
Intellectually, this isn’t at all difficult. To display an array, for example, starting from the TeX output, I just need to remove the leading blank from \, remove leading and trailing blanks from & , and then remove the carriage returns. Oh, and if the array contains integer zeroes, they must be replaced, either by real “0.” or by UC letter O. 
Nevertheless, it’s tiring. I’ve learned that after I edit TeX for a while, I’m utterly fried for other purposes. To put these comments out on the same day as I put out a technical post, I needed to draft these comments first.
And that’s what I did, even though I polished and published them afterwards.
Getting from my math to a Mathematica notebook which someone else could read is all one activity, call it stage 3; constructing a source for the blog is another, stage 4. And I do, by god, want credit for putting it out there, so that’s stage 5. Besides, getting from the source to something that actually displays is sometimes challenging. (“Formula does not parse” is all the help you get.)
A friend once chided me for having too long a to-do list. I changed the name from “to do” to “gimme credit”. I know I’m not the only person who has put something on a list just to be able to cross it off.
Anyway, stage 5 gets crossed off after the post is out here. Sure, stage 5 is easy; but stage 4 was more than enough work.
Why did I go through all that for myself? Because I discovered that I was forgetting about math that was between stages 2 and 3, more verbose than my work, not yet clear enough to post. I have arranged to keep track of it.
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