As I begin this draft, I am hoping to talk about the joy I take in mathematics, my sense of wonder, and something called “beginner’s mind”. We’ll see how it goes.
But first let me just talk about what’s been happening.
Once again, no posts went out last weekend. This time I had a different excuse.
Saturday morning, when I should have been drafting a happenings post, I discovered that I needed a mathematics fix. Never mind what I was supposed to do, I needed to do some mathematics. So I did.
I spent all of last Saturday and half of Sunday looking at regression (OLS, ordinary least squares). Finally, Sunday afternoon I returned to orbital mechanics. But that didn’t give me enough time to finish off a technical post.
As for the blog itself, sometime in the afternoon of June 10, one of the color posts (the CIE chromaticity chart) surpassed my only Fourier analysis post, moving into second place all-time.
First place is held by the first post relating the angle and axis of rotation to the matrix describing the rotation. (Over just the past year, that post is only fourth — but it was published long before the others and has a huge lead for all time.)
Oh, when I was reviewing the previous happenings post this morning — the May 29 post that originally said April 29 — I discovered that my attempts to cross out “April 29”, rather than to simply replace it, had succeeded in messing up the end of the post, putting lines through all of the stuff about comments, and the previous post!
Thanks to WordPress’s saving previous versions, however, I was able to restore the wrong-dated version — and made a clean correction without inadvertent cross-outs.
Okay, let me try talking about the joy I take in mathematics.
Let me begin with my inner child. Turning my kid loose in the morning is fairly straightforward nowadays, now that I know the rules.
Once in a while, my kid doesn’t even have to get up from the computer; he knows that he wants to work on something I was doing recently. And in that case, it’s usually a computation.
Sometimes it’s something where I’m struggling with the details. I’m very sure of what I’m supposed to do, and I’m just trying to get all the pieces right. This leads to a satisfied “okay” when I’m done. I have confirmed my understanding.
Sometimes, instead, I’m trying to figure out what someone did, by doing some computations, and seeing if I get their answer.
I can’t begin to tell you how many times I have found a description too vague to be useful. So I roll up my sleeves and try things, until I match their answer. This often leads to a noisy “yes, yes, yes!”. I have answered the question: what the hell did they do?
Anyway, if I’m in the middle of either of those kinds of calculations, there’s a good chance that my kid wants to pick them up again as soon as possible. And he’s been known to work way past his one hour allotment for play.
And that’s more than okay. Frankly, my grown-up is always happy when the kid is being “productive”.
My kid is not the only one who’s allowed to do that… my grown-up likes computation, too.
While I’m on the subject, let me say that I am always thrilled when I find an easier way to do something than the one I found in a book.
More often than not, however, there is no such exciting computation beckoning to my inner child. Now, my usual preparations in the morning give me ample opportunity to consider the books on the two bookcases directly in front of me, and all the books on the small desk and the small table (the books I want to read, and the books I have specific problems in). If my kid wants to play with any of these books, I know it even before I’m ready to turn him loose.
But if none of those books excites him, then I get up and walk toward my library.
I’ve been known not to make it — on the way there is yet another small table covered with books. This is effectively a “library cart”, holding random books that have not been re-shelved. Every once in a while something on that table grabs the kid’s attention as he passes by.
In any case, my kid is free to pick up any math book — actually, any quantitative book — any one at all that strikes his fancy.
As I said once before, I sometimes hesitated to pick up a book for no better reason than that it was different from what I was working on. After a couple of days of that, I decided that it was perfectly okay for my kid to shake my grown-up out of his rut. Sometimes that’s exactly why he picks up some particular book.
Still, he doesn’t do that very often. Sometimes my kid is looking for something he can compute.
I really like getting answers to problems.
I’m not sure what to say here. Only once in the past 20 years have I used calculus for work — and it was fun and satisfying; but much of my success with my colleagues comes from the fact that I take a personal delight in giving them numerical answers to their questions.
But sometimes, instead of looking for answers, my kid wants to indulge our sense of wonder.
And that’s a whole ‘nother topic, so I’ll leave you wondering.
Now I have an orbit post to work on for the blog… and the math of Boolean equations to make some progess in.