Well, it’s a little later than I would like on a Saturday morning, but that’s the way things go. (And yet, as it happens, it looks like this will go out like most of these posts, shortly after noon.)
My kid has already had his time playing. Right now he’s reading through Jänich’s “Topology”. No, of course that’s not on the small desk — the kid gets to rampage through my entire library, and he gets to grab anything he wants — well, anything of mathematics or applied mathematics.
I hope to speak more about Jänich’s “Topology”… but, for now, let me just say that it is one of several delightful “Undergraduate Texts in Mathematics” from Springer. Many of the books in that series seem to be standard textbooks — but the ones that especially delight me are those that either take one small topic, or take a stroll through a subject.
Examples of the former — one small topic, as a focus for the material — are Sethuraman’s “Rings, Fields, and Vector Spaces”, Kantor & Solodovnikov’s “Hypercomplex Numbers”, and Baker’s “Matrix Groups”.
Examples of the latter — taking a pleasant walk, surveying the landscape — are Jänich, and Stillwell’s “The Four Pillars of Geometry”, and Armstrong’s “Groups and Symmetry”.
Anyway, Jänich is really fun. Here, for example we have…. “Why are homogeneous spaces of interest? This is a damned far-reaching question and cannot be fully answered at the level of this book. But I will try to make some comments about it.”
And, frankly, he made some very interesting comments.
So that’s what the kid looked at this morning. Over the past month he has picked up logic and orbits, both of which will apparently make it to the blog — that is, my grown up has followed in the wake of my kid.
He has also picked up Armstrong’s “Groups and Symmetry” — which is why it ended up on the little desk — and catastrophe theory, Fermat’s last theorem, impact craters, and voting methods.
In fact, he has picked up orbits more than once… he wishes my grown-up would hurry up and write functions for doing computations — but the kid doesn’t always have the patience to wait for my grown-up to do that. (My grown-up thinks it’s fine if the kid loses his patience and works on them too.)
At one point, sometime earlier this year, I realized that my kid was picking up something just because it was completely different from anything my grown-up was doing. That’s not nice. It’s almost mean.
For a couple of days, I thought he should not do that.
Then I decided that my kid really does get to pick up anything at all remotely mathematical, for any reason whatsoever. Hey, there’s nothing wrong with shaking up my stodgy old grown up, waving new things in his face, and encouraging him to leave his well-laid-out path.
After all, my grown-up does get to make the final decision about what he works on. If the kid is desperate enough about a specific subject, he’ll put in his own time on it.
Oh, and the kid also picked up some unfinished business — which is still unfinished, because none of my promising leads has quite panned out: what I call the magic omega formula. That’s what brought the control of aircraft to a halt quite some time ago.
It’s funny, in a way. Sometimes when I don’t understand something, I keep going anyway, trying to get a better picture of what it will do for me when I do understand that thing.
Sometimes, on the other hand, when I don’t understand something, I put it down and pick it up again years later. Well, there’s this little equation that finally, at least, makes sense — it used to look completely ridiculous!
I thought I had found a derivation of it — but, no… that is, it ought to be a derivation of it, but it doesn’t look like the same equation.
I’ll be taking another look at it this weekend, I hope. Other things seem to be moving along, too. For logic, I have just about finished the mathematics for a couple of posts. For orbits, there is a specific example I need to work. For color, I have a specific idea to try out for constructing a residual spectrum to order; and there is a specific example I need to work.
Okay, I think I’m going to try the thing that might not work — just so I have more time to think about it… constructing residual color spectra to order.