...into big thanks to Anno, a.k.a. err... well... Anno. The original idea simply turned out not to be brilliant at all. It was all based on the wrong assumption that
overload.pm would not suffice. Instead it does, as diotalevi a.k.a. jjore correctly pointed out. At this point, the thread may have been happily terminated. Instead Anno went on taking my code and making it into a very good example about Inside-Out techniques.
Two positive circumstances:
I'm doing this as much for my own edification. I am glad for the opportunity to discuss general principles in the context of a concrete class implementation. If it hadn't been for the context of, specifically, 2x2 matrices I wouldn't have come up with the example of combining a matrix class and an angle class to form a class of rotational matrices. I've been looking for an example that makes some sense of using two classes in tandem, more than attaching a label or a time stamp to anything. I am glad the discussion brought one up.
To note that notwithstanding my absymal mistake, the original node got considerably upvoted. "Considerably" especially with respect to the replies it got, which constitute the authentically valuable part of the thread. At least I suppose the merit of the first post itself must have been that of having spawned them. Certainly the XP whore in me is happy, but in all earnestness I feel that (Anno's, especially) replies would deserve having earned more consideration. But it is well known that the voting system in PM sometimes exhibits seemingly strange social dynamics, and it is well known that complaining about it is likely to be heavily downvoted as well. So I do not complain!
PS: I created the "XP whore" node to which I refer above just before writing this entry, because... well I just needed it. (The significance may not be obvious to non-PMers.)