Ah, I didn’t realize until I entered the title for this post that it was St. Patrick’s Day. And last Wednesday, being 3/14, was Day. I can’t say I celebrated the latter, nor expect to celebrate the former – but who knows? I might remember to wear a green shirt… do I own a green shirt? – when I go out later today.
(Yes, I do sometimes stop doing math and leave my cave on weekends.)
Not much has been happening for the blog. No new books have come in, and, in fact, I have no books on order. The only major distraction is that I was out of town, on business, for 3 days. And I didn’t bring any math books to read in the airport and on the plane… instead, one history and one fantasy. (If you care, Will and Ariel Durant’s “The Reformation” and Anne McCaffrey’s “Renegades of Pern”.)
As for the blog itself, I haven’t even decided what the technical post will be for Monday. The 2 most likely candidates are:
Finding the frequency of a sampled sine wave.
I made some good progress on both of those topics last weekend… although it still remains true that I do not understand the apparent phase shift if I change the origin of the sampling. And it still remains true that I’ll consider putting the sine wave post out before I understand everything else about it. But if I do trusses instead, I’ll have more time to work out the exact value of the phase shift. (I know… it should be obvious… but I don’t get the answer that seems obvious to me!)
A less likely candidate is: group actions. This idea formalizes our intuitive understanding of a cyclic group rotating a regular n-gon, or a dihedral group spinning it about a diameter. In these cases, and in many additional useful situations, we have a group and we have a separate distinct set (in these cases, of vertices)… and such a nice combination of a group and a set is called a group action.
But that topic is still completely hypothetical… I have almost nothing written down for it… so I’d be surprised if it could be ready by Monday.
The more I think about it, trusses is the leading candidate. Still, the material is only at Stage III: the math is done, but absolutely none of the narrative.
As for other things…
My alter ego the kid was looking through Spivak’s “comprehensive introduction to differential geometry”. It turns out that volume 1 (of five!) starts “bundles” in Chapter 3. It’s been so long since I looked in this book that I had completely forgotten he did bundles early on. In fact, that’s probably why I quit reading the book so long ago: I just wasn’t ready to tackle either vector bundles or fiber bundles. (Google the terms if you want.)
My alter ego the undergraduate is supposed to still be working on electric circuits… but I don’t think he’s touched them in a month.
My alter ego the graduate student is still studying rings… not as rapidly as I would like, but he’s still working at them.
My alter ego Mr. Belvedere … very recently created and named … is working through the “multiple view geometry” book that recently arrived. Although the kid started looking at the book, he has moved on to other things. (Mr. Belvedere is named for the TV show nanny… what he does is clean up stuff that the kid picked up and put down. There’s a lot of that.)
So far, I am finding this to be a useful way of organizing things… to imagine that I wear different hats… and each alter ego maintains his own list of what he could be doing. They don’t always do something every schoolday … as I said, the undergraduate hasn’t done electric circuits or anything else in at least a month. Maybe he’s sick and tired of circuit theory?
Anyway, don’t worry about my multiple personalities…
I am eclectic; you are eccentric; he is barking mad. ~ Unknown.
so long as the posts are all by “Rip”, things are OK. If you ever see one by “Mr. Belvedere”, then I may have gone off the deep end.
(Once I realized that “the nanny” was Mr. Belvedere, I considered naming the kid, the undergraduate, and the graduate student… but it didn’t work for me. I know them too well by their titles.)