Some things are progressing… some are not.
I had thought that I could write up a group theory post on semi-direct products for this Monday… while they are not too difficult to describe, I want some examples to play with… and, sad to say, the examples require more familiarity than I have. On the one hand, this is a good thing: I have identified something else I need to understand in group theory. On the other hand, the post about semi-direct products will have to wait.
I had thought that I could write up a simple post showing how the parameters of a sampled sine curve could be identified from its DFT (discrete Fourier transform). It really is pretty simple – except for one thing, the phase.
I’m sure that once I understand it… actually, by my very definition of understanding… the phase will seem simple. It turns out that I’m very close to figuring it out, I think. (I worked on it this morning, before this post… in fact, before my stream-of-consciousness… and, I haven’t turned the kid loose yet.)
It posed an interesting conundrum. Should I put the post out before I figure out the phase? Or should I wait until I understand that, too?
Well, if I really want this blog to be about the doing of mathematics rather than just the done of mathematics, then it makes sense to post something I only partially understand yet.
On the other hand, it seems silly to post it if a few more minutes will clear something up in my mind.
As it happens, in this case the question is moot: I already have a post which I can use for this Monday. I said last week that the QR decomposition could be used to orthogonalize data… and I have already written up an example.
Still, it is good for me to remind myself that I do not have to understand everything before I post something.
(Understand everything? Ha!)
It’s a good thing that I have a post written. Last weekend, ironically enough, I was distracted by a PBS show about “the distracted mind”. Like most control systems – not that the narrator used that terminology – the mind needs to deal with both command following and disturbance rejection, but it must also sometimes determine that a disturbance should not be rejected. That is, ignore distractions in order to focus on a specific task – but sometimes we damned well better respond to a disturbance or distraction.
It appears that as we get older we let too many distractions in, and lose our train of thought more easily. Unfortunately, it doesn’t look like the show is going to be re-broadcast any time soon in my neck of the woods. If you’re interested, here’s a link which will let you download a list of showings nationwide.
Oh, the narrator also talked about the benefits of photographing nature. It offers a good balance: focus on a goal – say, a waterfall reached by such-and-such a trail – and plenty of opportunity to be distracted by other photographic opportunities. I think the point is to practice preserving a goal while letting some distractions become interruptions.
While I was wondering if I needed to take my own camera on a hike, I decided instead that mathematics offers the same benefits. I won’t speak for you, but I certainly need to have my eyes open to other possibilities even while I’m focused on a problem. As I believe Asimov said, the great line in science isn’t “Eureka! I found it!” but rather “That’s odd. I wonder what’s happening.”
Speaking of getting older… I was shocked to discover that one algorithm for translating cat years to human years says that my cats are 64 years old. (Call them 15 at 1 cat year, 24 at 2, and then add 4 human years for each cat year afterwards. Then 12 years elapsed is 24+40 = 64.
I know they’re not jumping as high as often, but they still seem relatively more athletic than I would expect a 64-year-old human to be.
As if that weren’t enough, I was distracted this morning by a German news station talking about German teenagers in English boarding schools… and I think the background music was the soundtrack from “Dead Poets Society”.
As it happens, I was recently looking at the history of mathematics education in the United States – Yuck!… furthermore, it turns out that the great gap in learning in the U.S. is not chinese vs. white or white vs. black, but rich vs. poor. Gee, could that be private school vs. public?
In addition, we were relatively poor when I was growing up, but my mother did decide that she could afford the tuition for a New England boarding school. Unfortunately, she also decided that she could not afford the wardrobe a young gentleman was required to bring. So I went to public school – as it happened, a pretty good one. But I’ve always wondered what it would have been like to go to prep school.
So much for distractions. Despite them, I have a post ready to go… my alter ego the kid has been looking at the “multiple view geometry” book detailed last week… and I’m hoping to tackle another example of compressed sensing this weekend.
Now, I have a comment to reply to, and then some maths to do.