Where to start? I have a few topics, but none cry out “I’m the lead story!”
Well, there was Sandy….
I have an electronic collection of the first hundred years of National Geographic. Unfortunately, it can’t be read by any of my current computers. (It’s all images of pages, but they wrapped them all in software which I can’t get running any more.)
But when I got them, I looked at the initial issues. The specific impetus for founding National Geographic and publishing things… was a major storm in about 1886. Think about what they didn’t have: a satellite picture of the whole thing. What they could try to collect was reports scattered in time and space, ranging from residents in the American midwest to ship captains in the Atlantic ocean. Like Sandy, the storm lasted several days, but accumulating and sifting thru the data took months, if not a year. And National Geographic’s first few issues tried to assemble and assess all that, to get a picture of just how far-reaching the storm had been. As I recall, it was bigger than they originally thought, and that was big enough to arouse their interest in the first place.
The post on arithmetic functions set off a record-breaking week: 2254 hits. Two weeks before was only the first time I had broken 2000 hits. To top it off, October shattered the previous monthly total, with 8750 hits, the first ever over 8000. Thanks to all of you who are reading me.
The course on computational investing….
As soon as we talk about the time value of money – if I loan you a dollar today for a year then I want back more than a dollar back from you in a year – this leads us to the closed-form solution of the geometric series: for |r| < 1,
Note that the index n started at 0. With that as a starting point, we could easily come up with alternatives for a summation starting at 1. One such is
Unfortunately, the professor started his summation at 1, and said it was equal to 1/(1-r). Not good. Worse, students are confused by his using a “discount rate” – the mistake has nothing to do with finance, but only with mathematics. (The finance might dictate whether his summation should start at 0 or 1, but the math is clear: if you want 1/(1-r) on the RHS, you darned well better start the summation at 0.) Anyway, that he has not corrected the mistake is disappointing – yes, it’s been pointed out. (I have plenty of experience making mistakes. I try to correct them.)
No technical post last Monday….
Sometimes I just don’t have a post ready… the material just hasn’t come together. But more interesting are the cases like last week: I knew exactly what I wanted to put out, but I just wouldn’t do it.
And what I’ve learned… what was reinforced again this week… is that sometimes I’m missing something and I don’t actually know it… all I know is that I’m uncomfortable with the proposed post. I’ve learned that when I don’t want to put a post out, there’s a good chance that my subconscious has a reason for telling me to hold off.
As far as I can tell, everything was right that I wanted to put out… but there were a few things that really need to be added to the post. I’ll even mention them now.
The post itself – control theory – is intended to illustrate phase margin and proportional control. It’s an example straight out of a book. It’s fine as far as it goes.
I had changed the example slightly. Did I need to stay with his numbers? (I think so.)
Along the way, I cancelled a common factor in the numerator and denominator. Is that OK? (In this case, yes.)
The final answer has a gain crossover frequency almost identical to the corner (break) frequency. Is that OK? (I think not – and that’s why I wanted his numbers.)
All the tuning rules, such as Ziegler-Nichols, which require that we get the system to oscillate at constant amplitude cannot be used… because the system cannot be made to do that. Can we look at other ways of assessing the tuning? (Oh, yes, indeed.)
I still have a fair bit of work to do, adding this material to the math I’ve already assembled, but it’s early Saturday morning… and I get an extra hour over the weekend, as we fall back from daylight savings time.