It’s been the kind of week where I looked briefly at a lot of things.
First, however, let me share something that I forgot to post last Saturday. It is especially relevant to the post about Freeman Dyson’s mental compartmentalization, physicist versus pure mathematician.
The following comes from “Empirical Model-building and Response Surfaces” (p. 219 ), by Box and Draper (0 471 81033 9):
We have sometimes been dismayed to find that the engineer newly introduced to statistical methods may put statistics and engineering in different compartments of his mind and feel that when he is doing statistics, he no longer needs to be an engineer. This is of course not so. All his engineering knowledge, hunches, and cunning concerning such matters as choice of variables and transformation of variables must still be employed in conjunction with statistical design and analysis. Statistical methods used with good engineering know how make a powerful combination, but poor engineering combined with mechanical and unimaginative use of inadequately understood statistical methods can be disastrous.
One of my newsgroups – strictly speaking it’s a mailing list to which I subscribe – tells me that there are a couple of iPhone apps for color calculations:
If you are interested in color, you might find the site itself to be very informative.
I also came across another interesting educational mathematics site. I was originally put off by its starting with arithmetic… but the fact is that it includes college-level mathematics, physics, chemistry, and economics:
As for my mathematical life… I have put down Dummit & Foote, having made it through all of the group theory material, with which the book opens. (No, I have not worked all the exercises – I have read them very carefully, but that’s not the same thing.)
What I want to do instead is – what else? – a whole lot of calculations for low order groups. This may turn out to be more than I can handle… but I would like to apply all the theory I just read to two things: taking a group apart, and putting a new group together.
Besides, I like having my alter ego the graduate student working his way through a book… but I wanted a break, a book of a different flavor. I have begun working through “Mechanics of Solids”, by Pilkey & Pilkey. Ah, simple and satisfying computation! (And it’s a prelude to “Vibration of Structures”.)
There are already two examples I’d like to show you – no, not today, not in a diary post. One of them is a two-dimensional truss, because I think I can organize the calculations nicely. The other is just a cute problem: the force required to push a wheel over an obstacle versus the force required to pull it over the obstacle.
On the bright side, in other mathematics, there’s a nifty estimate of the power released by the first atomic bomb – using dimensional analysis, specifically the Buckingham Pi theorem. Which I don’t understand properly.
I also learned how to do “ridge regression”” although the example in the book is marred by typos. We’ll see whether or not I end up recommending the book. As usual, I now know how – just not why or when. (Well, it’s supposed to be an alternative to OLS in the presence of multicollinearity.)
I also discovered a book on my shelves that uses some pretty serious differential geometry for control theory. Nice… it combines two of my Big Five. (The other three are dynamical systems, time series, and quantum mechanics.)
On the dark side, I felt a need to find and browse my book on tsunamis. (I hope you didn’t think that I didn’t own one.) As one would expect, it’s full of differential equations. Interestingly, it said that the third pulse is often the most intense… and, when asked if the intensity was decreasing over time, the respondent in Santa Cruz said that no, he thought the latest, the third one, was worse than the previous two.
(No, I don’t know why. Nor do I know why a harbor a few hundred miles north of us saw wave heights twice as high as Santa Cruz. I suspect it has to do with the details of the sea floor at and in front of the harbor.)
On the darkest side, I have not yet found and browsed my book on nuclear engineering….
There is a poignant scene from a TV series. Two little boys have gathered all their savings and counted it up – about $50. Their father thinks they are planning to spend it all for Christmas. He suggests that they might want to save some of it for a rainy day.
He misinterprets their answer: “It’s raining all over the world.” He thinks they will spend it on themselves because, after all, it’s a rainy day somewhere; what they do instead is donate it to charity, to send it to a country where, figuratively speaking, it is raining. (If you must know, season 11 of “Seventh Heaven”.)
Well, misfortune has been raining pretty hard in a few places this weekend. I wish them well.
But it’s a sunny spring day here, and I am going to curl up with some mathematics.