Happenings – 2012 Oct 6

It’s been a mildly interesting week.

I have figured out how to change the default sequence of colors for multiple graphs. I’ll explain this in more detail in a Mathematica note, but let me show it to you now. Suppose we take the first 5 Legendre polynomials… and plot them.

We actually got 5 distinct colors, but the fifth and first are rather close. I can select a better sequence – more importantly, I can select a better sequence without explicitly enumerating the colors. One of several possibilities is:

I’ll admit that I’m having trouble altering the thickness, but at least I know how to alter the colors. And, given a particular sequence, I might want to change my usual background color. As I said, I’ll show it to you in more detail.

I’ve continued with the online Introduction to R. I like pure programming once in a while, and I’m mostly having fun.

Sometimes, however, it can be very frustrating. My program was matching the design output, but my attempts to run the test-script were not giving the right output. Turns out that it’s not straight-forward – not for this rookie anyway – to keep the disk copy of the source matched to the copy in RStudio’s memory. My copy on disk was an ancient version – in fact, the very first one! – and, of course, it didn’t work.

Oh, I caught something on a PBS station, called “Into the Wild”. Back around World War I, a few friends decided to take a break from work and drive into the countryside. This was long before such jaunts were common… in fact, they helped publicize and popularize the idea of a car-camping trip.

Their names? Henry Ford, Thomas Edison, Harvey Firestone, and the naturalist John Burroughs. (Burroughs I had never heard of.)

Now try to imagine Henry Ford as your personal auto mechanic on such trip – he was. Try to imagine Thomas Edison arranging electric lighting so you all can read after dark – he did. One year, they rented a train… and Ford was the engineer and Firestone was the fireman. It reads like something out of “Atlas Shrugged”.

As for the next technical post, we’ll see. It might be control theory, or it might be resonance in a second-order differential equation… but I might change the subject completely, since I’m still thinking about number-theoretic functions. (If you know any, you know Euler’s phi function, also called Euler’s totient function: \varphi(n)\ is the number of positive integers less than or equal to n and relatively prime to n.)


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