Not for the faint of art. |
Complex Numbers A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number. The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi. Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary. Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty. |
As it is Sunday, I'm once again delving into the past to see if anything's changed and, if so, how. Another relatively recent one popped up (though I'm still limiting my retrospectives to exclude the past year), this one from my trip to SoCal early in 2022, when I visited NaNoNette and her family: "No Fault of Mine" It's a short entry and, since it's not very old, I only have a bit to expand upon. We took a drive around a place that's known for its landslides, marveling at all the doomed houses all built to appreciate a view of the ocean. I'm thinking a lot of them will get a much closer view of the ocean at some point. Oh, and did I mention there's also a fault line involved? Fun! I'm thinking this may have come across as joy in the misfortune of others. That wasn't my intention. While I'm not above a bit of schadenfreude from time to time, I normally reserve it for people I think deserve it for some reason. Just living in a place that you know is subject to seismic events doesn't qualify; there is no place that's not subject to the looming threat of disaster. If not earthquakes, then wildfires, tornadoes, fire tornadoes, sinkholes, meteor strikes, enemy missiles, avalanches, hails of gunfire (mostly limited to war zones and the US), floods, droughts (sometimes both at the same time), and that perennial favorite of the Atlantic coast, hurricanes. And lots of people don't have the luxury of being able to move, even if there is a safer spot to move to. My point is, life is uncertain and I can't fault (pun intended) someone for trading a nice view and generally wonderful weather for the possibility of sliding into the Pacific at some point. In that entry, I spoke of my plans to visit Catalina, a lovely island off the coast near L.A. I did, indeed, manage to get there, and wrote a bit about it in the following entry. Lastly, the link to the Wiki page for Santa Catalina Island is badly formatted; I have no idea if it broke in the past year or if I just didn't bother to double-check it because I was in a hurry. It's easy enough to get there with a couple of extra steps after clicking on the link, but here's an xlink anyway. |