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 |    Not for the faint of art. |
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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. ![Merit Badge in Quill Award
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| I've had an interest in astronomy for as long as I can remember. Today, I'll talk about one of the things that got me started. Readers Love Curious George. I Fell in Love with the Author’s Astronomy Books.  H.A. Rey recreated star maps with wit, grace, and accuracy. I read these books before I'd even heard of Curious George. Apparently, the same was true for this author. The little book that really got me hooked on the night sky was called Know the Stars, adapted from a longer work, Know the Constellations. The author was H.A. Rey. As for me, I don't really remember the names of the books, or even much of their content. Just that they were about astronomy. Hans’ first astronomy book, The Stars: A New Way to See Them, was published in 1952; Find the Constellations, aimed at younger readers, appeared in 1954. Although both books are monkey-less, there are clues they came from the same hand that brought George to life. I also remember that by the time I got my grubby paws on those books (whichever ones they were), some of the information in them was already outdated. While the stars don't tend to change much in a human lifetime, and especially not in the 15 or so years between their publication and my curiosity, science continues to find out new things, and information about, say, solar eclipses and planetary conjunctions does have an expiration date. Hans first took an interest in the stars while serving in the German army as a young infantryman during World War I... At night, during breaks in the fighting, Rey looked skyward. What he saw looked nothing like the fanciful pictures in the popular astronomy books of the time. In one early 19th-century textbook, Leo the lion is drawn with a full mane of fur and a looping tail; with paws thrust forward, it seems ready to pounce. Only with great effort do we see the “backward question mark” (also called “the sickle”) at the lion’s front end—the only part of Leo that’s relatively easy to spot in the springtime sky—with the bright star Regulus marking the “dot” of the question mark. As these were probably my first encounter with astronomy texts -- though my dad had taken me out on cold, clear nights and pointed out a lot of the stars and constellations -- I didn't have that prior experience with the "fanciful pictures." Hans’ diagrams, in contrast, are almost breathtaking in their simplicity. He drew the constellations with clean lines, almost like stick figures. And, remarkably, they look like the people and animals that the ancients imagined, and they look like what you actually see when you look up at the sky (far from city lights, hopefully). Constellations are not, of course, immutable. Stars move, albeit slowly in our limited perspective, and of course they'd look different from other places in the galaxy. And they don't have any innate meaning (not even the ones in the zodiac). They're basically pareidolia: images from our imagination projected on the semirandom distribution of visible stars. Other cultures saw different pictures up there, which is fascinating in itself -- a window into the things important to those cultures. The ones we're familiar with are, of course, from a European tradition (there are exceptions for some of the southern hemisphere constellations, because, as you might be aware, Europe is not in the southern hemisphere). But they -- star patterns such as Orion, Canis Major, Aquarius, Ursa Minor, etc. -- are used by astronomers to describe the relative locations of other astronomical objects, even those not visible to the unaided eye. Incidentally, it might have been these books by the Reys that introduced me to the phrase "naked eye," which of course sent Kid Me into giggle fits. As another aside, the Big Dipper isn't a constellation; it's a small part (an asterism) of the larger constellation Ursa Major, the other stars of which aren't as bright. But again, it's pretty arbitrary and based on Western mythology. Importantly, the star positions are accurate: Yes, he connected them with lines; but the stars are precisely where they’re supposed to be. Hans taught himself celestial cartography for this purpose, and to create the sky-view maps that appear in both The Stars and Find the Constellations. He uses larger dots to indicate brighter stars, and explains the “magnitude” system that professional astronomers use to denote the brightness of stars. I vaguely remember that, too. I think the ranges they use for magnitude have changed slightly since then, but it gave me a baseline. The Reys’ story is a remarkable one, and I’m embarrassed to admit that I only learned about it recently, through Louise Borden’s 2010 book, The Journey That Saved Curious George: The True Wartime Escape of Margret and H.A. Rey, and the media coverage that her book sparked. And it's a very interesting story, one which has been echoed many times: Jewish couple fucks off out of Europe when they see the shitstorm coming. Unfortunately, it was not echoed enough times. How much other cool shit has never happened because some asshole wanted to commit genocide? You'll have to read it at the link, though. When I went to the opthalmologist to get my eyes fixed, I had a choice for cataract surgery: standard lenses, which I was told would keep my distance vision but require me to wear reading glasses; or the fancy kind that allows for both distance and close-in viewing. The doc told me the pros and cons of each. Option A, he said, would result in clear distance vision, and furthermore are covered by insurance. Option B would give me relatively clear full-range vision, with the downside being that, at night, light sources would have a diffraction pattern. "Not usually a problem unless one of your hobbies is astronomy," he said. "Well, actually..." I replied. And yet I chose Option B because I like to read and use the computer. I don't regret the decision. But indeed, lights at night have these annoying halos. Streetlights, headlights, stars, the moon, whatever. So my interest in astronomy is limited mostly to books and websites now, albeit those geared to adults and not the fun children's astronomy books such as the ones by the Reys. Still, it's been nice, this winter, to be able to look at the stars, even if they do look a little blurry -- it's definitely an improvement over having cataracts. Just the other night, I looked up on my way home from the movie theater, and I stopped to gaze at Orion for a bit. I saw the constellation, even through the haze of the city lights... and I remembered. |
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