Complex Numbers (Book)

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Complex Numbers

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.

http://www.ddewey.net/mandelbrot/

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June 23, 2022 at 1:14am

#1034129

Queen of Sheba

The penultimate entry for June's "Journalistic Intentions"

[18+]

And I'm the Queen of Sheba

From that page:

Popular forms include "I'm the Queen of Sheba," "I'm a monkey's uncle," "I'm the Queen of England", and "I'm the King of Siam."

I gotta say, this is one of those tropes that, as long as you make the slightest effort at creativity on this one -- that is, not specifically calling out Sheba, monkeys, England, or Siam as above -- I do appreciate this trope with all its twists. In other words, don't use the popular ones, and do use a comeback that makes sense in-universe.

It's very likely that the first time I encountered this trope was in Star Trek. While the original series got canceled when I was 3, I became familiar with the show as a kid thanks to reruns in syndication. There's an episode (called "Who Mourns for Adonais") where the Enterprise famously gets grabbed by a giant green glowing hand in space and taken to the planet where actual Apollo lives.

The giant green hand in space was exceeded in its absurdity only by the one where they run into Abraham Lincoln floating in the void. Even one of the Abrams movies referenced it, albeit briefly and, if I recall correctly, during the closing credits.

That episode's title is one I always found interesting. Being raised by Jewish parents, I knew that Adonai is the English transliteration of one of the many Hebrew words meaning "God." When you find it in an English translation of the Bible, it's usually translated as "The Lord" as opposed to "God," which is reserved for the many words beginning with the Hebrew word "El," which is itself derived from the generic Semitic word meaning "a god."

Star Trek was -- and still is -- no stranger to adapting its titles from classical works. Often this was Shakespeare, as with the other TOS episode "The Conscience of the King." Turns out that this particular title, though, was adapted from a poem by Shelley (the male one, not the author of Frankenstein), which I didn't find out until much later. Not knowing its true origin, and this being the dark days before the internet, I often wondered if it had been some sort of pun, because I've always loved puns, too. That is to say, there's another cut dude from Greek mythology named Adonis, though, unlike Apollo, Adonis was a mortal in Greek mythology, loved by Aphrodite. I do have a vague memory of reading a misprint somewhere where the title was mistakenly changed to "Who Mourns for Adonis?" (The answer to that one, of course, is "Aphrodite," because Adonis died in her arms, but that's not important right now.)

Well, it turns out that the name Adonis is probably derived from an ancient Semitic language also, so it's no coincidence that it's similar to the word Adonai. Unsurprisingly, the root "adon" can be translated as "lord."

Yes, my love of language and mythology can be traced back to early Star Trek.

Anyway, the actual exchange in that show, which I scanned the trope page to make sure was included, was:

Apollo: I am Apollo!
Chekov: Yes, and I am tsar of all the Russias.

See? Both sarcasm and irony, because in the show, Apollo was, as I said, the actual Apollo (the episode gives a nod to the old idea that ancient cultures' gods were actually aliens); and Chekov never was the Tsar. Unfortunately.

One final thing about that episode. Well, a couple of things. I think it might have been the first real instance of the Theiss Titillation Theory of costume design: "The sexiness of an outfit is directly proportional to the perceived possibility that a vital piece of it might fall off." This is in regards to the skimpy costume that Apollo makes a young, attractive, female lieutenant wear. Said lieutenant was played by Leslie Parrish, who ended up married to famed author and navel-gazer Richard Bach, the author of Jonathan Livingston Seagull.

I'd say she traded down. He was no Adonis.

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