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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December 21, 2022 at 12:01am

#1041988

Elves: A Field Guide

I'm glad this one came up at random this week, on Solstice Day even. Otherwise, I might have had to cheat.

An Extensive(ly Silly) Guide To Telling Elves Apart

This is an important guide to identifying elves in the wild. While it's important at any time of year, December is when the general public actually pays attention to elves, who are then forgotten about for the next 11 months or so. Us Fantasy readers and gamers, of course, always have elves on the brain.

Regardless of your feelings about it, Hollywood is pumping out a lot of fantasy shows and the gaming industry is keeping up a steady stream as well. And with all the pointy eared people running around these days, it’s easy to get your Noldor mixed up with your Aen Seidhe.

It's hardly a spoiler to point out that the current Black Panther movie features a perennial Marvel character called Namor. While the Sub-Mariner isn't an elf, he does have pointy ears. So do Vulcans, and they're certainly not elves (though a case could be made that the original Star Trek tapped into archetypes: elves for Vulcans, orcs for Klingons, dwarves for Tellarites, and so on). But the pointy ears are definitely an elf's primary physical characteristic.

Elf on the Shelf

Except for this guy, apparently. Who the hell makes an elf with round ears? It's an abomination. Well... more of an abomination.

It’s just parenting 101 to teach kids at the youngest age possible that they are being monitored and any deviance from societal norms will prevent them from getting what they most desire.

What I don't get is that kids always misbehave. Always. Without fail, without exception. And yet, "Santa" brings them presents anyway.

I'm not going to copy all of these here. The article's there if you want to see.

The Elder Scrolls

The Mer as they’re known collectively have four distinct branches you can play in the games, each with different base stats and prowesses.

One of my favorite gaming universes for over two decades now. I probably know more Mer lore than I have any right to.

Dungeons & Dragons

There are a ton of Dungeons & Dragons species most people would look at and say “that’s an elf!” And then everyone would dunk on you hardcore. Just because they’ve got pointy ears does not make them elves. True elves are, on average, slightly shorter than humans.

That's... only conditionally true. D&D has changed a lot over the years, but various editions featured elven subraces that were taller, shorter, wider, winged, aquatic, space, or whatever.

Santa Elves

Okay, yes, I'm only highlighting this one here because of the season.

Collectively known as Santa’s Little Helpers, these guys are the most mysterious of the bunch. The best historically accurate source we have is from the 2003 documentary film Elf.

Confession: I've never seen Elf. Well, one time I saw a big chunk of it on a screen without sound or subtitles (I was in an airport or some shit), and in that mode it looked kinda lame.

Lord of the Rings

The elves that started it all. Our cultural conception of these noble fantasy folks all stem from J.R.R. Tolkien’s elves.

Gimme a Friggin' break. Tolkien stoleborrowed elves from Norse mythology, and the concept of "elf" probably predated even that.

Keebler Elves

Keebler cookies were the official snack food of my D&D games, back in my DMing days. I called them "Cookies of Elvenkind." For the uninitiated, this was a play on the various "X of Elvenkind" magic items in canonical D&D.

So, yeah, the Norse elves are somehow left out of this. I mean, I know a lot of people thought Marvel's Thor: The Dark World sucked, but they saw it anyway, and, well... elves. Not that Marvel didn't play fast and loose with Norse lore; they totally did. And while we're at it, Santa Claus probably has his roots in Norse lore as well. Whether he hims-elf is an elf or not, well, you'd have to remove his hat to check his ears, and who's got the stones to do that?

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