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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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| Everything's gotta start somewhere. As the title suggests, this article (from Cracked) goes into some of those beginnings. Although I suppose an argument could be made that nothing ever begins; it's all on a continuum. Many years ago, someone made a hammer. Afterward, following centuries of technological advancement and increased knowledge of human physiology, someone else made an updated version: a hammer with a rubber grip. As useful as that is, I think the addition of a claw on the back is an even more important innovation. It's like putting an eraser at the end of a pencil, undoing what the other end does. 5. An Early Remote Control Used Little Hammers But, sadly, not clawhammers. These are more like the hammers inside a piano. The Space Commander used audio tones — ultrasonic ones, so you didn’t hear them and get annoyed. It created these tones by hitting aluminum rods with clappers. Pressing this remote’s buttons was like playing a xylophone. Or that. When I was a kid, we didn't have a remote at home. We had to get up and manually change the channel. While I'm sure these exercise sessions contributed to health, remember that we lived on a farm, so it was superfluous. When we'd go visit my aunt in New York City, she had a remote with all of two buttons, and I thought it was sorcery. 4. Vacuum Cleaners Used to Be Drawn by Horses I'd make a joke about how it probably sucked, but you already thought of that. So did the article's writer. 3. The First 3D Movie Was Also Choose-Your-Own-Adventure Movies have used 3D for longer than they’ve used sound. The first 3D cinema release was called The Power of Love and came out way back in 1922. For the math-challenged, that was 101 years ago. Audiences didn’t view the film using today’s polarized glasses. Instead, the glasses isolated different types of light by tinting one lens red and the other green. Some of you reading this may have grown up with similar glasses even long after the 1920s. I think they used red/blue. 3D movies are kinda gimmicky, but not nearly as gimmicky as smell-o-vision. In any case, this was kinda ahead of its time, even if it was a silent film. 2. Computer Games Used to Print Their Output on Paper I have vague recollections of this. Mostly, lots of wasted paper. But this is the cool one, because it verges on steampunk: 1. They Had Clockwork Coffeemakers in Victorian Days I mean, literal steam. They had clockwork teamakers in Victorian days, but we chose the word “coffeemaker” in the above title in case you’re unfamiliar with dedicated teamaking devices. Such devices, called teasmades, used to be popular in the U.K. relatively recently,,, The article contains a helpful picture of a teasmade. If this sounds somehow both primitive and overengineered, realize that these products were marketed toward British people who had been used to having servants but who no longer could afford them thanks to changing times. Never underestimate the power of laziness. As I've said before, necessity may be the mother of invention, but laziness is the milkman. |
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