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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.

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October 16, 2019 at 12:25am
October 16, 2019 at 12:25am

The Coolest Scientist In History (You've Never Heard Of)

Okay, I'll grant "cool," but I wasn't ignorant of this guy's existence. Still, there's no harm in learning more, right?

Imagine that it's the late 1800s, you're living in some godforsaken Russian backwater, and as far as your barely educated ass knows, the greatest technology in human history is vodka.

To be fair, at that point, the greatest technology in human history was vodka.

Meanwhile, the teacher down the road is mumbling to himself about elevators to space, flights to the moon, and mankind achieving blissful immortality among the stars. And here's the kicker: He's not even drunk yet! Who the hell is this guy? He is Konstantin Tsiolkovsky.

There you go, the name. Now you don't have to visit the article, but you still should; I'm not going to quote the whole thing because copyright and such, and Cracked is funny.

After three years of study, Tsiolkovsky passed a teacher's exam and, assigned to a village that made the middle of nowhere look luxurious, began the profession that would sustain him for the rest of his life. When not teaching, he tried writing his own science fiction, but he kept getting distracted by the accuracy of the "science" half.

I feel yah, Konstantin. Every time I write science fiction, it goes something like this: *science thing as a plot device* "Wait, that can't work." "But can it?" *hours of wikiderp* "Just write it, Waltz." "But it's implausible!" "Just. Write. It. Waltz." And Tsiolkovsky didn't have Wikipedia.

Never forget that the future will always be a bizarre mix of the predictable and the baffling.


But good ideas can come from anywhere at any time. And that's how someone born 162 years ago played a big part in developing both real-life technology and many of the sci-fi tropes you enjoy today.

One thing the article doesn't mention: Arthur C. Clarke, whom I'm certain you have heard of, stole from Tsiolkovsky for one of his early novels, detailing the construction of a space elevator, or, as those of us who did know about dead Russian scientists call it, the Tsiolkovsky tower. You might recall that Clarke, too, was a visionary, probably most famously for either proposing the idea of geosynchronous communications satellites, or saying "any sufficiently advanced technology is indistinguishable from magic."

There are technical issues about space elevators that continue to make them impractical, but I have no doubt that if we don't nuke ourselves back into the stone age, one day we'll have the technology to build a tower into orbit.

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