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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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| Yes, this article is about math. Sort of. There's very little actual math involved, so no one's head should explode if you click it. New mathematical record: what’s the point of calculating pi?  The famous number has many practical uses, mathematicians say, but is it really worth the time and effort to work out its trillions of digits? I mean, really, when it comes right down to it, what's the point of doing anything? Why don't we just sit here and let shit happen to us, passively? Why climb Mount Everest? Why do research at the South Pole, why swim across the Atlantic, why break speed records, why build faster computers? Swiss researchers have spent 108 days calculating pi to a new record accuracy of 62.8tn digits. Okay, wow, that's a serious lot of digits. It’s an impressive and time-consuming feat that prompts the question: why? Because it's what we do if we're not uncuriously ignorant. Jan de Gier, a professor of mathematics and statistics at the University of Melbourne, says being able to approximate pi with some precision is important because the mathematical constant has many different practical applications. That's great. Even if it didn't, it would still be a good thing to do, as the impractical also has a purpose. In maths, pi pops up everywhere. “You can’t escape it,” says David Harvey, an associate professor at the University of New South Wales. This is true. It even shows up in basic cosmological equations. “I can’t imagine any real-life physical application where you would need any more than 15 decimal places,” [Harvey] says. This is also true. At least for now. Things have a way of expanding to require greater precision. Given that even calculating pi to 1,000 digits is practical overkill, why bother going to 62.8tn decimal places? De Gier compares the feat to the athletes at the Olympic Games. “World records: they’re not useful by themselves, but they set a benchmark and they teach us about what we can achieve and they motivate others. And sometimes, by achieving something like that, you discover new methods and other things -- some utilitarian, some not. There is no such thing as useless knowledge. Everything is connected to everything else, and just because none of us can see the Big Picture, that doesn't mean that someone, somewhere, won't make a paradigm-shattering discovery just by playing around with what us ignorant shitheels call "trivia." It's great to ask "why" in most circumstances. But when it comes to wondering why we should learn new things, push limits, search for new ways of looking at things... well, in those cases, it's perfectly acceptable to shrug and answer, "Because." Knowledge is its own justification. |
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