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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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Congratulations on winning an honorable mention for Best Blog at the 2018 Quill Awards for [Link To Item #1196512] . *^*Smile*^* This award was sponsored by the blogging consortium including [Link To Item #30dbc] , [Link To Item #blogcity] , [Link To Item #bcof] and [Link To Item #1953629] . For more details, see [Link To Item #quills] .](https://images.Writing.Com/imgs/writing.com/writers/badges/type-Blogging-2180.gif) ![Merit Badge in Highly Recommended
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| The past is shadows—a ghost, ephemeral, often lost in other shadows. A shadow can only be defined in terms of the object that cast it and the light that it interrupted. The present is nonexistent. By the time you perceive it, it's already the past. The future is intangible. We can only know what might be, not what will be—though, admittedly, to varying degrees of certainty. It follows, then, that nothing is real. But when nothing is real, and we're reduced to an illusion in a universe of illusions, we're still left with the nagging feeling that something must be, after all, real. Some cope with this dissonance by making things up and calling them real: tales and fables, gods and monsters. A few claim that, in a world where nothing is real, everything must be real. Others assert that the self is the only thing that's real, perhaps channeling René Descartes with his famous and much-parodied proclamation: I think; therefore, I am. Descartes wasn't just a philosopher, though; he was also a mathematician. We see his shadows everywhere, from maps to corporate conference rooms. If you remember plotting graphs in math classes, the whole concept of a graph with (usually) x and y coordinates was a thing that Descartes codified. It can be extended into three or even more dimensions (though any dimension higher than three is remarkably difficult to visualize or comprehend). By graphing points onto a coordinate system, we blur the lines between arithmetic, algebra, trigonometry, and geometry. It was this Cartesian coordinate system that made it possible to graph complex numbers. Real numbers are, by convention, plotted along the horizontal axis, while imaginary numbers use the vertical. Every number that's not on one of the axes is both real and imaginary, in an infinite space of possibility. The coordinate system, and maybe even infinity itself, is a construct of the mind, a way of mapping things, no more or less real than any other concept. There is no cold, hard line between reality and imagination; it's a continuum. We try very hard to file concepts in one pigeonhole or another, but they're all round pegs in square holes: if the peg fits, there's space at the corners; if it does not, the peg needs to be shaved down, rounded off, until it does; or, alternatively, we can reshape the hole. Or both. That, then, along with the multiple meanings of "complex" and "numbers," was the philosophical inspiration for this varied, interconnected, serious, humorous, personal and universal compilation of seemingly unrelated concepts. In case you missed it, I provided a more detailed explanation here: "Complexity"  . I'll also point out, I think for the first and last time, that "number" can also be parsed as "that which creates a sensation of numbness," which probably describes some of these entries quite well.One indication that something is real is that it doesn't last forever. I know some people like to invert that, and claim that reality is that which abides when all else has crumbled to dust. I don't see things that way. People are real, and they die. Books are real, and they fade. Mountains are real, and they erode. Entropy is inevitable, and even the Universe itself will wind down and stop, along with time itself. Well... probably. The future does hold varying degrees of uncertainty, and the past is ephemeral. The trick, for me, was coming to terms with this uncertainty, and accepting that entropy is both real and imaginary, just like everything else. Unlike the complex plane, book items here have a limit, and for this one, the limit is three thousand entries. After this one, the blog slips into the shadows of the past. I'll keep it around, for posterity and reference, but these are its final words. As for the future, I intend to start another blog tomorrow (after all, I don't want to break my streak), one with a different theme, though continuing in a similar vein. But, of course, it's entirely possible that I get hit by a meteor (it's not a meteorite until it hits the ground, and I am not the ground) sometime in the next 24 hours or so. Or that something else will interfere with the plan. But there is a plan. If I may be allowed a moment for a personal victory lap, I believe this has been, by many measures, the most successful blog on Writing.com. I take some credit for that, being the author. But I couldn't have done it without you, the reader. So: thanks for following along. Every comment, review, award, and Merit Badge is something I truly appreciate. You certainly have different interests, beliefs and priorities than I do. That's a good thing. I do hope that, sometimes, mine intersect with yours, or at least that you're open to other points of view, as I try to be. After all, you are also a complex number. |
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