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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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I highly recommend your blog.](https://images.Writing.Com/imgs/writing.com/writers/badges/Kudos-Highly_Recommended.gif) ![Merit Badge in Opinion
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PROMPT November 11th Today, your prompt is one word: Transformation. Everything changes and nothing stands still. -Heraclitus  The thing about those ancient Greek philosophers is that they lacked the 2000 or so years of history that we've experienced since they wrote their stuff. You might be tempted to say, "But Waltz, that quote survived all this time." Well, yes and no. No, because the original statement was written in Ancient Greek, and is thus subject to some of its meaning being lost in translation. It's not, as a physicist might say, time-invariant. Its meaning is also informed by one's cultural milieu. So even the quote about change changes over time. And yet, there's something inviolably true about it. Heraclitus also apparently was the originator of the nearly koan-like quote, "You could not step twice into the same river." (also on the wiki page linked above). I heard that quote a long time ago, without attribution. At the time, I was actively working in hydrology (the study of rivers and other water flow), so, being the technical-minded person that I was and am, I mentally changed it to "You can't step into the same river even once." Because between the time your foot touches the surface of the river and the time it touches the bed, the river has, in some sense, already changed - water has flowed out, evaporated, and/or seeped into the soil beneath; some has also, most likely, flowed or rained in. Which doesn't change the basic fact, or the metaphor: that change is constant, inevitable, and defines existence. We may not always see the change - after all, rivers don't usually change in a very visible, macro kind of way in the few microseconds it takes to set foot in one - but it happens, anyway. I think a most people feel a tension between the desire for change (preferably in a direction that benefits us) and the desire for things to stay the same, in defiance of all evidence and physical laws. That goes back to the "wish" entry a couple of days ago, doesn't it? What I mean is, maybe you want to win a major jackpot in the lottery, but what does winning the lottery actually look like? Ideally, you go on with your life as it was, only with more money, right? But you add that kind of money to a life, and it, necessarily, changes. Life is change. Or transformation; I'm using a synonym here, and synonyms are an example of transformation. I'd even go so far as to assert that reality is transformation. Periodically, we humans (including another famous ancient Greek philosopher, Plato) come up with ideas about things that are "eternal" and "unchanging," but to me, that's how I know that something isn't real: it's conceptualized as nontransforming. What is real is change, and the most pernicious lie ever foisted upon a gullible humanity is that what we see around us is illusion while "reality" is something unchanging. As I've noted before, this alters the definitions of "real" and "illusion" to the point where both words become meaningless. There is, however, as far as we know (though our understanding could change) one thing that is constant, and that is the speed of light. Interestingly enough, this seems to be a true constant, for both light and matter, which are the same thing but transformed into one or the other. Every particle, every thing in the universe is always moving at exactly the speed of light - through spacetime. If it's not moving at the speed of light, that is, the constant c, through space, it's also moving through time. What this means, if it means anything at all, eludes me. I've mentioned in previous posts the predicted heat death of the universe. Billions or trillions of years from now (can't be arsed to look it up at the moment, and even that theory is subject to change as new data is interpreted), all thermodynamic processes stop, and we won't be around to see it because we are thermodynamic processes. But even then, change will still be occurring, in the form of fluctuations as a result of basic quantum uncertainty. It is possible, and therefore, given the amount of "time" (which itself loses its meaning), inevitable, that such a fluctuation will bud another universe, like or unlike our own. And so change continues. Eternally. |
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