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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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| Well, here we are at the end of December, the end of 2019, and (in popular imagination anyway) the end of a decade. If I'm being pedantic, the decade ends a year and a day from now (2020 is a leap year). But let's not be pedantic. No one seems to know what to call this past decade. I came up with a name for the first decade of the 21st century: the noughties. It didn't catch on, though I did see the BBC use it once. It is, after all, rather British. I don't have a similarly awesome name for 2010-2019. Next month, I'm once again participating in "30-Day Blogging Challenge ON HIATUS"  [13+], so I'll switch back to that format tomorrow. But for today, I have an older article from 2013. I selected it at random, but it's appropriate enough.http://nautil.us/blog/we-are-all-princes-paupers-and-part-of-the-human-family We Are All Princes, Paupers, and Part of the Human Family Chances are, if you have a famous ancestor far enough back that finding out about them is a surprise, you share them with a small city of other people. And the farther back you go, the truer that is. Chances are, you have a famous ancestor, period. Ghengis Khan if no one else. Or at least a significant one. This line of thought led to the revelation that everyone of European heritage alive today is a descendant of Charlemagne, who ruled over much of Europe as the first Holy Roman Emperor. That gives me an excuse to post one of my favorite songs. It doesn’t get any less weird when you look at it from the other angle: While you more than likely have four distinct grandparents and eight distinct great-grandparents, past a certain number of generations back, your number of ancestors stops growing exponentially, because they start being the same people. A good point. Stretch this back a few thousand years and you can see how you wind up being related to every other member of your species. Stretch this back a lot farther than that and you can see how you wind up being related to your cat. Geneticist Luke Jostins did a nice mathematical analysis and estimated that you have only about a 12 percent chance of being genetically related to an ancestor 10 generations ago; by the time you get to a 14-generation ancestor, the probability is nearly zero. And that's why having kids just to pass along your genes doesn't make any sense. Never bought that argument for it, and I have plenty of other reasons not to have reproduced, but people keep talking about it. Yeah, biological drive and all that, but we also evolved to understand these things and have the persistent illusion of choice. (There are, of course, plenty of other reasons to have kids, and for most people, these seem to overwhelm the reasons not to. That's okay. I'm just talking about my own choices here.) And the illustrious folks we might like to lay claim to have so many descendants that being descended from them is kind of a moot point. I have a friend whose brother traced their family line back to Pocahontas. I don't know how accurate the genealogy was, but it was a point of pride for him. While this is cool, if true, I didn't tell him he's probably not one in a million, but one of a million. The article ends with: We’re all part of this enormous human fabric, full of fascinating tendencies and bizarre biochemistry. And research is revealing more and more about humanity as a whole and our incredibly beautiful, incredibly unlikely perch in the universe. That’s a tradition to be proud of. There is no "us" and "them." If I had one wish for the twenties, it would be that we continue to work toward ending tribalism, or at least its more negative effects. It's not going to happen, but the end of the year is traditionally the time for hopes, right? |
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