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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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Time for another trip to the olden days. This one's from way back in May of 2020: "Crossing My Path"  A 30DBC entry, this was written to a rather open-ended prompt: Start your entry today with the words: “I used to believe...” I could have gone pretty much anywhere with this one. I chose what I consider to be a safe route; some of my former beliefs are profoundly embarrassing to me now. For instance, for a while there, when I was much younger (but old enough to vote), I thought that libertarians had the right ideas. It pains me to even admit that, but there it is. As I noted to open the entry, though: I used to believe that we stayed basically the same person all our lives. Then I read something recently, but didn't bother to save a link, about how some scientists did a study on young people, then studied them again when they were older, and what they found that Old You doesn't really have anything in common with Young You. I mean, we've known this from a physical standpoint - cells get replaced and all that - but it kind of calls into question the idea of continuity of consciousness, and identity itself. I notice this even more with Drunk Me. He gets me the best presents from Amazon, though. So I banged on, in that entry that feels so long ago but really isn't, about an article I'd found about superstition. But what struck me today, revisiting this, was that I didn't really talk about "belief" itself. It's one of those words that's a bit slippery. Sure, one can quote a dictionary definition ("an acceptance that a statement is true or that something exists" or "trust, faith, or confidence in someone or something"), but dictionaries don't capture all the nuances of a word. It can also mean a conviction, which has got to be confusing to those not used to English, because "conviction" also means that the legal system has determined that you've done a crime. You can have a conviction that you didn't do the crime, but you've still been convicted. To me, there are three major kinds of belief: 1) a trust in someone (possibly yourself), as in "I believe in you!" This isn't the same thing as saying "I believe in aliens," because the existence of the "you" in that sentence isn't in question. Which leads us to my second kind of belief: 2) Certainty that something exists, despite a paucity of evidence, no evidence whatsoever, or evidence against. Belief in space aliens, God, Bigfoot, fairies, Russel's Teapot, etc. is in this category. And then there's: 3) Certainty that something exists, with solid evidence to back it up. Gravity, the (mostly)spherical shape of the Earth, evolution by natural selection, or cats, for example. Wait, okay, there's another one: 4) to understand or remember something in a certain way, as in "I believe they said they would do that." I'm not really counting that one, though; it's got nothing to do with certainty. So what we need is a different word for the third kind, in my opinion (or belief, if you will). Because saying "I believe in evolution" isn't equivalent to "I believe in leprechauns" in any way except linguistically. Assuming that it does leads to all sorts of confusion; for instance, one might say "I believe in climate change" and someone who doesn't accept the science might retort with "Sure, and I believe in Mothman." The difference is substantial. It's why I bang on about science in here and try not to use the word "belief" in those contexts. But I used to believe it wasn't that big a deal. |
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