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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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| Share an instance when something blew your mind. My mind isn't that easy to blow, these days. Call it age, experience, wisdom, cynicism... oh, wait, those are all the same thing. Most of my experiences along those lines come to me when I'm driving alone on near-deserted roads and letting my mind wander. That's one reason I like to take road trips. (The other is beer.) Most, but not all. Some external things can still blow my mind. My first thought when I saw the prompt was the eclipse of August 2017, and that certainly qualifies, but it's not like I wasn't expecting and anticipating what I saw - it was just really, really cool that I actually saw it. I don't know if anyone else does this, but I like to learn about physics and shit for recreation. I tell myself it's because I write science fiction, and that's true enough, but a deeper truth is that it simply intrigues me. To do this, sometimes you have to separate the wheat from the chaff, and boy is there a lot of chaff out there. No, you can't use quantum mechanics to create your own reality. No, seriously, you cannot. First of all, you don't understand quantum mechanics. I don't understand quantum mechanics. In the last century, since it became a thing, you could count on your fingers the number of people who did fully understand it - and one of them was confined to a wheelchair. Now, you can argue all you like that Stephen Hawking wanted to be in a wheelchair, but you'd have to back that shit up with some evidence. Point is, even the (arguably) most agile mind in the field couldn't shape his own reality just by thinking about it - so all the "quantum consciousness" bullshit is bullshit. Combine that with the unfortunate tendency of science reporters to sensationalize things or simply get things wrong, and you get something close to a pure application of Sturgeon's Law (90% of everything is crap). So I try to avoid the crap, or at least learn to identify it when I see it. Therefore, I'll try to render this revelation faithfully, without adding to the misinformation that's out there. On the other extreme from quantum mechanics is general relativity - the thing Einstein is famous for. And you probably already know that, Star Trek notwithstanding, no physical object or information can exceed the speed of light - and that as something accelerates toward the speed of light, time seems to slow down for that thing. This is called "time dilation," and it's mind-boggling by itself. Someone who zips around the world at speeds approaching that of light would age notably less than someone who doesn't; that sort of thing. In my search for a better understanding of this cosmic speed limit (though I'm still not sure we're looking at it correctly - the question may not be "why can't anything exceed light speed" but rather more like "why does anything not move at light speed") and time dilation, I came across a rather simplified explanation that... you guessed it... blew my mind. Basically, it works like this. Say you're in a car that can only go 100 kph. It can't go slower or faster. And you've got an enormous parking lot to travel in. You can go 100 kph in the "north" direction; you can go 100 kph in the "east" direction. You can go 100 kph in some angle in between, and when you do that, you have a "north" component to your velocity and an "east" component, both of which are (you're familiar with vectors? Or at least the Pythagorean Theorem?) something less than 100 kph, but the resultant velocity is, and has to be, 100 kph. Now, further say that there's an observer on the south side of the parking lot, measuring your speed. That observer doesn't have a radar gun and can only measure your speed relative to the east-west axis. If you're traveling entirely North, she measures your speed as 0. If you're only traveling East, she measures your speed as 100. If you're going northeast, though, she measures your speed as (using the Pythagorean Theorem) roughly 70.71 kph. Unless I screwed up the math, which is always possible. Here's the thing that blew my mind, though: Now pretend that the North axis is actually Time, and the East axis is actually Space. Based on General Relativity, space and time have to be considered as a single entity, spacetime. And just as the car in the example can only travel at one speed, everything in the universe also can only travel at one speed - that of light - but it's traveling through spacetime. Consequently, the less you move through space, the more you move through time. As you move more through space, approaching the speed of light, you're moving less through time. But you're always moving at the same speed through the continuum. Now, it's not a precise analogy - the actual equations are not circular but hyperbolic - but it conveys the situation fairly clearly, I think. And looking at it that way was, to me, mind-blowing. (Incidentally, don't bother commenting with the whole "time is an illusion" nonsense. That's part of the chaff I described above. Time is as real as space, as it's all part of the same thing. Different observers experience it differently, but that doesn't make it any less "real." And when you start questioning whether something that we experience is "real" or not, you go down the rabbit-hole of thinking that, well, everything must be an illusion, which makes the words "real" and "illusion" semantically invalid. So, stop it.) |
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