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# Complex Numbers

Rated: 18+ · Book · Personal · #1196512
Not for the faint of art.
 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.
February 4, 2021 at 12:05am
February 4, 2021 at 12:05am
#1003605
 Immigrant Song Entry #1 of 8 for "Journalistic Intentions"  [18+] Immigrant Song Ready for some music theory? No? Well, too bad.   Now, look, I'm not entirely ignorant of music theory, but some of the shit in the video at that link is way beyond me, kind of like how I have some knowledge of physics but then they start talking about quantum this and dark matter that and my brain shuts off. The analysis that guy goes through is the musical equivalent of literary analysis. And as with literary analysis, I think they often read into the art things that the artist didn't consciously intend. "Why did you play that particular note at that time?" One might expect the musician to launch into a detailed explanation of harmonics or dissonance or setting up a musical resolution or some shit, but chances are they just go, "Well, it sounded right." Making it sound right is the musician's job. Explaining why it sounds right is best left to theorists. As a writer, I've always been more focused on the lyrics than the music. As powerful as the tune is, I have to admit I dismissed it for a long time because, come on, enunciate, Plant. But of course when the internet came along, I was finally able to decipher the more obscured words. Also, apparently, "Waa-aa-aaaaaaaaa-AHH! is a word. That's an official Robert Plant lyric right there. Probably the most awesome use of the song in its 50-year history (don't you feel old now?) was in Thor:Ragnarok, and the decision to use it not once but twice in the same movie, for whatever reason (I can no more analyze movies than I can music) just works. This is how you choreograph a fight scene to battle music.   Few musical selections have fit the tone of a scene, or an entire movie, so well. Of course, no discussion of Immigrant Song would be complete without the inclusion of this seminal music video: As someone notes in the comments (yes, I ventured into that swamp): "The internet peaked when this was originally posted. It's been downhill ever since." Mini-Contest results! Seven responses, all relevant to the question. As I noted, I'm just picking one at random, but I appreciated all of the comments. The Virtual Dice returned a 4, so the Merit Badge goes to... (drumroll) (Hey stop with the bass line, I said drumroll)... Graham B. ! We'll do this again soon.