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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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| Here's one from The New Yorker on why what you're doing is Bad and You Should Feel Bad. Economics 101: There is no such thing as a free lunch. Listening to music on the Internet feels clean, efficient, environmentally virtuous. Alternatively, it feels like a lot of work and, while it has the advantage of breadth, sometimes finding a particular song can be a pain. And just try doing this while driving across country, through places with no service. And I never thought of it as particularly environmentally virtuous. Instead of accumulating heaps of vinyl or plastic, we unpocket our sleek devices and pluck tunes from the ether. Kind of like radio, only without inane DJ chatter. The ostensibly frictionless nature of online listening has other hidden or overlooked costs. Not many things don't have such costs. Exploitative regimes of labor enable the production of smartphone and computer components. And everything else. Conditions at Foxconn factories in China have long been notorious; recent reports suggest that the brutally abused Uighur minority has been pressed into the production of Apple devices. And yet, no one cares enough to do anything about it. Child laborers are involved in the mining of cobalt, which is used in iPhone batteries. Gotta find some kind of use for kids. Spotify, the dominant streaming service, needs huge quantities of energy to power its servers. Huge compared to what? A house? A city? A Bitcoin mine? No less problematic are the streaming services’ own exploitative practices, including their notoriously stingy royalty payments to working musicians. And yet, again, we put up with it. But Devine isn’t interested in inducing guilt; he simply wants us to become more aware of the materiality of music. He writes, “There is a highly intoxicating form of mystification at work in the ideology of musical culture more generally.” As a result, music is “seen as a special pursuit that somehow transcends the conditions of its production.” Devine’s critical history of recording formats throws a necessary wrench into that mythology of musical purity. Yes, this guy's promoting his book. Fine. Anyway, I'm pretty sure Neal Peart said it better: One likes to believe in the freedom of music But glittering prizes and endless compromises Shatter the illusion of integrity, yeah And that song ("The Spirit of Radio") came out in 1980, when the height of music technology was the cassette player, you either bought LPs or tapes because CDs weren't a thing yet, and the internet was barely a spark in ARPA's eyes. Point being, it's not a new observation. The linked article goes in to some of said history, and for once for this publication, it's succinct and worth reading. “Musically, we may need to question our expectations of infinite access and infinite storage,” he writes. Our demand that all of musical history should be available at the touch of a finger has become gluttonous. It may seem a harmless form of consumer desire, but it leaves real scars on the face of the Earth. Some sacrifices are going to be necessary, sure -- purposeful or otherwise. But no. You can't have the Apocalypse without a soundtrack. It just isn't done. And since I quoted the song above, here it is -- also to demonstrate that yeah, there is indeed "magic at your fingers," even today. For now. Off on your way, hit the open road There is magic at your fingers For the Spirit ever lingers Undemanding contact in your happy solitude |
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Talk about retaining water... 
